NASA / C R_2002-211730

The Interstellar Probe (ISP): Pre-Perihelion

Trajectories and Application of Holography

G. L. Ma tlo ff

Pace University, New York, New York

G. Vulpetti

Telespazio Company, Rome, Italy

C. Bangs

Art Resource Transfer, Inc., New York, New York

R. Haggerty

Pace University, New York, New York

Prepared for Marshall Space Flight Center

Under Contract H-29712D

June 2002
NASA / CRy2002-211730

The Interstellar Probe (ISP): Pre-Perihelion

Trajectories and Application of Holography

G.L. Matloff

Pace University, New York, New York

G. Vulpetti

Telespazio Company, Rome, Italy

C. Bangs

Art Resource Transfer, Inc., New York, New York

R. Haggerty

Pace University, New York, New York

Prepared for Marshall Space Flight Center

Under Contract H-29712D

June 2002
NASA / CR_2002-211730

The Interstellar Probe (ISP): Pre-Perihelion

Trajectories and Application of Holography

G.L. Matloff

Pace University, New York, New York

G. Vulpetti

Telespazio Company, Rome, Italy

C. Bangs

Art Resource Transfer, Inc., New York, New York

R, Haggerty

Pace University, New York, New York

Prepared for Marshall Space Flight Center

Under Contract H-29712D

National Aeronautics and

Space Administration

June 2002
Acknowledgments

The contribution of many people to this research is discussed throughout the text. We would like to thank R. Baggett,

M. Herrmann, J. Hood, and Les Johnson, NASA Marshall Space Flight Center (MSFC), for their assistance and hospitality.

During our stay in Huntsville, many people affiliated with The University of Alabama in Huntsville, especially Jeanelle

Hodge, Gerald Karr, and Chuck Karr, were most generous and effective in expediting the Summer Faculty Program.

Robert Foward of Tethers Unlimited supplied invaluable information about the effectiveness of white-light holography

as an information storage medium. We appreciate additional discussions of holograms with Nikolai Kukhtarev

of Alabama A & M University and David Maker of Teledyne Brown.

The research supported by NASA Contract H-29712D was expedited by a number of people. They include Contracting

Officer Ronald Smith, NASA MSFC, and Pace University grant office personnel Lindsley Homrighausen and Len Williams.

Available from:

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076-1320

(301) 621-0390

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22161

(703) 487-4650
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or) <c< -.L
E. Mallove and G. L. Matloff, The Starflight Handbook, Wiley, NY (1989).

A. R. Martin, ed., "Project Daedalus "The Final Report on the BIS Starship Study,"

supplement to JBIS (1978).

A. R. Martin, "World Ships Concept, Cause, Cost, construction, and Colonization,"

JBIS, 37, 243-253 (1984).

G. L. Matloff and E. Mallove, "Solar Sail Starships the Clipper Ships of the Galaxy,"

JBIS, 34, 371-380 (1981).

G. L. Matloff and E. Mallove, "The Interstellar Solar Sail Optimization and Further

Analysis," JBIS, 36, 201-209 (1983).

R. A. Mewaldt and P. C. Liewer, "An Interstellar Probe Mission to the Boundaries of the

Heliosphere and Nearby Interstellar Space, presented at Space 2000, Sept. 19-21,

2000, Long Beach, CA.

G. Vulpetti, "The Aurora Project • Flight Design of a Technology Demonstration

Mission," in Missions to the Outer Solar System and Beyond, 1st IAA Symposium on

Realistic, Near-Term Scientific Space Missions, ed. G. Genta, Levrotto & Bella, Turin,

Italy (1996), pp 1-16.

il-3

CHAPTER. 3. ADYANTAGi=$ OF RFT_AIN!NG THF ,,SA!,L,.TO THI=

HELIQPAUSE

Current planning for the NASA Interstellar Probe (ISP) mission assumes that

the spacecraft will be accelerated by solar-sail from starting from a perihelion as close

as 0.2 AU from the Sun and will detach from the solar sail at or near the orbit of jupiter

(5.2 AU from the Sun). This report chapter considers the kinematical advantages of not

dropping the sail.

We start this analysis with Eq. (4.26) of Matloff, Deep-Space Probes (Matloff,

2000):

v,,= +

para,init (3-1)

where Vfin - final spacecraft velocity relative to the Sun,

Vinit -initial spacecraft velocity relative to the Sun,

Vpara,init - solar parabolic (escape) velocity at perihelion

Vpara,fin - solar parabolic velocity at end of sail acceleration

qsail- sailcraft lightness factor (the ratio of solar radiation pressure force to

solar gravitational force on the sailcraft).

It is assumed in the derivation of Eq. (3-1) that the sail is fully opaque, is fully unfurled

at perihelion and is always oriented normal to the Sun.

We next simplify Eq. (3-1) by assuming that the pre-perihelion trajectory is

parabolic. Therefore, Vinit- Vpara,init- Vpara-peri, where Vpara-peri is the solar

parabolic velocity at perihelion. Substituting in Eq. (3-1) and manipulating,

V n=V ,,2r ,ara,J!n1

para-peri_sail. [ l- - __araperi_sail ............... J

1/2

(3-2)

In any interstellar solar sail expedition, the solar parabolic velocity at the end of

solar-sail acceleration will be small compared with the perihelion velocity. Therefore,

bn "_ Vpara-peri_;/ai2, [ 1- ".2 ......... r_ ._,;.... 2_ara-peri_sail J

Equation (4-27) of Matloff (2000) is an approximate expression for the

II1-1

(3-3)
calculation of spacecraft final velocity if the sail is dropped an infinite distance from the

Sun. For such a situation,

Vfin,oo _ Vpara-peri_s]a/i2l. (3-4)

we next define the parameter K, where K is the fractional loss in final interstellar

cruise velocity if the sail is dropped at 5.2 AU from theSun instead of an infinite

distance from the Sun:

K n,oo n,5.2au I II ._

Vfi/Z, o0

_sai!-) !to_zp2ara, fin--5.2au

= 2 2 .....

_sail ] Vpara-peri

(3-5)

From the definintion of solar parabolic or escape velocity,

K= I,7,o,l- 1(-1o14: ....)

ilV_s a i l

(3-6)

Applying Equation (4.19) of Matloff (2000), we can approximate sail lightness factor

O.00078.7(1+RE_,_il")

T]sail _-- --_

Us/c

(3-7)

where REFsaii - (fully opaque) sail fractional reflectivity and os/c is the sailcraft areal

mass thickness in MKS units.

Figure 3-1 shows parametric solutions of velocity loss factor K as a function of

sailcraft lightness factor and perihelion distance. Note that retaining the sail beyond

Jupiter can increase terminal interstellar cruise velocity by a few percent. Velocity loss

factror K increases for tow-mass missions and high perihelion velocities. Using the

software described in the next chapter, Giovanni Vulpetti has also found a kinematical

advantage to retaining the sail throughout the ISP mission.

There are potential non-propulsive applications for a retained ISP sail. a

properly shaped sail could function as a communications antenna, also, if circuitry is

emplaced around the outer edge of a disc-shaped ISP sail, the sail could function as a

magnetometer during interstellar cruise without a substantial payload mass penalty.

111-2
Fig. 3-1 Terminal Velocity Fractional Loss factor K as a Function of Saiicraft.Lightness

Factor and Perihelion Distance.

K

0.025

0.020

0.015 .__

m

0.010

0.005 ._._

lightness factor = 3.0

lightness factor = 2.5

lightness factor = 2.0

lightness factor = 1.5

,, ,I ........... !............... 1........

! ! _!

0.1 0.2 0.3

Rperi,au

I

ill I

111-3
Chaoter 3 Reference_

G. L. Matloff, Deep-Space Probes, Springer-Praxis, Chichester, UK (2000).

111-4
CHAPTER IV

SAILCRAFT TRAJECTORY OPTIONS FOR THE INTERSTELLAR PROBE:

MATHEMATICAL THEORY AND NUMERICAL RESULTS

Giovanni Vulpetti 1, Telespazio SpA, Via Tiburtina 965, 00156 Rome, ITALY

IV.1 Introduction

Gregory Matloff dealt with the purposes of NASA Interstellar Probe (ISP) in the previous chapters of this report

to NASA George C. Marshall Space Flight Center. Les Johnson provided report authors with basic input

(Johnson, 2001). Preliminary design of ISP baseline mission and sailcrafl systems can be found in (Mewaldt et

al., 2000) and (Liewer et al., 2000). This chapter aims at identifying other options for the ISP mission based on

solar-sail propulsion. Unavoidably, mission strategies and results are interrelated to the sailcraft technology, in

general, and the sail system, in particular. Although literature on solar sailing has been enriching since the

Eighties, perhaps the general reader is not full aware of all aspects on advanced space sailing. Thus, we arranged

this chapter as follows: §IV.2 and §IV.3 present a background on fast solar sailing and considerations about

modeling the translational motion of a sail in space. §IV.4 focuses on the important topic of optical sail

degradation, whereas §IV.5 shortly describes the computer code we have employed to get the numerical results

presented in §IV.6 and §IV.7. Considerations on the ISP feasibility and suggestions about some items of next

ISP research & design are given in §IV.8 and §IV.9.

IV.2 Background on Fast 3D Trajectories by Solar Sailing

In this section, we summarize the basics of fast heliocentric sailcraft trajectories by using a formalism developed

in the last decade of the 20 thcentury. Details can be found in Vulpetti (1996, 1999a, 1999b) and the references

inside. With regard to nomenclature, symbols will be explained on the way; normally, bold letters refers to as

three-dimensional column vectors whereas capital Greek letters denotes matrices, unless otherwise specified.

Although the used formalism is coordinate-free, however, we shall use coordinates, implicitly or explicitly, that

are defaulted to the Cartesian ones.

2.1 Frames of Reference and Units

In the present theory and related numerical code, we use two heliocentric reference frames and one sailcraftcentred frame. The first flame, hereby called the Heliocentric Inertial Frame (HIF), has been built starting from

the realization, named the International Celestial Reference Frame (ICRF), of the International Celestial

Reference System (ICRS) that is provided by the International Earth Rotation Service (IERS). The strict

definition of ICRF and its related documentation can be found at http://www.iers.org. Here, we very briefly

report that the origin of the ICRF is the barycenter of the Solar System and its orientation is close to dynamical

equinox and mean equator at J2000. HIF has been obtained by rotating the YZ-plane of ICRF counterclockwise

about its X-axis by the value of Earth obliquity (23 ° 26' 21.16") at J2000. HIF is centred on the Sun barycenter

and it is oriented close to the dynamical equinox and mean ecliptic at J2000. That is particularly useful when

planetary perturbations are included, via standard ephemerides, in the sailcrafl motion (as a matter of fact, apriori one does not know whether the sailcraft will be flying-by some planet).

The second frame, hereby named the Extended Heliocentric Orbital Frame (EHOF), is defined as follows:

2D motion in HIF with trajectory curvature supposed not to diverge at any time

1. If motion is direct or counterclockwise (in HIF), then the reference direction & orientation are those

ones of the sailcrafl position vector R; the reference plane is given by (R, V), V denoting the sailcraft

rv-i Chief Scientist, Full Member of the International Academy of Astronautics

IV-1
velocityvector,andtheZ-axiscoincideswith the direction& orientationof the orbital angular

momentum per unit masS H=RxV

2. If motion is retrograde or clockwise (in HIF), then the X-axis is the same as in (1), but the Z-axis is

oriented opposite to H and, consequently, the Y-axis is in the semi-plane (R, -V).

3. At some time, say, t* where H=0 (if any), the Z-axis is the limit of the Z-direction of either (1) or (2)

when t approaches t*. It is easy to show by considerations of geometry and vector analysis that such a

direction, here denoted by h*, exists and is unique.

3D motion in HIF with trajectory torsion assumed to be limited at any time "

a. If flight begins with a direct motion (in HIF), then EHOF axes are defined the same way in 2D-1

b. If flight begins with a retrograde motion (in HIF), then EHOF axes are defined the same way in 2D-2.

The direction of the Z-axis is denoted by h, whereas r is the direction of R. At any time t, there is a well-posed

triad (r, h x r, h), which defines the extended orbital heliocentric frame. The attribute extended refers to the fact

that a general sailcraft trajectory may be composed of pieces separated by at least one point where the orbital

angular momentum vanishes. General discussion on the EHOF can be found in (Vulpetti, 1999a). The case

characterized by H=0 for a finite interval of time can be also dealt with appropriately, but is beyond the scope of

this report and the realistic options related to the Interstellar Probe.

The third frame, named the Sailcraft Orbital Frame (SOF), has its origin on the vehicle's barycenter and it is

instantaneously at rest, according to Special Relativity (SR). In general, its orientation differs from that of EHOF

by an amount due to the aberration of light, which is a first-order effect in speed. For ISP, the orientations of

EHOF and SOF are very close to one another.

The computer code described in §IV.5 is fully based on SR. However, we shall use the classical approximation

for ISP, here, to simplify presentation of solar sailing theory and discussion/comparison of the results. Evenly,

HIF/EHOF-related time and SOF proper time scales can be considered equal to each other. Julian Date (JD) has

been used for astronomical events and coordinates such as position and velocity of planets in HIF at different

times, whereas sailcraft thrusting and/or coasting time intervals could be specified in either SI seconds or days (1

day = 86400 SI seconds) or standard years (1 standard year = 365.25 days).

2.2 The Lightness Vector Formalism

Let us consider the vector solar-pressure acceleration that acts on the sailcra_ center of mass. Think about this

vector (1) resolved in EHOF, (2) normalized to the local solar gravitational acceleration. Let us denote it by L

and name it the lightness vector. We call its components the radial, transversal and normal numbers as follows:

L - [_r _t _n ]W )_ --ILl (IV-1)

L is a function of time. Its magnitude is called the lightness number here; it should not be confused with the

same-name parameter defined in (Wright, 1993); that one is a particular case of the current A(t) function. The

motion of the sailcraft barycenter in HIF can be described by the following system of ordinary differential

equations (ODE)

dR- V

dt

R2 -_-OL + Pg pR2 E-(1-)Vr)r + _,t h × r + )_

d

m - --...msail dt ACS

(IV-2)

where m is the sailcrafl mass, V its velocity, R=[R] is the Sun-sailcrafl distance; g denotes the solar gravitational

constant, whereas Pj represents the gravitational perturbation of the j-th of Np planets on the spacecraft,

IV-2
].

according to Celestial Mechanics. The symbol p idenotes a switch, either 1 or 0, for including planetary

perturbation(s) or not, respectively. _ denotes the matrix of rotation from EHOF to HIF; it is equal to

(r h x r h)HIF, according to what defined in sect. IV-2.1. The scalar differential equation in IV-2 accounts for

any mass consumption, for instance due to some small-rocket control of the sail orientation; one supposes that

mass is exhausted at zero total momentum in SOF, namely, no residual force acts on the vehicle barycenter.

Some remarks are in order: first, although in principle equation IV-2b may be valid also for an (ideally) rocketcontrolled spacecraft, in practice, however, only a sailcratt is characterized by the fields appearing in the

acceleration equation, namely, two conservative fields and one non-conservative (aside from planetary

perturbations). Second, if )_ is sufficiently high, the features of the heliocentric spacecraft trajectory are

determined mainly by solar gravity and solar pressure (even though some close planetary fly-by may affect lowspeed trajectory arcs). Third, as such, equations IV-2 do not contain any reference to sailcraft technology; in

other words, all sailcraft trajectory classes can be studied by reasoning only in terms of L's magnitude and

components. Subsequently, a real mission shall be analyzed by connecting dynamics and vehicle technology

(§IV.3). Such observation is particularly important since it allows the analyst tO be aware of strong non-linear

behaviors that a conventional spacecraft does not have.

From the above observations, it is convenient to focus our attention on the solar fields here for illustrating and

discussing solar sailing behaviors. Thus, unless otherwise specified, we refer to the following simplified

equations

dR V

dt

dv = R2U,F-(1-Xr)r . +Lthxr +x.hqJ dt

(IV-2A)

It is a simple matter to show how sailcraft energy and (orbital) angular momentum evolve under'equations IV2A. By introducing the quantity

H = H. h ¢=> I-I = H h H=__IIHII (W-3)

which is an invariant, named the H-function, one gets the following equations for energy

_t

E = _V 2 - (1--_r)- _-

dE=H__ __d H

dt R 2 dt

(IV-4)

and the following equations for angular momentum and invariant:

d _t Hx--H - H)_ --r

dt " R

d H - '(_, h X h×r)

dt R t ,

d H_t d H-X _t _ E__, t

dt t R dt R 3

(iv-5)

In words, sailcraft energy depends of the radial number; energy rate does on the transversal number (through

equation IV-5c), whereas the normal number drives the angular momentum bending. The evolution of H does

not depend explicitly on the radial number. Equation IV-5c is a basic equation for controlling sailcraft trajectory;

trajectory classes depend on the initial invariant value and how it evolves (Vulpetti, 1996, 1997, 1999a). One

should note that, unless the analyst knows the vector functions L(t) and h(t) in advance, equations IV-2 and IV5c have to be integrated simultaneously to propagate a sailcraft trajectory. As a point of fact, in general, one does

not know whether/when sailcraft may reverse its motion or not.

IV-3
If vectorL were aligned with the radial direction r, for instance after the sail deployment at some suitable

perihelion Re from the Sun, the saiicraf_ energy change would amount to _,__/Rp; as a result, the hyperbolic

excess would be V® _/Vp2 - 2 (1 _ ) _t/ Rp. A very good way to get a high cruise speed would be to make a

sailcraft with high lightness number and launch it on either parabolic or quasi-parabolic orbit down to Re. This

results in the following speed

V® = _[(1 +e)_t/g] 2 - 2(1--_r)_t/Rt, (IV-6)

In equation IV-6, (e,g)denote the eccentricity and the magnitude of angular momentum, respectively, of the preperihelion orbit. Options for pre-perihelion acceleration have been investigated extensively (Matloff and

Mallove, 1983) and summarized critically (Matloff, 2000). One should realize that the value, say, V_ obtained

from equation IV-6 (or an equivalent one) by parabolic pre-perih_lion mode could be taken as a useful reference

with which actual fast trajectories may be compared. As a point of fact, one knows that a mission obeying

equation IV-6 is somewhat hard to implement, in practice. In addition, one should note that V_ represents an

upper limit only for supercritical sailcraft (§IV.6).

When perturbations are added to the sailcraf_ motion, equations IV-4 and IV-5 are to be modified. For instance,

the invariant's evolution equation changes to:

dn = _t _1' -+- R hxr. P (IV-7)

dt R

In equation IV-7, P denotes the sum of sailcraft accelerations other than solar gravity and photon-sail interaction.

However, a good quasi-optimal profile of a 3D trajectory could be carried out by using the simpler form again,

especially around the perihelion.

2.3 The Motion Reversal Mode

A sailcraft with X = _ moves on a "generalized" keplerian orbit inasmuch as it senses the Sun with an effective

mass equal to (1- Lr)_t. However, there is no way to change energy, according to the last equation in IV-5,

since any transversal components of the lightness vector vanishes. Thus, if one wants to increase sailcraft speed,

some non-radial control has to be applied. The problem is not simple even because, if any non-radial component

of the lighmess vector is different from zero, the sailcraft equations of motion admit no Lagrangian. It is possible

to show strictly by the theory of Lie Groups that no analytical solution to IV-2A exists (Vulpetti, 2001).

However, many important properties and features of solar sailing trajectories can be drawn by analyzing

equations IV-2A through IV-5 appropriately.

Let us consider the evolution equation of the invariant. It is easy to recognize that, if the transversal number is

negative (and not too low) and the trajectory arc time is sufficiently long, some point can be reached where

either H vanishes or achieves a local low minimum (or a local high maximum, if the initial motion is retrograde).

It can be proved that the first possibility can arise in 2D motion (Vulpetti, 1997), whereas the second one

pertains to either mixed 2D/3D-trajectory arcs or full 3D-trajectory arcs (Vulpetti, 1996, 1999a). Only for special

cases, conditions can cast them in simple form such as

-1-< _Lr < 1

- Rp 2D trajectories, L = constant (IV-8)

<_(tp )l.t < R*

t "Rp Vp R

Here, the lightness vector is assumed constant throughout the flight. The subscript p denotes quantities evaluated

at the perihelion, whereas starred quantities refer to the H=0 event. Another special case is the mixed 2D/3D

trajectory in which one has a piecewise-constant lightness vector. In this case, one gets

IV-4
t_[to ,tn] tA>t*

r

_._ -L A

0

(with constraims IV-8)

2X<ILB[ <1 _r

t _(t A, tf] _'t < 0 Xt -LB -const.¢: L A

(W-9)

A realistic 3D trajectory class shall be dealt with extensively in §IV.3.

Why an analysis on sailcrafi mission shouM consider the option in which the orbital angular momentum of the

vehicle may reverse somewhere?

The strict mathematical treatment of the motion-reversal sailing mode is beyond the scopes of this report. Here,

we limit ourselves to show what happens semi-quantitatively. Let us begin by calculating the along-track

component of the total acceleration, namely, the time derivative of the sailcraff speed

d v - V.id/V -[--(1--_r)COSq) + _tsin(p]bt/R z + v.P -(IV-10)

dt

In IV-10, the quantity (p" (p _ [0,2n), RVsin (p- H denotes the generalized angle between saitcraft's position

and velocity vectors, v stands for the direction of V. Note that the normal number does not appear in equation

IV-10. If one ignores small perturbations, this along-track quantity vanishes when

cot q) - Z,/(1- Zr) (IV-11)

For simplifying discussion, let us assume both radial and transversal numbers constant throughout the flight; this

means that there are two values of the _oangle satisfying equation IV-11 as follows

{;<(Ps <n/2 _/>0 _r<l /2 < q_s < n _t<0 "

q)e = q)s + 71: (W-12)

fzc < q)e < _n _t>0 "

n < q_e < 2n _,<0 "

It is possible to show that the angle labeled by S refers to local maximum or minimum of sailcraft speed,

occurring at time ts, if At is positive or negative, respectively. Typically, if sailcrafl starts from a near circular

orbit such as the Earth-Moon barycenter orbit (plus an hyperbolic excess) with a sufficiently positive transversal

number, say, At _ A/3, it accelerates while increasing its distance from the Sun. Rapidly, it achieves the

maximum of speed, then decelerates though it can escape the solar system radially (if the lightness number is

high enough). There is no local minimum of speed, since dV/dt is always negative past the maximum. As a point

of fact, the invariant H is positive and increases monotonically; consequently, the angle between position and

velocity can pass through neither zero nor 180 degrees. In such a trajectory class, _0e does not represent a

physical solution. Even more, this happens for. slow spiraling-out trajectories (for which X is low), whereupon

sailcrafl speed changes through local maxima and minima characterized by _0=_0s.

A quite asymmetrical situation arises from a sufficiently negative transversal number. Since H may vanish, the

_0=q_esolution can physically exist at some time te. Consequently, one may integrate (the main terms of) equation

IV-10 from time ts to time te

IV-5
R2 dt + Xt R2 dt (IV-13)

(The fact we are dealing with the simplified problem of L=constant (throughout the flight of interest) has been

highlighted). If _ < 1, the first term gives its highest positive contribution when q____-, namely, around a point

where the angular momentum is zero or close to zero, whereas the second term is strongly positive when

q) _=3_ / 2, that is around the perihelion of the reverse motion arc. Around the perihelion, the first integral gives

a total vanishing contribution, while the far dominant term is that one related to the transversal number. In

addition, perihelion is not the point of maximum speed; in fact, maximum speed is achieved past the perihelion

because of % > 3_/2. Thus, sailcraft goes on accelerating for a long (asymmetric) arc of solar fly-by performed

by reversing its initial motion. The sailcraft speed amplification may be high indeed, depending on the perihelion

and lightness vector. It is an easy matter to show that the escape point (E=0) is achieved before the perihelion.

Many other properties of sailcraft trajectories can be inferred by studying trajectory curvature and torsion

(Vulpetti, 1996, 1997). Among them, the pseudo-cruise branch is of concern here. It has the following

properties: (a) it begins at few AU from the Sun, (b) it passes through the solar system with a small speed

decrease, (c) although it is generally lower than Vmax, however Vcruise can be significantly higher that V0, the

sailcrat_ injection speed (close to the mean Earth Orbital Speed, or EOS, that equals Dr AU/yr). These

considerations apply to 2D trajectories for which the normal lightness number is zero. This is an ideal Case

useful for reference mission: %-% = _. It is possible to prove (Vulpetti, 1999a) that a real 3D reversal

trajectory must have both non-radial numbers variable at least in a time interval around the reversal time. Such

variability is essential to guarantee the orbital frame to be smooth and to cause motion reversal. Here, H does

vanish, but its magnitude exhibits a local minimum. In such trajectory class, q_(t) approaches Jr closely, then it

reverses back to values less than Jr/2. One gets % + % -_; when perturbations are active, such relationship is

well approximated.

Equation IV-13 admits non-reverse motion solutions, plainly. As a simple good example, one could think of

performing an attitude maneuver at some time (to be determined)in the [ts ,t*) interval such that X, --_-X,,

(the transversal number being high enough as above). Since H remains positive this case, the angle between

position and velocity never achieves 180 degrees; thus, the second term in equation IV-13 is dominant and

positive again for a long trajectory arc about the Sun. At, say, 1-2 AU another attitude maneuver adjusts the sail

orientation in either the inertial or the orbital frame. The cruise speed for this class of direct motion and that

related to the motion reversal may be quite comparable in realistic cases; they also depend on the departure

planet position and velocity at the sailcrat_ injection time or epoch.

Both the direct and the reverse motion strategies share a basic rule: if a sufficiently light sailcrafi is planned to

exit from the solar system with high speed, it has to lose most of its initial heliocentric energy (passing through a

minimum) before accelerating fully.

It is not difficult to show that the H-reversal class for sailcrat_ trajectories exhibits large launch windows, from

several days to a few weeks, depending on the distant target coordinates. For targets well beyond Pluto, e.g. the

heliopause or the solar gravitational lens, wide favorable injection into the solar field repeats on annual basis.

Thus, the motion reversal represents a full mission opportunity, which has the following additional features"

confirming/extending the feasibility of a mission from a dynamical viewpoint, examining the critical role of the

(external) optical degradation on unconventional sailcraft trajectories. Both points are among the main aims of

this report.

IV.3 Specifying Sailcraft Barycenter Motion: the Connection Equations

As emphasized above, each component of the lightness vector may act as a dynamical control variable.

However, any real L stems from the actual physical interaction between the solar photons and the sail material

and configuration. Such interaction generates a thrust in the sailcraft frame of reference. Thus, there is a link

between the direct control variables/parameters of the sailcraft and L's components. We call them the

connection equations. Moreover, such equations contain geometrical/physical features of the source(s) of light

IV-6
andenvironment-relatedeffects.Here,weshall,verybriefly,reportsailcrafl-relatedphenomenaandsourcerelatedperturbations.Very extensiveexplanationsof photon-metalinteractions,both from physicaland

mathematical viewpoints,canbe foundin manyexcellentclassicaltextbookson optics.A sailing-oriented

descriptionof thesolarradiationpressurecanbereadin (McInnes,1999,chapter2).Intrinsicandenvironmentinducedchangesof theidealsailbehaviorwill bementionedin §IV.4.

Intermsofradiantflux,99percentofthesolarspecmmarngesfrom1000A to40,000Ainwavelengththatcan

affect spacesailing.The light a sail receivescanbe specularlyreflected,diffuselyreflected,absorbed,

transmitted.A goodsolarsail shouldexhibitvanishingtransmittance2, low absorptance(a), low diffuse

reflectance(d) andhighspecularreflectance(r). Therefore,r + d + a = 1, a condition well achieved even by

very thin Aluminium-Chromium films. For .the moment, we only mention that such optical quantities are

someway averaged over the essential solar spectrum. We shall return on that below. In general, the local solar

radiant flux impinges onto the sail surface at an angle 0 of incidence, as seen from the sailcrafl. (If an and dn

denote the azimuth and elevation in EHOF, respectively, of the sail axis n, oriented backward with respect to the

reflective sail side, then one has cosO=cosct n cos5 n strictly only if the vehicle speed is zero). Specularly

reflected light generates (main) momentum along n, while absorption causes a momentum along the incident

radiation direction. The process of light diffusion by the sail's front side induces two additional momenta on the

sail: the first one acts along the incident direction, the second one is along n and ig proportional to the surface

coefficient, say, Zf (for an ideal Lambertian surface Z = 2/3 ) and the d-value (which, in turn, depends on the

sail roughness). The energy absorbed by the sail materials is re-emitted from front-side and backside according

to their respective emissivities, _f and gb. We suppose that each sail side behaves as a uniformly diffuse gray

surface. Emissivity is only function of the sail temperature: the sail thickness is so small that one can use the

same temperature Ts across the sail film. This value follows from the equality between absorbed power and

emitted power in vacuum at any distance R from the Sun: By neglecting the cosmic background radiation

temperature, the absorption-induced thermal effect consists of a net momentum along the-normal-to-sail

direction proportional to the following factor

_: = Zf gf(Ts) - Zb _b(Ts) (IV-14)

 i(rs) +

(In equation IV-14, we have highlighted the dependence on sail temperature). The sail of a fast sailcrafl should

be composed of a high-reflective layer and a high-emissivity coating. As a result, the function r is negative for

Aluminum-Chromium sails; in other words, there is a thrust acceleration, along-n, stronger as absorptance and

temperature increase. Even this component of the total thrust is not negligible, especially around the perihelion

and for a degraded sail.

The above picture of sail-photon interaction is rather simplified. In addition to detailed aspects of this

interaction, a more general treatment should include other meaningful items. These ones are photon aberration,

features of the light source, curved sail, and optical degradation, in the order, according to the progressive

removal of some underlying assumptions such as:

A1. direction of incident light along to the X-axis of the sailcrafl frame

A2. point-like Sun

A3. fiat sail

A4. ideal optics.

We have mentioned that physics in the spacecraft orbital frame does not coincide with that of the heliocentric

orbital frame. By neglecting 2hal-order and higher terms in the vehicle speed, it is possible to carry out the

following connection equations

rv-2 We use optical terms ending in 'ance' since they apply to real specimens regardless of their geometric thickness and physical surface

state. Terms ending in 'ivity' are normally used to highlight optically smooth specimens.

IV-7
L=Xon x [(2rn_+x:d+Ka)(l" -2f3x)-2rnyf3y]n+(a+d) .-.-O_yJ?" (IV-I5)

In equation IV-15, we have set

Ico, l V m

_- C Jsi;q)[=-_ , _-angle(R,V), V - [V,, _0--_ °'c,o. a-=--S

L ..I --

c_-2 -wl'U =O.O01538 kg m -2 W_,v=1367 Wm -2 g_,v =O.OO593 ms-_ (IV-16)

glxU C ' '

cos cos F":I

withthe sail directioninEHOF givenby n= sin(x, cosS, ---]ny /

sin_, Ln_J

where m is the (instantaneous) sailcraft mass, S denotes the sail area, C is the speed of light, o- is the total vehicle

mass divided by the sail area and is usually named the sailcrafl sail loading. Thequantity denoted by c c is the

so-called critical density. Vector 11accounts for photon aberration, which is linear in the sailcratl speed. The

h"factor is given by equation IV-14. An important thing to be noted about vector equation IV-15 is that the

various optical sail parameters are weighted by quantities of significantly different physical nature. Each optical

parameter appears in two independent terms.

Ideally, by a perfectly reflecting planar sail at rest in HIF and orthogonal to the vector position, one would get

L_a,at = [1 0 0] r crc / cr with the maximum allowed thrust, or equivalently, with a thrust efficiency equal to 1.

Thus, in general, sailcraft thrust efficiency can be defined as the actual-on-ideal thrust ratio at any time. It is

related to the sailcraft sail loading by the following relationship:

x = )_ _/c e (IV-17)

When the sailcrat_ sail loading equals the critical density, X < 1 since thrust efficiency is less than unity in any

real case.

We have removed assumption A1 in carrying out equations IV-15, which hold for a point-like Sun. If sailerat_

comes sufficientlyclose to the Sun, say, at R z 15 R e (1AU =_ 214.94 Ro) , then it begins by sensing the finite

size and the limb darkening of the photosphere. They ultimately cause a reduction of the thrust on sail; the nearer

the spacecrat_ is the weaker the tlmast is (standing the same sail orientation, distance and speed) with respect to

the point-like Sun thrust. Thus, by removing assumption A2 and using the standard gray-atmosphere model, it is

possible to carry out exact formulas for an arbitrarily oriented sail (and in relativistic motion too). A modem

symbolic-math system on computer is appropriate for achieving this goal. Closed-form solutions are very long.

However, we like to report simple classical-dynamics formulas without any terms in vehicle velocity for

isolating the mentioned effects on the sail. This results in the following modified connection equations:

L--- )_'0 ([2]" U 1 + (_f d'_" l(a) uz]n+ (a + d) w ) (IV-18)

In equations IV-18, we employed the following definitions:

{-R/R o uz =-n_ wr= 1 (2n_k nyq

192

nzq)

IV-8
Ul=_ (59-9nx2 _64 ,/ 2-1+2(3nx2

2 2 2 .

9I(nx -3)_3+2(nx +l)_+(1-3n x )/_]ln _+1

_1)(9+16 1 lj 2)+

2

k = 9(_ 2 - 1) 2 In _+1 + 32, (_2)3/2-1 -2_25._( _:2+9)_

q-9(3_4-2_2-1)ln_+l + 32(2_ 2+1)4_2-1 _ 2(59_ _9)_2

Obviously, even though sunlight distribution has a cylindrical symmetry in this model, a non-radially oriented

sail destroys this symmetry in generating thrust. If the sailcraft moves at a distance _ >> 1, the actual-Sun

lightness vector approaches that one from the point-like Sun, as described by equation IV-15 with zero speed.

(The general formulas are coincident in the limit of _ _ oo for any sail orientation and velocity, of course). We

close this topic here with mentioning a few values for the pure radial case" at _, = 4 (that is at 3 solar radii from

photosphere), a correction factor equal to 0.9858 should be applied to the point-like model, whereas at

= 21.49 (0.1 AU), the correction factor would amount to 0.99951. Finally, at 0.2 AU, deviation would result

in -0.00012, namely, about 1/4of the photon aberration for a sailcraff traveling at such distance with 15 AU/yr.

Now, let us remove the assumption A3 to have a fiat sail. Currently envisaged sails may be grouped into two

large classes: (I)plastic substrate sails, (II) all metal sails. A representative of class-I is a three-layer sail

consisting of a plastic layer of a few microns thick on which thin reflective and emissive films may be deposited

(one film per side, typically). Such a sail may be suitable for (many) interplanetary transfers. Class-II regards

bilayer sail configuration consisting of reflective and emissive films alone. Since sailcraft of class-II has a sail

loading considerably lower than class-I, it would be appropriate for high-speed missions. Photon pressure on a

large surface induces a large-scale curvature that, in turn, causes pressure redistribution and thrust decrease. In

class-I, curvature increases when sail temperature increases. Depending on the supporting structure, large-stress

values can result in small-scale folds in the sail materials known as the wrinkles. One deems that wrinkles may

interact with large-scale curvature by producing hot spots. During the AURORA Collaboration (January 1994-

December 2000), a few promising experiments (Scaglione, 1999) were performed for getting a light sail for the

AURORA concepts of mission to either the heliopause or the solar gravitational lens. The sail would be

manufactured in the following multi-layer mode: Aluminum-Chromium-buffer-UVTplastic, where the buffer

layer consists of diamond-like carbon (DLC) 3. UVTplastic stands for plastic substrate transparent to the solar

LW photons. Once deployed in a high orbit about Earth, solar UV light reaches the DLC buffer and weakens its

chemical bonds at the interfaces such that it and the plastic film soon detach from the A1-Cr layers. Closely

related to techniques for achieving metallic sails without infrastructures in orbit, are the deployment and the sailkeeping methods. The AURORA collaboration studied a circular A1-Cr sail to be deployed in orbit by a small sailrim-located toms. This is a hydrostatic beam-based deployment system with load-supporting web (Genta et al.,

1999); deployment is effected by inserting gas into this peripheral ring. The sail shall take a pillow-like shape,

symmetric with respect to the sail axis, with a maximum axial shift depending on the Sun-sailcraft distance (and

sail orientation). For instance, a circular sail of 300-m radius exhibits maximum slope of 4.4 degrees at a

perihelion as low as 0.15 AU (or, equivalently, a sunward shift of 14 m). Large-scale curvature radius takes on

3.3 km, by entailing a thrust reduction factor of about 0.998 (with respect to the ideal case of fiat sail). These

figures would hold only around such perihelion distance. Although some differential equations used for this sail

deformation analysis are simplified, nevertheless there is a strong indication that the whole flight of smaller-sail

AURORa-type spacecratt, designed for higher perihelion (Re _>0.2 A U), is compliant with the assumption of a

large-scale fiat sail. This statement is of great concern with regard to ISP, here.

Finally, we shall remove the assumption A4 regarding ideal optics for a sail. Since this is a special topic with

strong consequences on dynamics, we shall devote next section to it. However, before proceeding, we have to be

iv-3 DLC is a metastable digordered solid that shows a mix of diamond and graphite structures.

IV-9
morepreciseabouthemeaningof theopticalparametersenteringtheconnectionequations.Theset{r, d, a}

represents the fractions of the incident photons that are specularly reflected, diffusely reflected and absorbed,

respectively. Although they are not defmed as one usually does in Optics, nevertheless they can be related to the

strict optical quantities known as the bi-directional spectral reflectance Pspec(.._,0,{p}), the directional

hemispherical spectral reflectance Pdg (£,0, {p}) and the directional spectral absorptance c_(£,0). (The reader

may consult some standard handbook such as the Handbook of Optics by Optical Society of America, 2001,

http_://www.osa.org ). Here, Z; denotes the wavelength of the incident light, whereas {/9} emphasizes parameters

characteristic of the reflective sail layer. The above reflectance terms are averaged over all possible orientations

of the incident electric field. Note that easy measurable quantities are the total spectral reflected light,

giving p (Z , 0, {p}) , and the scattered light (via laser, for example). It is possible to show (Vulpetti, 1999b)that

the parameters entering the sailcratt motion equations (through the connection equations) have the following

meaning

Jo (z)az

r = Pspec (0,{p}) = -_ f.F._, Ospec (._,O,{p}) ¢Z_(_.,)dZ

(IV-19)

a = 1-(r+d)

In the above equations, 't/(.£) denotes the spectral radiant exitance of the Sun, which may be assumed as

blackbody source with 5777 K, (corresponding to the solar constant value of 1367 W/m 2, §IV.5.4). Wavelength

could range from 1,000 A to 40,000 A for a number of physical reasons. For a given sail material and film

deposition method, entries in the thrust parameter set {r, d, a} depend only on the photon incidence angle,

though, in some case, some parameter may exhibit a quasi-independence on this angle. Anyway, they are

assumed to not change with time. That is what we mean by ideal optics here. Actually, any d > 0 entails a sort of

intrinsic degradation in terms of thrust because of the different coefficients that the specular and diffuse terms

have in the connection equations. One needs a device separating these contributions to the total reflectance.

Particularly appropriate to the solar sailing thrust modeling is the Scalar Scattering Theory (SST), where the

main parameter is the root mean square roughness of the reflective layer, hereafter denoted by _. It is closely

related to the sail making process that causes irregularities in the deposited Aluminum film, for instance. The

underlying assumptions of SST are discussed in (Vulpetti, 1999b) relatively to space sailing. Here, we limit to

report the simple equation between total and diffuse reflectance:

, = z ) (IV-20)

Total spectral reflectance does not depend on 6; however, light scattering causes specular and diffuse

components to be distributed differently. Equation IV-20 shows that diffuse reflectance augments non-linearly

with roughness. Strange enough at first glance, 9a_ achieves its maximum value at normal incidence 0- 0.

Depending on the actual sail, consequences to sailcra_ dynamics could be significant, through equation IV-15.

17.4 External Optical Degradation

Space is known to be a very complex environment that behaves very differently, even as seen from different

artifacts and with respect their goals. In addition to classical design items (spacecraft thermal control, spacecraft

system & sub-system protection, payload degradation and so forth), modem objectives regard tests on inflatable

structures too (Stuckey et al., 2000). These systems can include different structural elements that have to be

capable of tolerating space environment for the time necessary to allow the payload mission. From this point of

view, any sail system is a special deployable system. Apart from some simple Russian tests in orbit, a full

IV-IO
preliminaryexperimental missionsailcrafthasyet to be flown (August2001).Thereareonly very scarce

experimentaldataspecificallyorientedto solarsailinghitherto.We shallusepart of themfor exploffng

consequencesonfastsailcratttrajectorysuchastheISP's.To this aim,wehaveto buildsomemodelthat

accountsfortheenvironment adeep-spacesailcrattsailisableto sense.Sinceourinterestisin all-metalsails,as

•

explained above, we may focus on two major causes that could induce a decrease of the sail performance, that is

a modification of the ideal-optics conditions as stated in §IV.3. These causes are the solar ultraviolet photons and

the solar wind particles that will continuously impinge on a space sail. In this current investigation for NASA, it

has been agreed that, considering the very limited amount of experimental data, only effects stemming from

solar wind should be considered. Nevertheless, we present calculations that should hold even in a next research

phase about the influence of the solar UV flux-on the mission design of a fast sailcraft, namely a sailcraft flyingby the Sun at low perihelion. By using the concepts of exitance, radiance and irradiance from classical optics, it

is a simple matter to carry out the integrated flux of UV photons onto a sail of a sailcraft in the time interval

[t o ,t]. One gets the energyfluence

cos(O)

W_ = f_ Wla U _oa(O)

. R2 dt (IV-21)

Equation IV-21 holds for a sail having absorptance a and distance R from a point-like Sun. UV beam impinges

on sail with an incidence angle 0 from the sail normal n. (The relativistic energy shill, sensed in the sailcraft

frame, has been neglected). Symbolfuv represents the ultraviolet fraction of the solar constant; it may be easily

estimated by the blackbody distribution at 5777 K. For instance, fuv = 0.122 over the 1,000-4,000 A range,

namely, 167 W/m 2 of UV flux at 1AU. An important thing to be noted in equation IV-21 is that the absorptance

function is no__At exhaustively given by equations IV-19 as they hold for (time-independent) ideal optics. We shall

return on this topic in § IV.4.1 since it regards the lightness vector computation.

As far as the energy deposited by the solar-wind particles on a moving sail, we make some simplifying

assumptions here. They are: (i) solar wind flows radially from the Sun with a speed constant from _ 20R o to the

termination shock, (ii) solar-wind number density scales as 1/R2 everywhere in this range of dist_ce, (iii)

interplanetary magnetic field does not interact with sail. A few remarks about these points. Solar wind is an

expanding momentum-dominated high-conductivity super-alfvdnic (pseudo)supersonic collisionless plasma for

which a continuum description applies. Very schematically, it may be viewed at large as composed of quiet

background plasma of low speed, on which non-radial fast streams of essentially electrons and protons overlap

almost periodically. Solar-wind speed changes with the helio-magnetic latitude and reaches a minimum close the

interplanetary current sheet. Our assumption (i) is somewhat elementary, but it hasthe great advantage to make

calculations affordable in the context of this report. In contrast, assumptions (ii) and (iii) appear rather realistic

also on considering that here one is interested in fast sailcraft receding from the Sun. Thus, in the sailcraft frame

of reference, the (differential) flux of proton energy arriving at the sail during the time dt is given by

d tPsw = ViAump(W 2-2WVcOsCp+V 2) W-Vcos(p

-_ 2 R 2 -V sin q_ •n (IV-22)

0

In equation IV-22, W is the solar-wind speed in heliocentric frame, mp denotes the proton mass and via U

represents the (mean) proton number density at 1 AU. The energy per unit area absorbed by the sail in the time

interval [t o ,t] can then be written down as

Wsw (t) = _o(1-ypep)( \dtPsw at ! dt (iv-23)

In IV-23, yp and ep denote the proton backscattering yield and the proton backscattering energy fraction,

respectively. Actually, computation of IV-23 is a long iterative process, which may be simplified by estimating

the proton backscattering properties in the energy range related to the sail and sailcraft under consideration. By

using a sophisticated Monte Carlo code, such as SRIM 2000 (Ziegler, 2001), it is possible to study the

IV-11
interactionof protonsandAluminum.Wehavefocusedattentionona number of fast sails and missions; for

instance, fast-stream proton energy, as sensed by the sailcratt, ranges from 1.8 to 3.4 keV. A radial-in-EHOF

200-nm sail, too.ring at 15 AU/yr, is characterized by a backscattering yield equal to 0.039 and a backscattering

energy fraction of 0.205; therefore, 99.2 percent of the solar-wind proton energy flux is deposited on the sail (in

' a max depth equal to 110 rim). On the other side, a 130-nm 22-AU/yr sail at perihelion absorbs 97.8 percent of

the proton energy flux (in 115 nm). Along a trajectory, sailcraft experiences differential proton energy flux,

which changes as sail orientation and sailcratt position & velocity evolve.

Energy from UV photons and solar-wind protons, absorbed by the reflective sail material through a very short

thickness, alters reflectance and absorptanee permanently. Mathematically, the independent variable is the

energy fluence, of which equations IV-21 and IV-23 represent our present evaluation. Here, we adopt the

following model of optical-parameters change

5a - aactual -- a ,a_a,= A ( _ )

(?'ideal+ dideat)(l--g) + aideaI + _)a -1

=:_ (IV-24)

r_auat = (1 g) r_d,at , da_tuat= (1- g) didea t

This model entails that we should have some experimental data about absorptance change, namely, the function

A of fluence at time t, from which we could calculate the alteration in reflectance (since we know how to

calculate the ideal or reference optics discussed in §IV.3). The second equation in IV-24 assumes that the

relative changes of both specular and diffuse reflectance are equal to one another. Thus, immediately we get

=A(v)/ + (rv-25)

Equations IV-24 have been written to having changes as positive quantities. Finally, though sail material

emissivity does not change as a temperature function, however its actual range is shifted according to the

absorptance change. Thus, all thermo-optical sail parameters entering the sailcratt motion equatiom are modified

by the UV field and solar plasma that the sail gradually experiences.

On a conceptual basis, one can note that when surface roughness (an internal degradation) is introduced, part of

the specular reflectance turns into diffuse reflectance. In contrast, when external degradation is considered, part

of the total reflectance turns into absorptance.

4.1 Integro-Differential Equations of Sailcraft Motion

Despite the simplicity of the above particular model, the mathematical problem that. stems from any optical

degradation model consists of parameters depending on some quantity that is, at any time t > 0, function of the

previous history of the sailcratl trajectory. The optical parameters, modified through the energy fluence that

depends on the sailcraft state evolution in [t o ,t], determine the actual lightness vector at time t that affects the

saileratt motion during the interval (t,t + dt]. Equations IV-2, IV-15 (or IV-18), IV-24 and IV-25 are coupled.

As soon as the last three equations are substituted into IV-2, equations of sailcraft motion appear as a system of

integro-differential equations ODE). In other words, whereas the ideal optics for sail entails a system of ODE,

the introduction of optical degradation requires the numerical integration of a system of IDE for computing the

sailcratt motion.

In the computer code shortly described in §IV.5, we had to modify some of the routines of the numerical

integrators used for ODE in order to deal with the problem of optical degradation (even though model IV-24 is

formally simple). In §IV..6, we shall show that some sailcratt trajectories are significantly affected by a

progressive change of the thermo-optical sail parameters.

IV-12
4.2 Experimental Data Fitting

What remains to do here is to discuss the determination of the function A(W). We began with the experimental

data reported in (Werts et al., 2000), but we proceeded with using a different fitting procedure in order to be

compliant with our present optical model. As of September 2001, the paper by Wertz was the only one, on this

matter, supplied by NASA/MSFC to the author of this chapter. In addition, some of the public space literature on

the UV-photon-induced degradation either regards organic materials or has contradictory results about thin metal

films. In such literature, topics are not oriented specifically to solar sailing materials. Thus, in using data from

Wertz paper, we had to assume that electron-dose damage may be similar to solar-wind proton's. No reliable

data about UV-induced damage of A1-Cr films have been found by the author at the writing time. Nevertheless,

the theoretical model described in this section and some consequences reported in §IV.6 may be of considerable

importance for solar sailing in general, even though we deal with only one of the pieces to the actual change of

the thermo-optical sail parameters. With this in mind, we proceeded to the computation of the A-function into

two steps. First, we fitted the experimental data of absorptance as function of the (electron) dose by considering

that (1) if dose is very low, then the actual absorptance practically coincides with the ideal one, (2) if dose is

very high, then the material is completely degraded, in practice aa_,,,t --_ 1. This has carried out the following fit

U

¢-

e_

L_

o

0.8

0.6

0.4

0.2

Aluminum Absorptance vs Dose [Mrads]

i !I ii_

__1 I i

i i lil

1 10 100 1.103 1.104 1.105 1 -106

Electron Dose [ Mrad ]

Figure IV.4-1

In the above plot, D e denotes the electron dose expressed in Mrads (1 Mrad = 10 4 Gy). Experimental data

regarded beams incident orthogonally to the specimen surface. This fit produces absorptance residuals of zero

mean (<lE-14) and standard deviation equal to 0.00085.

The second step consisted of transforming dose into energy fluence by utilizing the specimen materials, their

geometrical configuration (Wertz, 2000) and noting that aideat (0------0) = 0.0720 (independently of rouglmess) for

Aluminum. That has resulted into the following absorptance change law

A (qJ) = 0.92027 tanh (0.25215 _t'sw) + 0.00793 (IV-26)

In IV-26, the energy fluence is expressed in MJ/m 2. The last term in equation 0V-26) represents the difference

between the experiment control value, taken at (small) non-zero fluence, and the ideal absorptance value given

above. It has been retained as a small conservative bias; for a real mission, some bias will probably happen due

to the non-negligible time between sail making (on ground) and sail deployment (in space).

IV-13
IV.5 A Computer Code

The numerical cases of trajectory optimization presemed extensively in §IV.6 have been computed by using a

computer code named Starship/Spaceship Mission Analysis Code (SMAC). The author has implemented SMAC

on PC in the 1986-2001 timeframe.

5.1 General Description

SMAC has been designed and is maintained for computing spacecraft trajectories related to propulsion modes

such as nuclear/solar electric propulsion, antimatter propulsion, space ramjet, laser/microwave sailing, solar

sailing, plasma-driven sailing and any physically-admissible combination two-three modes. Obviously, some

combinations of modes are hard to be realized in practice; they are useful for evaluation analysis and/or

performance limit. User can perform trajectory computation in either classical or (full) relativistic dynamics.

(SMAC was used by the author in his research on interstellar flight in the 1988-90 timeframe and during the

AURORA Collaboration mentioned in §IV.3). SMAC is now in full Fortran-90/95 and currently runs under MSWindows 98-SE. User graphic interface (GUI) has been designed in MS-Visual Basic 5. SMAC includes a 3D

graphic module for quick output visualization.

Current SMAC version (A.45.93a) consists of about 24,600 lines. Employed compiler is a commercial highly

optimized compiler for Pentium-III.

Solar-sail mode is one of the most detailed propulsion modes in SMAC. The whole of the solar sailing theory

described in the previous sections comes from as special case of a more general solar-sailing model embedded in

a set of Fortran modules and procedures; these ones are designed to grow with the user needs.

With regard to the Interstellar Probe mission concept, Normalized Solar Units (NSU) have been used by setting

GMstm = 1 and Astronomical Unit (AU) = 1. Internal computations have been performed in full double precision

according to IEEE 754.

5.2 Integrators

SMAC user can select different numerical integrators for different trajectory arcs, according to the propulsion

types, star and planetary fields. The available methods for integrating ODE are:

Adams-Bashforth-Moulton (variable stepsize, variable order)

Bulirsch-Stoer (variable stepsize)

Runge-Kutta-Shank (modified)

Fixed step

Automatic variable stepsize

User-defined variable stepsize

The above three methods are known to be based on quite different principles. They are useful also to compare

high-precision integration of difficult mission profiles. Each integrator consists of Fortran procedures arranged

into three nested levels- the driver routine, the stepper routine and the algorithm routine. The above integrators

were originally implemented only for ODE in SMAC. Subsequently we have modified the drivers for also

dealing with the integro-differential equations system stemming from the optical degradation problem.

5.3 Optimizers

The user can use SMAC in either propagation-mode or optimization-mode. Trajectories can be optimized in the

Non-Linear Programming (NLP) sense; the analyst can minimize one objective function chosen out of five

criteria. Optimization may be constrained on either control or state, or both. Additional linear/non-linear

constraints, relevant to special propulsion modes (e.g. the solar sailing) are dealt with. Very shortly, a trajectory

can be segmented into a number of arcs each of which is characterized by its own propulsion mode (one or more

depending on the research purposes), star field, planetary perturbation(s), attitude control parameters,

state/control constraints and so on. Through the GUI, the analyst can choose which controls are to be optimized

arc-by-arc, including launch date and/or part of the initial spacecraft state relatively to either the departure star or

the departure planet. Similarly, the final spacecraft state (at target) can be partially left open.

SMAC knows two robust optimization algorithms" the Marquardt method revised by Levenberg-MarquardtMorrison (or the LMM algorithm), the Levenberg-Marquardt method improved by Mor6 (Argonne Lab., 1980)

IV-14
ortheLMEalgorithm.Theoriginalimplementationof LMEwasinFORTRAN-IV;it was ported to Fortran-90

by Vulpetti in the Nineties. Its current version in SMAC is either standard or interactive. Due to the different

minimum-search policies of the two methods, the analyst may utilize both algorithms for solving problems

exhibiting many local minima that differ slightly in value or by small amounts of the (optimized) control

parameters, or both.

5.4 Constants and Standard Files

In addition to what explained in § IV.2.1, the following constants have been used in the present investigation by

this computer code:

Solar Gravitational Constant

Astronomical Unit

Unit Mass

Solar Constant

1 AU/standard year

Solar radius

1.327124400180E+20 m3/s 2

1.495978706910E+11 rn

the spacecraft initial mass [kg]

1367 W/m 2

4.740470 km/s

6.961E+05 km

Basic physical constants have been taken from Particle Data Group (2000) available from CERN, LBNL and at

htt0://0dg.lbl.9ov. File DE403/LE403 from Jet Propulsion Laboratory (JPL) has been used for planetary

ephemerides. With regard to the assumed value for the solar constant, it is an excess-rounded (by about 0.7

W/m 2) average of the daily-means of the total solar irradiance (that is time-variable) measured by satellite

throughout the year 2000. For details, visit the site http://obsun.pmodwrc.ch. We have considered such value in

this mission analysis of the Interstellar Probe, for a presumable launch in 2010/2011, namely, about one solar

cycle from now. Some care about it should be used, in general. Sometimes, one might adopt a round value (1.4

kW/rn 2) in rapid computation of solar sail trajectories This entails higher lightness numbers that, in turn, could

induce some non-negligible shit_ of some key quantity (e.g. the perihelion distance). The resulr,rnay be a nonlinear (generally optimistic) change of the trajectory performance index.

IV.6 The Case for Interstellar Probe

We shall study ISP mission opportunities involving sailcrat_ motion reversal. They might be added to the

mission profiles already analyzed by JPL (Mewaldt et al., 2000). We deal with trajectories from sailcraft

injection into the solar gravitational field to the target distance of 200 AU in the heliopause nose direction.

6.1 Investigation Line and Problem Statement

In its most general form, the lightness vector depends on variables and parameters of different physical origin

that one may group as follows: (a) source-of-light parameters, (b) physical/geometrical sail parameters, (e)

sailcrati state variables (mass, position, velocity), (d) environmental parameters, and the time elapsed since

deployment. In particular, L is proportional to Oc/O; o is a (technological) control parameter. We shall

analyze aspects of the ISP mission concept through different values of the sailcraft sail loading that, in turn, is

strongly related to the whole sailcraft technology, including the scientific payload. For each value of o,

typically we first discuss one (optimized) trajectory opportunity with ideal sail optics and, then, the

corresponding opportunity with optical sail degradation. For the case o = 2 g/m', more than one ideal-optics

profiles will be presented. The meaning of the term "corresponding" used above is the following: once the idealoptics trajectory has been optimized (in the sense described below), one switches from ODE to IDE by

considering optical sail degradation; then, optimization is performed by inserting the ideal-optics optimal

controls as the guessed or starting control set. In the next sub-sections, we will discuss six profiles by o ranging

from 2.2 to 1 g/m 2.

We computed admissible ranges of geocentric vector position and velocity (or the hyperbolic state) of a sailcraft

in the fuzzy boundaries of the Earth-Moon-Sun system. We considered some of the current launchers capable to

deliver a spacecratl of (at least) 200-350 kg with hyperbolic excess up to 1 km/s. Significantly higher values of

the hyperbolic excess are excluded here, simply because both direct and reverse motion modes have to obey the

IV-15
basicrulestatedin §IV.2.3.(Obviously,launcheris a primaryconstraint;however,indicatingany specific

launcherisnotaitemof thisreport).The hyperbolic sailcratt state is added to the Earth state at the injection

time, or the misgion epoch, of the sailcraft into the solar field. We assume that, at such JD value, sail deployment

& attitude acquisition and any other preliminary operations have been completed. The whole sailcmtt trajectory

is here segmented in five parts: four sailing thrusting arcs (or T-arc) plus one coasting arc (or C-arc) from sail

jettisoning to target. The first three T-arcs entail a three-axis stabilized attitude control, whereas sailcraft is spun

in the fourth one. (Why sail is not jettisoned at few AU past the perihelion has been explained in Chapter-Ill of

this report). In order to simplify the ISP H-maneuver, we have considered the following trajectory control

parameters"

(1) Epoch (to)

(2) Direction of the geocentric hyperbolic position (resolved in HIF) at to

(3) Geocentric hyperbolic excess

(4) l_t T-arc duration and sail direction constant in EHOI_ (IV-27)

(5) 2_a T-arc duration and sail direction constant in HIF

(6) 3_dT-arc duration and sail direction constant in EHOF

(7) 4 thT-arc duration and sail direction constant in HIF

(8) 1,t C-arc durati on

Control sets 4-5-6 represent a simple realization of the 3D H-reversal motion detailed in (Vulpetti, 1999a). In

addition, we have set the following constraints:

men(H) > 0

men(R)>_0.2AU

max(Ts) < 600 K (IV-28)

t:-t o < 18 yr

The following endpoint conditions have been applied

[R(to)-R a.h (t0) [= 0.01776 AU

R (t/) = 200 A U (W-29)

A(t/) = 254.5 ° ®(t:) = 7.5 °

We chose the flight time upper limit in IV-28 such that, combined with the optimized coasting speed, the whole

ISP mission, with a potential prolongation from 200 AU to 400 AU (Liewer et al., 2000), may last less than a

typical human job time (HJT) or 35 yr. However, the sailcmt_ distance baseline was frxed at 200 AU. The third

row of IV-29 represents the ecliptic longitude-latitude coordinates of the sailcraft target position. The other

endp0int values have been left free and optimized accord'rag to NLP. The index of performance, here, is the

sailcrat_ speed at 200 AU. Thus, the current problem of astrodynamics can then be stated as follows:

Given either the previous ODE or IDE system, describing the motion of a sailcrafi in the solar

system, with vector state S -- [m R V] r driven from SO to S/ (partially-fixed states) by the

IV-30

control {U} (defined in IV-2 7), find the special set {U °pt} that maximizes the sailcrafi speed at

t/ while satisfying the linear and non-linear constraints 1V-28.

As far as the planetary perturbations are concerned, we considered both inner and outer planets; eventual

planetary swing(s)-by of the sailcraft is(are) computed during the trajectory optimization process. When in the

solar field, gravitational perturbation from the Earth-Moon system to the sailcraft is modeled as stemming from

their barycenter.

IV-16
6.2 Arrangement of the Results

In the following subsections, we discuss the numerical results of the problem stated in §IV.6.1. For each case

and for each optimization, we have arranged the main results in six-Figure tables (on a one-per-page basis),

which are grouped sequentially in §IV.6.11. Each table contains an header reporting the values of thequantities

by which we made mission profiles distinct. They are: sailcraft sail loading (input), root mean square roughness

(input), optical sail degradation switch (input), actual sailcraft perihelion (output). Each Figure in a set is labeled

by both paragraph (of discussion) and progressive number. Figures 1-2 regard the projection of the sailcraft

trajectory onto the ecliptic, or the XY plane, and the YZ plane. The orbits of the first four planets are also shown

in the two plot windows. Figure 3 shows the evolution of the H-invariant. On the let_ side of the H minimum, the

sailcraft motion is direct, whereas on the fight side it is reversed. The ensuing sailcraft cruise phase "saturates"

the invariant. This behavior, which looks like a sort of"square root", is quite general for the 3D H-reversal mode

aimed at getting away from the solar system. Time at which the vector H crosses the ecliptic plane is shown by a

vertical segment in Fig.-3. Reversal time decreases with the sailcraft sail loading. Figure 4 is the plot of the timehistory of the lightness vector components (in EHOF). Motion reversal line is shown again. Controlling the first

three T-arcs entails L(t) continuous, whereas the optimal spin-stabilized T-arc requires an attitude maneuver.

After such a maneuver, supercritical sailcraft results in a quasi-radial lightness vector. In contrast, sub-critical

sailcraft shows high non-radial numbers" the transversal number increases energy while the normal number

steers to the target direction. During the spin phase, the radial number is close to unity or higher, so

counterbalancing or overcoming the solar gravitational acceleration. Sailcraft speed and orbital energy are

graphed in Figure 5. There, the perihelion time (vertical) line is added to show that maxima of speed and energy

take place past the perihelion, with the following distinction: supercritical sailcraft exhibits a local maximum of

speed and an asymptotic maximum of energy, whereas sub-critical sailcratt evidences asymptotic maxima of

both. With regard to Figure 6, we plotted the history of sail temperature for the ideal sail optics (i.e. switching

degradation to off); when degradation=ON, we reported temperature, fluence and change of optical sail

parameters altogether.

All Figures focus on suitable time windows that highlight the behaviour of functions. In discussing results, we

limit ourselves to some points, whereas other considerations, which can be read out easily from Figures, are left

to the reader.

Table IV.7-1 summarizes the main input and output values. We shall refer also to this table in discussing results.

Unless otherwise specified, the root mean square roughness has been fixed to 20 nm. This means that a

roughness uncertainty from 3 standard deviations or 60 nm is reasonably compliant with the construction of a

large surface with Aluminum-Chromium film nominally 200 nm thick.

Sailcrafl sail loading will be given with two decimal digits. Units are grams per square meter. This means that, in

the range considered in the present analysis, two mission profiles differing by less than 0.01 g/m 2 in this

technological quantity can be considered identical, in practice.

6.3 The 2.20 g/m 2 case

This case has been considered to show the difficulty of a sailcraft of 2.2 g/m 2 to move as fast as the ISP mission

concept would require.

Figures IV.6.3-[1-6] show the optimized profile for ideal optics. Radial, transversal and normal lightness

numbers are such that motion reversal can take place. Orbital angular momentum decreases in magnitude and

bends progressively until it lies on the ecliptic plane, 1.492 years after injection. At such a time, the transversal

number vanishes and the normal number achieves its local positive maximum, according to the theory. Since this

instant on, the transversal component of the lightness vector becomes positive whereas angular momentum

bending continues as the normal number is still positive. As a result, sailcraf_ motion reverses while energy

increases. Sailcraft moves toward the Sun with increasing speed not only because potential energy decreases but

also since total energy augments significantly. It achieves the escape point (E=O) and rapidly rises before the

perihelion. Acceleration keeps on after the perihelion, but now the normal number goes to zero from the fight

side, while the sailcraft distance from the Sun rapidly increases because of the very high speed. All this means

that angular momentum stops bending and the H-function evolves asymptotically. The subsequent attitude

IV-17
maneuverforgettingaspinningsailcraftcompletesbothspeedkeepingandsteeringof sailcrafttowardthetarget direction.

In thecurrentframework,theabovedescriptionappliesqualitativelyto anyH-reversal evolution. However, as

we decrease the sailcratt sail loading, we will find a corresponding progressive shifting of values (not of

behavior) that is important in the ISP context.

In the present case, the direct motion arc - always characterized by the H-invariant decrease - is slow because

the transversal number, responsible for the energy change, is not negative enough. Even the radial number is not

sufficiently greater than 1/2 for allowing a high perihelion. Consequently, if one wants a cruise speed satisfying

the mission flight-time constraint, then perihelion has to be low. Getting a cruise speed more than 14 AU/yr

entails a non-negligible perihelion violation, namely, Rp=0.175 AU here. Such a low perihelion may not be a

problem, in general, for an advanced sailcraft. The true problem arises in the presence of optical degradation.

To figure out better, a sailcratt trajectory - satisfying active constraints - may be generally regarded as a sort of

delicate compromise between conflicting key quantities such as hyperbolic state (with respect to the departure

planet), time interval to perihelion, perihelion distance, sail temperature effects, range of lightness numbers, and

so on. They "interact" to each other, of course. As pointed out, in the current case the lightness numbers arenot

so high to decelerate sailcrafl fast enough. Thus, solar-wind energy fluence increases and induces a strong

absorptance change. This one, in turn, increases sail temperature significantly. On the other side, if one

decreased the hyperbolic excess at epoch, then a time-to-perihelion reduction could take place; nevertheless,

since the radial lightness number does not depend on hyperbolic excess, one would have a further lowering of

perihelion and an additional increase of the fluence on the sail. Thus, in getting a trajectory satisfying perihelion

and temperature constraints, both baseline and extended-mission flight timesexceed their limits, as reported in

Table IV.7-1, as cruise speed falls down to 11 AU/yr. The present value of o- may be considered in a transition

zone (relatively to the ISP mission concept) where some constraint, unavoidably, cannot be satisfied.

6.4 The 2.10 g/m 2 case

As pointed out above, L depends on o- non-linearly. With respect to the previous case, a decrease of 4.5 percent

in o- induces a change of 9.6 percent in the range of the optimal transversal lightness number of the directmotion arc (ideal optics, Figures IV.6.4-[1-6]). This quantity is the major responsible for the change of key

values with respect to those ones related to 2.20-g/m 2. As a point of fact, even though the radial number varies

by about 1 percent, H-reversal time and perihelion time are back shifted by 15.7 and 13.1 percent, respectlxvely.

Every constraint is satisfied; in particular, perihelion takes place at 0.204 AU. Note that the duration of the 2nd Tarc decreases from about 60 to 33.5 days. In this arc, the angular momentum bends and reverses by passing

through a minimum in magnitude. The interval of such a T-arc is a non-linear function of the sailcraft sail

loading. Its allocation atter the 1 st T-arc, where the sailcraft's deceleration occurs, is a key factor for achieving

the condition of motion reversal.

Optical degradation brings on perihelion rising of 0.044 AU with a delay of 84 days (or about 14.9 percent) with

respect to the just-mentioned ideal-optics case. However, relatively to the 2.20 g/m 2 case, the "gain" in terms of

mean distance and time in the pre-perihelion motion is such that fluence at perihelion decreases down to 0.57

MJ/m 2 or-3.4 percent. This is enough to not violate the temperature limit and get a good margin. Fluence

saturation is achieved two years after injection, namely, one year (or 30 percent) in advance with respect to the

2.20-case. Trajectory profiles are shown in Figures IV.6.4-[7-12]. One has only a slight violation (0.1 yr) of the

baseline flight time. Cruise speed amounts to 12.23 AU/yr.

In the current framework, the 2.10 g/m 2 case could be considered the lower bound of the above-mentioned

transition from mission infeasibility to mission feasibility.

6.5 The 2.00 g/m 2 case

The present cr value is very close to that considered for ISP in (Mewaldt and Liewer, 2000) and (Liewer et al.,

2000). We first present a number of trajectory profiles with different values of the root mean square roughness.

Key values are collected in background-colored rows of Table IV.7-1.

IV-18
In principle,thebestcaseonemayenvisageisasailwithneitheroughnessnordegradation. Plots related to this

special case of optimized trajectory are shown in Figures IV.6.5-[1-6]. Pre-perihelion trajectory is almost

tangential to the Mars orbit. Motion reversal begins after 321 days (since injection) with Hmin=0.0226 AU2/yr.

The sailcraft proceeds to perihelion, in about 76 days, with a speed of 16.78 AU/yr; maximum speed is as high

as 17.79 AU/yr. However, since the max value (0.736) of the lightness number is less than unity even in this

ideal case, speed has to decrease while sailcraft recedes from the Sun. Nevertheless, a cruise speed of 15.22

AU/yr is achievable by satisfying constraints widely. This results in baseline flight time of about 14.2 yr with

additional 13 yr to accomplish the prolonged mission. In one HJT, sailcratt could reach 516 AU.

Figures IV.6.5-[7-12] show that this performance is decreased only slightly if the sail were made with a root

mean square roughness equal to 10 nm. This is a direct consequence of the diffuse-reflectance law given by

equation IV-20. The most visible differences are: earlier launch date (on October 7) by almost three days, the

increase of the hyperbolic excess from 10 m/s to 70 m/s. Both compensate for the (low) reduction of transversal

lightness number; thus, without remarkable changes in the other decision parameters, perihelion remains

unchanged and cruise speed can be kept over 15 AU/yr. In one HJT, sailcraft could reach 509 AU.

There is still a good margin in accepting a sail made with higher roughness _ and, at the same time, finding a

perihelion very close to the value given in (Liewer et al, 2000). The set of plots for _=20 nm and ideal optics are

displayed in Figures IV.6.5-[13-18]. The pre-perihelion arc elongates beyond theMars orbit, H-reversal delays

by 61 days (Hmm=0.0115 AU2/yr) and perihelion occurs at 0.24 AU. As a result, cruise speed decreases to 13.17

AU/yr. However, both baseline and extended mission flight times satisfy the related constraints (even though the

extended mission lasts four years more). In one HJT, sailcraft could reach 443 AU.

This t%20 ideal-optics solution is important since it is changed exiguously, injection date included, by the optical

degradation (Figures IV.6.5-[19-24]). As a point of fact, the lightness numbers are still sufficiently high to

ultimately keep fluence below 0.55 MJ/m 2 around the perihelion. Thus, temperature constraint is not violated

(Tmax=587 K). Fluence achieves saturation (0.7 MJ/m 2) in 1.7 yr. From Table IV.7-1, one can s_e that both time

to and speed at 200 AU are such that 441 AU could be achieved in one HJT. In addition, the current cruise speed

of 13.13 AU/yr compares well to V_ or 14.41 AU/yr, given by equation IV-6 (which does not include any

degradation).

From what so far described, one should note that decreasing the sailcraft sail loading from 2.2 to 2.0 g/m 2 means

moving from risk to feasibility, at least from the nominal-mission viewpoint.

6.6 The 1.80 g/m 2 case

In full degradation conditions, the value of 2.00 g/m 2 would cause a temperature violation if one attempted to

use a perihelion even reduced by 0.011 AU. For instance, some sail control errors may force to flyby the Sun at a

lower distance during the real flight. On the other hand, some meaningful perihelion decrease is necessary to

increase the cruise speed. That may be accomplished by further reducing the sailcraft sail loading. In the idealoptics mode, 1.80 g/m 2 would allow the sailcraft to flyby the Sun at Rp=0.20 AU and to complete the extended

mission in 26.2 years. One would get 538 AU in 1 JHT.

However, in the optical-degradation mode, perihelion cannot be lower than 0.22 AU. At this value, fluenee takes

on 0.5 MJ/m 2 that induces 597 K of max sail temperature. Fluence saturates at 0.64 MJ/m 2, practically achieved

in 1.1 yr. With this perihelion, cruise speed comes to 14.8 AU/yr; whence, baseline flight time amounts to about

14.4 yr and the extended mission lasts 27.9 yr. After a time equal to 1 HJT, sailcrafl would achieve 505 AU.

Plots of the current case are displayed in Figures IV.6.6-[1-12].

The main advantage stemming from making the ISP sailcraf_ with 1.8 g/m 2 instead of 2.0 g/m 2 would consist of

flight error counterbalance through a set of admissible backup trajectories with respect to a nominal trajectory

having 0.22 AU < Rp < 0.25 AU, especially if the actual energy fluence were to result meaningfully different

from the predicted one.

IV-19
6.7 The Critical Case

As we know, the attribute critical refers normally to the equality between the sailcratt sail loading and that ideal

value, which would allow a sailcrat_ to balance the solar gravity exactly. We mentioned in §IV.3 that such value

pertains to a perfectly reflecting sail (at-rest in HIF) oriented radially and receiving light from the point-like Sun.

However, any real sailcraft at criticality, i.e. with cr = Cc, would exhibit a maximum value of the lightness

number lower than unity at any time, as its thrust efficiency is certainly less than unity throughout the flight.

Besides, the max value of this efficiency in this case is close to 0.87. Consequently, such a sailcratt would not be

dynamically critical, inasmuch as the lightness number would be meaningfully lower than one throughout the

flight. We shall go forward to analyzing some sub-critical cases.

6.8 The 1.28 g/m 2 case

In terms of o-, this sub-critical 1.28 is as distant from O'c as 1.80 is. For an ideal-optics sail, the pre-perihelion arc

is characterized by a mean value of the transversal number equal to -0.375. This is sufficient negative to lower

aphelion, increase energy loss and achieve perihelion (0.20 AU) in 212 days. After the attitude maneuver at the

beginning of the fourth T-arc (at 0.27 AU), the post-perihelion trajectory arc exhibits comparable values of all

components of the lightness vector. This allows both energy and speed to evolve with profiles practically fiat

throughout the fourth T-arc (that ends at 120 AU). Strictly speaking, the local maximum of sailcratt speed still

exists, but it is so broad, on the right, that it is rendered indistinct from the cruise level or 20.8 AU/yr. Baseline

mission could be accomplished in 10.2 yr. Sailcratt could reach 716 AU in 1 HJT.

When optical sail degradation is considered, the pre-perihelion arc is still so fast that, very close to the

perihelion, solar-wind energy fluence is as low as 0.37 MJ/m 2 at which sail temperature rises to 578 K, its max

value. Sail achieves fluence saturation (0.48 MJ/m 2) in 0.7 yr since injection. The optimal profiles for opticaldegradation are very similar to those ones without it. One value for all, ISP would reach a distance, again, equal

to 716 AU in 1 HJT.

This case is shown in Figures IV.6.8-[1-12].

6.9 The 1.00 g/m 2 case

In contrast to the above cases, some lightness number can now be greater than unity in some T-arcs; in

particular, one gets _, _ 1.24, _._--1.17, ;_, _=_0.34 (ideal optics) in the spinning-sail T-arc. The main result

consists of obtaining the sailcraft speed increasing as sailcraft moves far away from the Sun. As a point of fact,

once the sailcraft overcomes the perihelion, some maneuver can be accomplished in order to reorient the sail

with a radial number constantly greater than unity. Thus, the local speed maximum of the previous cases has

"evolved" into an asymptotic absolute maximum. The H-reversal arc duration is still quite manageable (2 days).

The optimal profiles are shown in Figures IV.6.9-[1-6].

By including optical degradation, the above set of lightness values changes into

_,---1.14, E_---1.08, _t -=0.29, which allows sailcmft to accelerate again asymptotically. The related profiles

are shown in Figures IV.6.9-[7-12]. Sail temperature takes on a max value of 547 K at fluence equal to 0.31

MJ/m 2. The dynamical output one gets at 200 AU consists of sailcraft speed equal to 23.5 AU/yr. Baseline

mission lasts 9.03 years, whereas the extended mission to 400 AU may be accomplished in less than 18 years.

809 AU could be reached in one HJT.

From Table IV.7-1, one can note that the current max value of sail temperature is the lowest one out of all cases

hitherto analyzed. (The temperature margin may be used to design a new profile with perihelion less than 0.2

AU, but still keeping fluence sufficiently low not to violate 600 K. Such an analysis may be among the topics of

a future study on faster ISP). Finally, one shouldnote that, in this case of sub-critical sailcraft sail loading, Vf

amounts to 21.34 AU/yr, namely, lower than the current cruise speed. It is to be ascribed mainly to the large

transversal lightness number that can change energy (equation IV-5c) to overcome the pure-radial solution

significantly.

IV-20
.

Further Remarks

Keeping the sail attitude constant, or so, in the sailcmft orbital flame entails that the sail axis has to be

rotated sufficiently fast in the inertial frame, especially when sailcrafl moves around the perihelion. For

instance, the attitude control system has to output about 9.7 deg/day and 15.1 deg/day for the 2 g/m 2 and

1 g/m 2 case, respectively. In the present model of sailcrafl, although detailed system description and

modeling is beyond the scope of this report, we assumed a small-rocket attitude control; each pair of

micro-engines (endowed with small solar panel) is placed on the sail rim. In the fastest trajectories here

analyzed, maximum fuel consumption is less than 1 percent of the initial sailcraft mass. In general, a

"mixed" attitude control system may be considered: non-rocket devices (Wright, 1993) and microthrusters, depending on the distance from the Sun and the trajectory control requirements.

The optimal trajectory profiles presented in this report are characterized, among many things, by a

double-crossing of the ecliptic plane, with the perihelion between the two. Perihelion latitude ranges

from-14.8 ° to-47.8 °. Therefore, there is no geometric problem in the sailcrafl-Earth communication

around the perihelion. What shall be analyzed in detail is the location of the onboard antenna with

respect to the sail.

3. In addition to the mission unfeasibility-feasibility transition, there exist another special value of the

sailcrafl sail loading. For the ISP-mission A1-Cr sail spacecraft with H-reversal motion, this value is very

close to 1.3 g/m 2. Below it, the pre-perihelion trajectory arc can be so fast that (despite the angle

between sailcraft position and velocity is significantly greater than 90° for over 50 percent of time), the

optimal performance indexes of the ideal-optics and the optical-degradation flights can be considered

equal to one another (< 1 percent). Above this limit, the influence of the energy fluence on mission

feasibility cannot be neglected. Reasonably, such a feature should hold even for a direct-motion fly-by

of the Sun. At the time of this writing, though, it is not known.

4. A sailcrafl with 1.2 g/m 2, or less, would be able to fast explore the solar gravitational lens in deeper

focal zones. For instance, if sailcrafl were able to fly-by the Sun at perihelion equal to 0.15 AU

(Vulpetti, 2000), it could navigate the interval from 763 AU to 821 AU in 2.3 yr and reach 821 AU after

32.2 yr since injection. That would be appropriate for observing distant photon sources in the range

from 160.4 GHz to 122.3 GHz (Maccone, 2000). At 122.3 GHz, the photon path bending due to the solar

gravity is counterbalanced by the contrary deflection caused by the solar corona plasma. Photon

frequencies different from such no-lensing value behave differently in total deflection. In the context of

a generalized ISP mission concept, such a potential flight may be revisited by adding optical

degradation, telecommunication system and launcher constraint.

IV-21
6.11 Figures

Case id: cr=2.20 g/m2, r.m.s. 6=20 nm, Degradation=off, perihelion=0.175 AU

Figure IV.6.3-1

Notion Reversal" the October Opportunity

! i

optimized il_jection date 2011 10 3 11 i 14 37

• !

i ! ....... J i

""'-...... ....,../

i / I / ..... [ ":_ i

, / i/ / ] 'i i

.......................................... :::: ........................ 2>.:........... !,............ .<2............. i-.......................... i

', ' .."i i

.................................. i..................................................... On ecliptic plane

J /" i...................................................

-2 -1 0 1 2

X[AU]

<

N

Figure IV.6.3-2

Notion Reversal" the October Opportunity 1

0.5 .................................................................... i............................................................................................................

0 ........................... ......... _:,:.:": i_..::i.......,-,!!,_:_._i;;'_ .............. •......... i.........................

"0.5 ........................................................................................................................................... _................................._.........................

normal to ecliptic plane

-I

-3 -2 .1 0

Y[AU]

1 2 3

6.5-

5.5"

4.5"

>" 3.5"

7

2.5"

<

1.5"

0.5"

"0.5

Figure IV.6.3-3

t

irect Motion

) .25 __ 5 0.75 1 1 25

Evolution of the Solar-Sailing Invariant

ev

Reverse Motion

.5 1.75 _ 2!25

Time from Injection [ yr ]

Figure IV.6.3-4

• " 1.2

,.¢

0 1.1

z

O. -

_oua

0.7-

z

0.6-

:_ 0.4-

0.3-

0.2-

__ 0.1

o

_l -'0.1

,, -0.2

-0.30

Optimal Control: the Lightness Vector L

, , , _ i

t_v

i

...................................................... ;Lt

i

0.125 0.5 0.175 I1 1.125 1.5 1.175

Time from Injection [ yr ]

2'_, 2.5

25-

>" 20-

<

-o 15"

(an

" 10"

v-t 5

i '

uJ

"-5 •

Figure IV.6.3-5

Behaviour of Sailcraft Speed and Energy

i i

ttev ,_ ENERGY x 9

/_ sPEED

'5 12 2.125 :_.5

Time from Injection [ yr ]

600

500 -

r---n

400-

I1)

i_.

"-3

"-' 300 -

_3

I-.

E 200

i--

100 -

Figure IV.6.3-6

Sail Temperature Evolution

I I I I

0 I I I

0 0.5 1 1.5

Time from Injection [ yr ]

T < 600 K

2 2.5

IV-22
2

1

0

-1

Case id" c=2.20 g/m2, r.m.s. 6=20 nm, Degradation=ON, perihelion=0.261 AU

Figure IV.6,3-7 Figure IV.6.3-8

Motion Reversal" the October Opportunity

i _,\\ .... T-....

--4

"_"'\"...................... i- i

optimized injecti2 2011 lO 6 14204"

I M onec,,o,,c o,.ne

I , / ' ! .

-2 -1 0 1 2

N

0.5

-0.5

Motion Reversal" the October Opportunity

i i

i

i t

l ' [

i [ _

i

i i i

normal :o ecliptic I:

"3

lane

-2 -1 0 1 2 3

Y[AU]

X[AU]

6.5"

5.5"

4.5"

>" 3.5"

2.5"

1.5"

Figure IV.6.3-9

Evolution of the Solar-Sailing Invariant

|

tr_v

tion '

e Motion

I I I i Et I I I

0.4 0.8 1.2 1.6 2 2.4 2.8 3.2

Time from Injection [ yr ]

I

3.6

1.2

0 1.1

z

1

0.9

0.8

0.7

0.6

0.5

0.4

i 0.3

0.2

0.1

0

8 -o.1

.5 -0.2

-0.3

Figure IV.6.3-10

Optimal Control: the Lightness Vector L

i i I i i

trbv

_L n

! !

_t

11.6 '2 :_.4 :_.8 31.2

Time from Injection [ yr ]

Figure IV.6.3-11

25-

Behaviour of Sailcraft Speed and Energy

20

15

" I0

5

).

_o_ tu

-5

i

trlev

1'.2 11.6 '_2

Time from Injection [ yr ]

G'Y x 15

PEED

2.8 31.2 I I 3.6 4

0.8

6_ 0.7

e.-

t,,I

0.6

._

13.

O 0.5

•_. o.4

o.3

!--

0.2

E

0.1

¢-

"0.1

"0.2

Figure IV.6.3-12

Optical Param Changes ( Solar Wind )

I I I I I I I

_ F _

i............J,:.......i;...

- _ 6r

I I ! I I I I

0 0.5 1 1.5 2 2.5 3 3.5 4

Time from InJection [ yr ]

IV-23
<

6.5"

5.5"

4.5"

3.5-

2.5-

1.5"

0.5"

-0.5"

25

_o

,.., 10

<

I-i

P

,,5

Case id" cr=2.10 g/m2, r.m.s. 6=20 nm, Degradation=off, perihelion=0.204 AU

• Figure IV.6.4-1

1 -

0

-1 ....

-2 I_--

t

-2

Motion Reversal" the October Opportunity

optimized i jection date Ol 1 10 6 16 38 33

2 ..........

1 F " t

,\ t /i

"7...................... :

[_-Ti ......... 4--- on ecliptic pline

-1 0 1 2

X[AU]

r--i,

Z_

<

N

0.5

-0.5

Figure IV.6.4-2

Motion Reversal: the October Opportunity

....... __':r:=_;:='_" _ .....................

i

i

..........t............................................................................ ,,........ _ .......

i i l

! normal io ecliptic plane

-2 -1 0 1 2 3

Y[AU]

Figure IV.6.4-3

Evolution of the Solar-Sailing Invariant

, o:_ d.5 o!75 'l 17;5 -It5 1.'75

Time from Injection [ 7r ]

2.'=5 _.5

i i

1.2-

1.I

z

1-

0.9

0.8

0.7

0.6

0.5

0.4-

0.3-

i 0.2 -

0.1

0

-0.1

,, -0.2

-0.3 0 0125

Figure IV.6.4-4

Optimal Control: the Lightness V_-'tor L

i i i 11 i i I i

t#ev

i

i

!

(.

X t

.5 I Il 0.75 1.25 11.5 1!75 2 2!25

lime from Injection [ yr ]

• 2.5

Figure IV.6.4-5

Behaviour of Sailcraft Speed and Energy

i

t_ev

__, ENERGY x 10

k , i , ,

_510_ 0.75 I1 ':_25, , 1.'75 _ 2!25

_.5

Time from Injection [ yr ]

600

500

v

,..-, 400

i..

"-' 300

I..

E 200

100

I

0 0.5

Figure IV.6.4-6

Sail Temperature Evolution

I I I I

I I

1 1.5

Time from Injection [ yr ]

T < 600 K

I

2 2.5

IV-24
< 0

>-

6.5"

5.5"

4.5"

>" 3.5'

?

2.5'

1.5"

0.5"

-0.5

25"

>" 20"

_ 15.

t/I

" 10"

,-..,

_ 5"

E'

c

w

Case id" e_=2.1 0 g/rn2, r.m.s. 5=20 nm, Degradation=ON, perihelion=0.248 AU

Figure IV.6.4-7

Motion Reversal: the October Opportunity

f

optimized ihjection date _01 ! 10 5 8 6 45 !

H\ \- .... J

----=i .......-/----_....... ::-:_=4_- __L___......

.....4.............i _-_...._--_---_-t--...... '......... j x I

i ". ! N _...... i..._Vl" / I / 1

i ",. i "--... ....i7 ....." i.i ,

--_f ................. -_--f............ :"........_i--_::................. ,t:................4......

i ! i

! i / on ecliptic plahe

............... _............................. i.......................... ..-..l..._..................i .............. J.................... i

II ii _/ !! '_! .......

-2 -1 0 1 2

XFAU]

,(

N

0.5

-0.5

Figure IV.6.4-8

Motion Reversal: the October Opportunity

I

, i

J

t .....

i i

i

I

normal

l

!

J

io ecliptic i_lane

!

•-2 -1 0 1 2 3

Y[AU]

Figure IV.6.4-9

Evolution of the Solar-Sailing Invarlant

t ev

Direct Motion

Reverse Motion

0.25 0.5 0.75 1 1.25 1 5 1 75 2 2 25 2 5

Time from Injection [ yr ]

,D

1.1

. 1

f

_ 0.8 0.7

i 0.6

0.5 L

i 0.3

0.2

0.1

0

_.1

,, -O.2

-0.3

i

o!25

Figure IV.6.4-10

Optimal Control: the Lightness Ve_:lr L

i 1 i i i

t_v

_'r

d5 o!75

-

I i

,_ /5 ,!75 '2 ' " 2.25 2.5

Tlme from InJecUon [ yr ]

Figure IV.6.4-1 1

Behaviour of Sailcraft Speed and Energy

t_ev

' ENERGY x 12

X/

I!25' 11.5 '

SPEED

5 _2 2!25 2_.5

Time from Injection [ yr ]

0.8

0.7

"_ 0.6

0.5

0.4

__ 0.3

0.2

E o.1

o

8

"0.1

"0.2

Figure IV.6.4-1 2

Optical Param Changes ( Solar Wind )

I I I I

- F --

_L °° _...-

..... -. lSd !

I I I I

0 0.5 1 1.5 2 2.5

Time from Injection [ yr ]

IV-25
D

<

L_

Case id" c=2.00 g/m 2, r.m.s. 5=0 nm, Degradation=off, perihelion=0.20 AU

Figure IV.6.5-1

Motion Reversal. the October Opportunity

t

'./, ........................ :

I\\\i>' //1

"_L

-I 0 l 2

X[AU]

0.5

"0.5

Figure IV.6.5-2

_ Motion Reversal: the October Opportunity

i r

....................... i................................................i...........................i....................

• ._ -

J

t

................................ _ ........................... G .............................

i

norn_al to ecliptic plane

-1 o

Y[AU]

1 2 3

6.5"

5.5"

4.5"

_" 3.5-

< 2.5"

,....,

1.5"

0.5"

"0.5

Figure IV.6.5-3

Evolution of the Solar-Sailing Invariant

1

X t_v

i o:_'l' 6.5' 0:75: . v. ,!_ /.5 1!75 2!25_.5

Time fromInjection[ yr ]

1.2-

0 1.1

z .

1

0.9_ 0.8

0.7-

0.6

0.5

_" 0.4-

0.3-

• " 0.2-

0.10

-0.1-

..a -0.2

-0.3

0

Figure IV.6.5-4

Optimal Control: the Lightness Vector L

!

!

tdev

I

!

i

i

J

_'r '

!

i

i I i i i i

_n

I

0!75 ' _ 1.125 11.5

Time from Injection [ yr ]

I!75 19 2.125

Figure IV.6.5-5

Behaviour of Sailcraft Speed and Energy

25t . . .

_, t_v ,_ ENERGY x 8

20

D

<

15 : ....

o_

m 1!25 11.5

-5

SPEED

,!7s h 2!25 _.5

Time from Injection [ yr ]

600[ I I

500

L_ 400

300

E 200

100 -

Figure IV.6.5-6

Sail Temperature Evolution

I I

0 I

0 0.5

T < 600 K

I I I

l 1.5 2 2.5

Time from Injection [ yr ]

IV-26
-1

-2.

Case id: cy=2.00 g/rn2, r.rn.s. 5=10 nm, Degradation=off, perihelion=0.20 AU

Figure iv.6.5-7

Motion Reversal" the October Opportunity

/ i

optimize_ injection da_ 201110 7 7 9 S

i

_....._-_--'-_L

...... _._./"-':::"i-___ "-\..-..L...,. _\

I : I /- ....... \

i I/ " \

It f,.,t t lJ /_ i

,. It "., t . ,

i - i'..)'--ft"/// !

/ /

t i

t [ on ecliptic pLu_

' /

-2 - 0 1 2

X[AU]

Figure IV.6.5-8

Motion Reversal" the October Opportunity

Y[AU]

6.5"

5.5"

4.5"

>" 3.5"

?

< 2.5"

1.5"

0.5"

"0.5

Figure IV.6.5-9

Evolution of the Solar-Sailing Invarlant

!

 il--

I 0.125 d.5 0!75 t il 1!25 11.5 1!75 '-.'25

Time from Injection [ yr ]

:_.5

1.

1°'I

0.8

0.7

I .6

0.5

_ 0.4

_ 0.3

i 0.2

0.1

0

-0.1

.a -0.2

-0.3

Figure IV.6.5-10

Optimal Control: the Ughtness Vector L

i i ! i i i i i

t_

!

i

!

i

i

i

_'r ,_ t ,f

i

_'n __

0!25 0.5 0!75 i II 1!25 11.5

11me from InJectJon [ yr]

,!7, _ ,_.'25 2.5

Figure IV.6.5-11

Behaviour of Sailcraff Speed and Energy

"_ tr_v t ENERGYx 8 "

-_ 2o

15 : "' SPEED

,-, 10 "

e-

,,, 1'.5 1!75 _2 2!25

Time from Injection [ yr ]

_.5

600

500

Y 400

:3

•-' 300. E

iD

E 200

100

0

0

Figure IV.6.5-12

Sail Temperature Evolution

I I I I

m

T < 600

I

0.5

I I I

I 1.5 2 2.5

Time from Injection [ yr]

W-27
< 0

>-

Case id" cy=2.00 g/rn2, r.m.s. 6=20 nm, Degradation=off, perihelion=0.24 AU

Figure IV.6.5-13

Motion Reversal: the October Opportunity

i optimizedimjection date! 2011 10 6 13 14

_ ! i

........... _...................... r T _..............

............... ............. Ii

, P _ r

-2 - 0 1 2

X[AU]

0.5

< 0

N

Figure IV.6.5-14

Motion Reversal" the October Opportunity

i j

.......................................... .:::,:,,.::___.,_._. ..., ,,_._, ..............................................

l

t

f

J

J

l

normal ito ecliptic I_lane

-2 -1 0 1 2

Y[AU]

Figure IV.6.5-15

Evolution of the Solar-Sailing Invariant 6.5

t_ ev

5.5

• Motion

2.5

,....,

0.51.5 i,

t - I I i I I

0.25 o.5 o75 1 ' 1.25 1.5 1!75 '_

-O.5

2!25 _.5

Time from Injection [ yr']

Figure IV.6.5-16

I" f

l:l

;¢

0.9-

0.8

0.7

0.6

0.5

_ 0.4

_ 0.3

i 0.2

0.1

0

--0.1

--0.2

-0.3

0

Optimal Control: the Lightness Vector L

i i ! i i i i i I

i

tfev

r

;_n

I I

Time from Injection [ yr ]

25

r-i

i.

>" 20

_[ 15

" 10o,_, 1

,..,_ 5 , /L

e- i ____.5 0.75 I1 ' 1!2_

w

!

-'5 ,

Figure IV.6.5-17

Behaviour of Sailcra_ Speed and Energy

!

tFev llt_l

ENERGY x 10

SPEED

1'.5 1!75 _ 2!25 i._

Time from Injection [ yr ]

Figure IV.6.5-18

Sail Temperature Evolution

600 5 _ _ _ _

i-.-,s

400

i..

300

E 200

_J

100

T < 600

0 I I I I

0 0.5 I 1.5 2 2.5

Time from Injection [ yr ]

IV-28
Caseid"_=2.00 g/m2,r.m.s.6=20 nrn,Degradation=ON,perihelion=0.24AU

FigureIV.6.5-19

2

I

i ....

1 .......................................... ./:.i:......I.............. _ .... =......

,. . /

0 ......... i ! ...........

•,,, ",x,,,

-1 ...................... ,_ -- "" -

/ J

__, _)n ecliptic pla le

/,

-2 -I 0 I 2

X[AU]

Motion Reversal" the October Opportunity

optimizediinjection date_ 2011 10 05i23 22 53

................. :................................... i............................ i

i 1-.......

J

f

.......... _ .................................................

..... t\

i .....1...............

J _

/i /

i/

!

<

N

0.5

"0.5

Figure IV.6.5-20

Motion Reversal" the October Opportunity

i i i

i j

i l J

.i , r

f i z

t i

i

i

i

J _

,i j normal Io ecliptic I_lane

i

-3 -2 -1 0 1 2

Y[AU]

6.5"

5.5"

4.5-

>" 3.5"

?

2.5"

1.5"

0.5"

--0.5

Figure IV.6.5-21

Evolution of the Solar-Sailing Invariant

t ev

,0.,,5 2!25

Time from Injection [ yr ]

:_.5

! t

1.2

1.1

_ 0.9

_ 0.8 0.7

_ 0.6

0.3

i 0.2

o.t _'0

0

--0.1

_ -ti.2

Figure IV.6.5-22

Optimal Control: the Lightness Vector L

I I I I I f

t_ev

;Lr

I

0.75

,_ _.j

i

!

,, ,!_ ;_ ,.'75 '_

"nine from Injection [ yr ]

25-

>. 20"

L-.

8 ]5,

U3

" lO"

:D

<:

..4 5"

>.

w

Figure IV.6.5-23

Behaviour of Sailcraff Speed and Energy

l !

t_ev tp:

|

i

o_5 o!75 ', ,!25

!

Time from Injection [ yr ]

ENERGY x 10

SPEED

11.5 1!75 _ 2!25 :_.5

Figure IV.6.5-24

N

I I

1 1.5

Time from Injection [ yr ]

I

2.5

IV-29
< 0

L_

>-

6.5"

5.5"

4.5"

>" 3.5"

?

2.5"

1.5"

0.5"

"0.5

25"

_ 20"

<

" IO"

<

5"

c_

e--

LU

Case id: c_=1 80 g/m2, r.m.s. 5=20 nrn, Degradation=off, perihelion=0.20 AU

Figure IV.6.6-1

Motion Reversal: the October Opportunity

optimized t_jection date iO! 11014 l

4613

!

" i

n ecliptic plane

r 1! } '

-1 0 2

X[AU]

0.5

-0.5

Figure IV.6.6-2

Notion Reversal: the October Opportunity

...................................... ............. i ....................

normal to ecliptic plane

-2 -1 0 1 2

Y[AU]

Figure IV.6.6-3

Evolution of the Solar-Sailing Invariant

_ot . tev _"

ion /

,:3575

Time from Injection [ yr ]

Figure IV.6.6-4

Optimal Control: the Lightness Vector L

1 i i i

i

0.8I 0.9I I1 1I.1

Time from Injection [ yr ]

i

i

II.2 1.3

Figure IV.6.6-5

Behaviour of Sailcraft Speed and Energy

!

tdev

0_0!45 d.6

|

|

!

tp_..__ ENERGY x 7

SPEED

_ 1!o5l'o_-1!351.5'

Time from Injection [ yr ]

600

500

v

,...., 400

v

"-' 300

tD

I,,,,,

E 200

¢U

100

Figure IV.6.6-6

Sail Temperature Evolution

I I

I I

0.5 1

Time from Injection [ yr ]

T < 600 K

IV-30
Case id" c=1.80 g/m 2, r.m.s. 8=20 nm, Degradation=ON, perihelion=0.22 AU

Figure IV.6.6-7

Motion Reversal: the October Opportunity

i optimized i _jection date 20 ! 1 10 i0 d, 46 13 2 ................................

1 .................. i......................../_: ....................................../.__::., ,,<,<:. ......................... i...................................................... i

0 i _ L ! i : !

\, \:,\,"........ -7",,i I

i .... "<........... ' .......... " /

i i ii 2 k°,<,o,,,, a

....................................................... ......................... "/-!-............................ i............

"-2 -I 0 I 2

XrAU]

,.__,

N

Figure IV.6.6-8

Motion Reversal: the October Opportunity

1

i

I !

i

, 1 !

0.5 ' i..................... i

i

I

1

-0.5

i

I

i

I

normal

I

-I -3 "2 -I 0

Y[AU]

to ecliptic r lane

1 2

6.5"

5.5"

4.5"

3.5-

?

2.5-

1.5"

0.5"

--0.5

Figure IV.6.6-9

Evolution of the Solar-Sailing Invarlant

tl ev

Direct Motion

n

) 0.15 C[3 0.45 d.6 0.,; d.9 1!05 1'.2

Time from Injection [ yr ]

lJ35

Figure IV.6.6-10

Optimal Control: the Lightness Vector L

!

1.2 - t_ev

1.1

z

I

0.9

(1.7

I 0.6 _'r

0.5

0.4

_ 0.3 "

"I =0.10"10"20 _Cn 'J _*"_

_.-o., _., _.___,

"0"30.6 0.7 0.8 d.9. I1 11.1 11.2

Time from Injection [ yr ]

!

I

L.,.._.

1.3

25"

>. 20"

8 _s.

I,#'l

" 10"

,.._,

::3

5"

,,..,,.,

fUJ

Figure IV.6.6-11

Behaviour of Sailcraft Speed and Energy

i

t_ev

0.45 0.6 0.75 d._

i

tp

ENERGY x 7

SPEED

_!o5 _'.2 1!35 1'.5

Time from Injection [ yr ]

0.8

6b 0.7

t5

"_ 0.6

m

e,l

0 0.5

•_. 0.4

_ 0.3

I-

_ 0.2

E

_ 0.1

_ o

_ "0.1

-0.2

Figure IV.6.6-12

Optical Param Changes ( Solar Wind )

I 1 I I I- I I

F

0 0.2 0.4 0.6 0.8 I 1.2 1.4

Time from Injection[ yr ]

IV-31
2 _--_

Case id" ct=1.28 g/m2, r,m.s. 8=20 nm, Degradation=off, perihelion=0.20 AU

Figure IV.6.8-1

Motion Reversal" the October Opportunity

optimizedililectiondate 011 10 I I 8 53 9

..,

f,..,t"-"" ......

........................... !iiii .............

-2 -1 0 l 2

X[AU]

)n ecliptic plalle

::)

N

Figure IV.6.8-2

MoUon Reversal: the October Opportunity

1

i

............ i......

_£Z:':'............................................

o

Y[AU]

I

norn_al to eclipti I plane

1 2 3

Figure IV.6.8-3

EvoluUon of the Solar-Sailing Invarlant

7" I

6 t_ev

_ se Motion

/

Io 6., e._e.__.4_, _.__., _.=J., '_

J. -1 '

11.1 11.2 1".3 11.4 II.5

Time from InJection [ yr ]

! i

t_v

1

0.8

i 0.2

o- _'n

-0.2-

_ _'t I

-0"40.4 0.45

Figure IV.6.8-4

OpUmal Control: the Lightness Vector L

i ! I

.5 0155 0.6I 0165

Time from InJecUon [ yr ]

_. 2o

]5'

t/)

" 10"

5"

tu

Figure IV.6.8-5

Behaviour of Sailcraft Speed and Energy

, i ENERGY x 4

tr_v

Time from Injection [ yr ]

SPEED

(J.7 d.8 d9 I1

Figure IV.6.8-6

Sail Temperature Evolution

600 i i i i I l

T < 600 K

500

v 400 -

I_

"-' 300 - E

E 200

I--

100 -

0"' I I i I

0 0.2 0.4 0.6 0.8 1

Time from Injection [ yr ]

IV-32
Case id" c=1.28 g/m 2, r.m.s. 6=20 nm, Degradation=ON, perihelion=0.20 AU

Figure IV.6.8-7 Figure IV.6.8-8

Motion Reversal: the October Opportunity

i

I optimized i ijection date _011 10 10 1l 42 20

.................l

_,:.... ...........

/ Ii'/."......i\ \.."\_

--li......

i ..q

........ )n ecliptic plai le

t

-2 -1 0 1 2

X[AU]

0.5

"0.5

Motion Reversal: the October Opportunity

i

1

i

!

J

!

I

!

i

i

i

i

"2 -1 -

i

i

!

i.............

i

!

i

t

i

i

! _ •

i

J norma to eclipticiplane

T , '

o 1 2 3

Y[AU]

Figure IV.6.8-9

Evolution of the Solar-Sailing Invarlant

> d.1 d.2d.3 44:d.s d.6d.7 d.sd.9 '1 1_.1_.21_.3_.4_.s

o

Time from Injection [ yr ] " " "

!

1

z

i 0.8

0.6 _'r

0.4-

_ 0.2-

i0-

-11.2

...... !

"%., o145

!

t_v

Figure IV.6.8-10

OpUn_l Control: the Ughtn_s Vector L

! ! !

,_._ oI_ & oI=

Time from Injection [ yr ]

Figure IV.6.8-11

Behaviour of Sailcraft Speed and Energy

25

,-, ' _ ENERGY x 4

_. tr_v

20 ,: ' SPEED

15 , .

!

,.. lo : :

I I I I I

m I0 • - ," - 10.6, 0.7 0.8 0.9 1

.-5_m

Time from Injection [ yr ]

Figure IV.6.8-12

Optical Param Changes ( Solar Wind )

O.5- F

0.4

0.3

0.2

_ 0.1 _

E o

° t

."-o._ "_

E 6r

-0.2 I I I I I I I I I

0 0.1 0.2 0.3 0.4 0.5 0,6 0.7 0.8 0.9

Time from Injection [ yr ]

IV-33
2

Case id" (_= 1.00 g/rn2, r.m.s. 8=20 nm, Degradation=off, perihelion=0.20 AU

Figure IV.6.9-1 . Figure IV.6.9-2

Motion Reversal: the

optimized illjection date

October Opportunity

i

_011 10 11 g 26 57

t

i .....

1

//*

.................................................................................. .............

! :}n ecliptic plan_ ) i

o 1 2

X[AU]

0

\ .. \,

\

\ x,,,,

-1 ........................................................................ ?._:,

"2

"2 -l

N

Motion Reversal" the October Opportunity

I )

)

I

............................................................ ,..............................

l t

)

i

i I

t

j

........................................................................................... i ............................. !.................................

•

inormal to Jiecliptic plan. i

i )

-!

0.5

-0.5

-3 -2 -I 0 l 2 3

Y[AU]

7"

6"

5"

r-,

L. 4'

_' 3"

2"

I"

Figure iV.6.9-3

Evolution of the Solar-Sailing Invariant

t;v

.o_ : /

/

) O.I ().2 d.3' _.4 0.5 0.6 0.7 0.8 0.9 II

!

Time from Injection [ yr ]

Figure IV.6.9-4

1.2

1.1-

1

z 0.9-

0.8

0.7

0.6-

0.5 _'r 0.4

0.3-

0.2

o.1 _n )

"J I I I

-%35 037 039

Optimal Control: the Lightness Vector L

I I I ! I

t_ev

i

i

!

i

............................................................................................

I

0.41 0!43 0!45 I I 0.47 0.149 0.51

Tlme from Injection [ yr ]

I

0.53 0.55

Figure IV.6.9-5

Behaviour of Sailcraft Speed and Energy

25T , ; .....sPE_D

/ tPev tff'_ ..

,, ERGY x 3

15 , ,

"' .8

| !

-5

Time from Injection [ yr ]

600

500

r---s

,--., 400

i_

300

i,..

Q.

E 200

100

0

0

Figure IV.6.9-6

Sail Temperature Evolution

I I I

T < 600

w

m

I I

I

0.2 0.4 0.6

Time from Injection [ yr ]

0.8

IV-34
Case id" c=1.00 g/rn2, r.rn.s. 6=20 nm, Degradation=ON, perihelion=0.20 AU

Figure iV.6.9-7 Figure IV.6.9-8

i

Motion Reversal: the October Opportunity

optimized i ection date 2_)11 I0 12 I 1 39 37

!

..!.....

.............

..

on ecliptic plme

0.5

2

/

1 /

i /" ....... I-... "_'-\

f , if/ IX,

o.............. \t....... tJ\t\ t,.._/., 1-),/

-1 i

i

I

i

i

f

i !

-2 -1 0

X[AU]

Motion Reversal: the October Opportunity

I

i

t

E

t

-2 -1

.-____ _,-:::,'.,-. .....................

I

normal

i,

o

Y[AU]

toediptlc rllme

1 2

Figure IV.6.9-9

Evolution of the Solar-Sailing Invarlant

i

_M tr_v_/'

orion

_!_ Reverse Motion

I I i i I I I

i 0.1 0.2 0.3 0.4 0.5 0.6 0.7 d. 8

I

I

Time from Injection [ yr ]

CJ.9

1.2

I I.I-lz 0.9-

0.8-

0.7-

0.6-

0.5- 0.4 :'"

0.3-

0.2-

0.1 -

i

-0.1

-0.2 0

I -0.3-

_j -0.4

"0"50:35

_n

Figure IV.6.9-10

t¢ov

w

!

!

!

i

OpUmal Control: the Ughtness Vector L

i i i i i I

I

0!37 0.k39 0!41 0:43 0.45 I 0.47I 0!49 0.$1 0!53

Time from InJection [ yr ]

i

.=

0.55

2,] _. 20

=...,

15"

" 10"

5"

c

m

Figure IV.6.9-11

Behaviour of Sailcrat_ Speed and Energy

SPEED S

t_ev

ENERGY x 3

_'8 0.156 0!64 0!72 d.8

i o

t i

| i

Time from Injection [ yr ]

c_

5 0.5

m

0.4

Q.

o

v 0.3

es

0.2

I0.I

lg

0

-0.1

-0.2

Figure IV.6.9-12

Optical Param Changes ( Solar Wind )

I 1 I ! I' I I

- F "

T/1000

.......... i........ ........ ;;......... ........i.......71

| I I I I I I I /

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Time from Injection [ yr ]

IV-35
IV.7 Summary Table

H

I

O_

Table IV,7-1, ISP H-reversal trajectory opportunity: main features from the optimal profiles discussed in §IV.6, Constraint

violation is marked bold,/ta#cfigures in the rightmost column represent the flight time of the extended mission to 400 AU,

2.20

2.10

2.10

2.20 20 Off

20 ON

20

1.80

1.80

1.28

1.28

1.00

1.00

20

iiii?!_!_ili!iiiiii!iOOii!iii!iii_iiiii!ii!iiiiiiiiiii

off

ON

0.175

0.261

0.204

0.248

Aphelion in

pre-perihelion

arc [AU]

2.130

2.636

1:938

2.118

Time to

Aphelion

[year]

0.931

1.283

0.806

0.922

Time to

H-reversal

[year]

! .492

1.934

..1.__.

1.258

1.393

Time to

Perihelion

"[year]

1.776

2.470

1.543

1.773

Max Sail

Temperature

[K]

530

574

490

584

Speed

at 200 AU

[AU/yr]

14.34

11.02

13.20

12.23

Time to

200 1400AU

[year]

15.698 129. 65

20.565 138. 7]

16.667131.82

18.0961 34.45

i!iiiiiiiiiii!iiiiiii!!i!iii!ii201iii_iii!ili_i!!i!i!!ii_i!i!!!ii

_iii!Siiiiii_:iiii_ili!i,i!iii20iiiiiiiiiiiiiiiiiiiii_

20 off

20

2O

2O

20

20

ON

Off

ON

off

ON

0.20

0.20

0.20

0.20

O.20

1.426

1.470

1.158

1.159

1.099

1.099

0.457

0.485

0.257

0.257

0.201

0.201

0.736

0.769

0.462

0.464

0.390

0.391

0.913

0.967

0.581

0.582

0.496

0.496

487

597

471

578

458

15.79

14.84

20.79

20.79

23.57

23.46

13.565126.23

14.429 12 7. 91

10.201119.82

10.202119.82

8.986 ] 17.47

9.026 117.55
IV.8 Feasibility of ISP fromTrajectory Design Viewpoint

These following considerations complement those made in §W.6.10. As it is well known, Interstellar Pi'obe is

not only a sophisticated scientific mission concept; among the main things, it should prove that it is possible to

travel fast to distant targets with low cost and high reliability. These features generally depend on sailcraft

operations, no other propulsion (apart from lifting off, of course), strong increase of the launch window, higher

number of missions per time unit (e.g. on a quinquennium basis) and so forth. Thus, the existence of an

additional launch opportunity for the ISP mission concept should be of high concern. Previous sections have, no

doubt, shown that there exists such an opportunity for ISP sailcraft, in October of every year. This could be

accomplished by utilizing one of the several peculiarities of space sailing: the fly-by of the Sun via motion

reversal. A spectrum of fourteen optimized mission profiles have been computed by a code that takes into

account a high number of real effects. Distinct trajectories correspond to different key parameters such as the

sailcrafl sail loading, sail roughness and optical sail degradation due to solar wind. (Ultraviolet-photon

degradation was not considered by lack of experimental data appropriate to solar sailing). Solar wind fluence has

been recognized relevant to a sailcraft approaching the Sun closely. In addition, a major item has consisted of

dealing with integro-differential equations for modeling sailcraft motion appropriately. Optical degradation, with

constraints on temperature, perihelion and flight time, has resulted in a key item for designing some fast sailcraft

trajectory to many hundreds of AU. By considering both baseline and extended mission concepts, ISP is

certainly feasible from motion-reversal trajectory viewpoint/f the sailcraft sail loading is lower than 2.1 g/m a.

The current literature value of the ISP-sailcraft sail loading is very close to 2 g/m 2. This is a value sufficiently

lower than the above threshold to allow the following time line (since injection): (1) launching in October, (2)

flying-by the Sun at 0.24 AU after 1.40 years, (3) achieving 200 AU after 16.6, (4) extending the mission to 400

AU by 15.2 years more. (A slightly lower value of the sailcraft sail loading in the range [1.9, 1.95] g/m a is

suggested to deal with small attitude control errors). These ones and the other numerical results, discussed in this

document, should be considered realistic enough due to the many key elements and detailed features included in

the present dynamical model of sailcraft motion.

IV.9 Conclusions and Future ResearCh

The analysis performed so far, and presented in this report, is sufficiently general in some aspects to allow us to

suggest some major lines for future investigation. They may be expressed as follows

A. ISP feasibility: additional aspects are to be investigated and improved, of course; however, it is hard that

the ISP concept may result unfeasible from mission viewpoint. That is enforced by two launch

opportunities per year. By considering how complex and various are solar-sailing trajectories, it would

be interesting to investigate whether there is some other opportunity.

B. Optical sail degradation: there is the need for additional experimental data about solar wind and new data

on UV. Once again, we stress that the evolution of the optical sail parameters is one of the major aspects

of solar sailing. Other potential missions close to the Sun may benefit from such data; for instance, a

solar-sail mission to solar poles, with final orbit achieving 90° in heliographic latitude, should be

investigated with respect to this critical point as well. Furthermore, a future interplanetary sail shuttle

might be limited in lifetime by optical degradation before any other system fails.

C. A sensitivity analysis on the baseline ISP profile is strongly recommended. The optimization process

performed in this work was rather complicated; although not reported here since beyond the present

aims, however it revealed that many decision parameters affect the solar sailcraft flyby very differently.

D. Aluminum-Chromium is appropriate for the ISP of first generation (400 AU). Assessing feasibility for

second-generation ISP (800-1000 AU) with perihelion at 0.15 AU would deserve a dedicated study. New

sail materials, e.g. according to the line open by Matloff (Matloff, 1997-2000), should be investigated for

third-generation ISP that, for instance, may achieve 10 light-days in one human job time, or less.

IV-37
IV.IO References •

Johnson, L., Options for Interstellar Probe, private communication, June 2001

Matloff, G. L. and Mallove, E. F., The Interstellar Solar Sail: Optimization and Further Analysis, Vol. 36, No. 5,

pp. 201-209, 1983

Matloff, G. L., Interstellar Solar Sailing: Consideration of Real and Projected Sail Materials, JBIS, Vol. 37, No.

3, March 1984

Matloff, G. L., Interstellar Solar Sails: Projected Performance of Partially Transmissive Sail Films, paper IAA97-IAA.4.1.04, the 48 thInternational Astronautical Congress, Turin - Italy, 1997

Matloff, G. L., Deep Space Probes, Springer-PraMs, ISBN 1-85233-200-X, 2000

McInnes, C. R., Solar Sailing- Technology, Dynamics and Mission Applications, Springer-Praxis, ISBN 1-

85233-102-X, 1999

Mewaldt, R. A., Liewer, P. C., An Interstellar Probe Mission to the Boundaries of the Heliosphere and Nearby

Interstellar Space, Space 2000, Long Beach (CA), Sept. 19-21, 2000

Liewer, P. C., Mewaldt, R. A., Ayon, J. A., Garner, C., Gavit, S., Wallace, R. A., Interstellar Probe Using a

Solar Sail: Conceptual Design and Technological Challenges, COSPAR Colloquium, The Outer Heliosphere:

the next frontiers, Potsdam, Germany, July 24-28, 2000

Maeeone, C., Sun-Lensing the Cosmic Microwave Background from 763 A U by virtue of NASA's Interstellar

Probe, 3rd IAA Symposium on Realistic Near-Term Advanced Scientific Space Missions, Aosta, Italy, July 3-5, 2000

Genta, G., and Brusa, E., The A URORA Project: a New Sail Layout, Acta Astronautica, 44, No. 2-4, pp. 141-146

(1999)

Stuckey, W. K., Meshishnek, M. J., Solar Ultraviolet and Space Radiation Effects on Inflatable Materials,

Aerospace Report TR-2000 (8565)-9, August 20, 2000

Scaglione, S., and Vulpetti, G., The AURORA Project: Removal of Plastic Substrate to Obtain an All-Metal

Solar Sail, Aeta Astronautica, 44, No. 2-4, 147-150 (1999)

Vulpetti, G., 3D High-Speed Escape Heliocentric Trajectories by All-Metallic-Sail Low-Mass Sailcrafi, 2 "d IAA

Intemational Conference on Low-Cost Planetary Missions (Laurel, Maryland, April 1996) and Acta

Astronautica, Vol. 39, No. 1-4, pp. 161-170, July-August 1996

Vulpetti, G., Sailerafl at High Speed by Orbital Angular Momentum Reversal, Acta Astronautica, Vol. 40, No.

10, pp. 733-758, 1997

Vulpetti, G., General 3D H-Reversal Trajectories for High-Speed Sailcrafi, Acta Astronautica, Vol. 44, No. 1

pp. 67-73, 1999a

Vulpetti, G., The AURORA Project: Estimation of the Optical Sail Parameters, Acta Astronautica, Vol. 44, No.

2-4, pp. 123-132, 1999b

Vulpetti, G., Sailcrafi-Based Mission to The Solar Gravitational Lens, STAIF-2000, Albuquerque, New Mexico,

Jan-30- Feb-3, 2000

Vulpetti, G., Solar Sailing: Symmetry Groups, in progress research, 2001 (unpublished)

Werts, G. E., Edwards, D., Hubbs, W., Space Environmental Effects Testing and Characterization of Candidate

Solar-Sail Material Aluminized Mylar, Test Report, August 2000, Work Request WR-ED 32-243

Wright, J. L., Space Sailing, Gordon and Breach Science Publishers, Amsterdam, 1993

Ziegler, J. F., and Biersack, J. P., SRIM-2000, Ion Beam Interactions with Matter, version 40 (Feb. 2001),

http://www.SRIM.org

IV-38
Chaoter V- A Prototype Ho!oaraphic Me,s,saqe Plaa.ue for !_;P

Members of the International Academy of Astronautics (IAA) Committee on

Space • Society, Culture, and Education suggested to committee membe C Bangs,

that she curate an art show in conjunction with the meeting Missions to the Outer

Solar System and Beyond, 3rd IAA symposium on Reafistic Near-Term Advanced

Scientific Space Missions, in Aosta, Italy on July 3-5 2000, chaired by G iancarlo

Genta of Politechnico di Torino. Through the not-for-profit gallery/alternative-space she

is affiliated with (Art Resource Transfer inc., 210 1l th Avenue, New York, NY 10011,

phone" 212-691-5956), Ms. Bangs posted a "Call for Art."

Approximately 35 artists participated in this show, which was called "Messages

from Earth." The premise was to show what a selection of artists would mount on an

interstellar probe as a message plaque. The work was submitted on 21 X 27.5

centimeter color xeroxes. Copies of these are in the permanent collection of the Aosta

City Hall. Copies of many of these pieces are permanently installed at Marshall

Spaceflight Center in the office of Les Johnson, Space Transportation Directorate.

One of the participants in the Aosta IAA Symposium was Dr.' Robert Forward,

who suggested to Ms. Bangs that holography was a good medium for the art in an

interstellar message plaque. As well as encouraging Ms. Bangs, Dr. Forward

suggested to Les Johnson that some funds should be devoted to this effort.

A monochromatic hologram is produced by the interaction of two mutuallycoherent laser beams. One is the unmodified original or reference beam; The second

is separated from the original beam by an optical beam splitter, passed around the

target object and then recombined with the original beam. The interference pattern of

the two beams is recorded on a photographic plate. If the exposed photographic plate

is then placed within the monochromatic reference beam, a three-dimensional

photograph, or hologram, of the original object, can be viewed (Caulfield, 1979 and

Saxny, 1988).

A rainbow or 'Benton" hologram utilizes the interference of two partiallycoherent polychromatic beams to produce a three dimensional image of an object that

can be viewed in white or polychromatic light. The "master" holgram, produced in

monochromatic light is masked off to a narrow horizontal slit which forms an image

hologram in which the vertical information in the master is replaced by a diffraction

grating. When the image hologram is flipped, the slit image is projected close to the

eye of the viewer. When the image hologram is illuminated with polychromatic light,

the slit's image varies in position as a function of wavelength. The viewer sees a threedimensional image in white light of the original object, in which the spectral hue

depends upon the height of the viewpoint. Variations in the image-exposure process

on the master can result in a polychromatic rainbow hologram.

It is possible to expose many "multiplexed" holographic images on the same

rainbow hologram. Individual images are viewed in white light by altering the angle

between the viewer and the photographic plate.

The hologram prepared by Ms. Bangs has seven independent images. One is

an Apollo 16 photograph of the full Earth that is printed on acetate and serves as a

backdrop to the holographic images. The six holographic images include twoV-1
dimensional and three-dimensional representations. The four two-dimensional

representations include equations of solar-sail acceleration, a representation of ISP

trajectory and Earth's location in the solar system and galaxy and line drawings of two

figures. These figures include an adult human male with his palm raised in greeting

and an adult human female standing for scale near a representation of the ISP

payload. In the spirit of the Pioneer 10/11 message plaque (Sagan, 1975), both

figures incorporate features of an amalgam of the various human races. The two threedimensional images are scuplted and painted representations of a woman and man.

The rainbow hologram was created at the Holocenter • Center for Holographic

Arts (45-10 Court Square, Long Island City, NY 11101 , phone 718-784-5065) during

Spring 2001. Holocenter staff assisting with the preparation of the rainbow hologram

included Sam Moree, Ana Maria Nicholson, and Dan Schweitzer. The dimensions of

the holographic plate are 40 X 50 centimeters. The finished piece was framed by

Simon, Liu Inc. 645 Dean Street, Brooklyn, New Ygrk 11238 (718) 638-7292. in

framing the piece the acetate with the image of the Earth had to be separated from the

actual hologram.

The finished and framed rainbow hologram was delivered to Les Johnson of the

MSFC Space Transportation Directorate during summer 2001. Under normal

illumination, all but one of the images (that being the image of trhe IS P trajectory and

Earth location) can be readily viewed. Photographs of the images on the rainbow

hologram in sunlight were shot in July 2001. Some of these are included as Fig. 5-1.

In his NASA / ASEE Summer 2001 faculty fellowship presentation, the PI

attempted to estimate the information content of holographic interstellar message

plaque. This estimate is partially based upon discussions with Dan Schweitzer of the

Holocenter, who states that at least 30 separate multiplexed images can be exposed

on one holographic plate.

Assume that the active portion of the photographic plate has dimensions 35 x

46 cm. A rainbow hologram can store three-dimensional reduced-size images

Assume that each stored image has dimensions of 2 X 2 cm and is placed on one face

of a three-dimesional cube. Each multiplexed image stored on the holographic plate

can include more than 250 cubes or more than 1000 reduced-size images. Since 30

separate multiplexed images can be included on one rainbow hologram, more than

30,000 separate reduced-size images can be included on one 35 x 46 cm rainbow

hologram. A rainbow hologram's minimum thickness is in the micron range. John

Caulfieid of Fisk University suspects that a state-of-the-art holographic message

plaque could accomodate as many as 300,000 reduced-size images.

Chaoter 5 References

H. J. Caulfieid ed., Handbook of Optical Holography, Academic, NY (1979).

C. Sagan, The Cosmic Connection, Dell, NY (1975).

G. Saxby, Practical Holography, Prentice-Hall, NY (1988).

V-2
Fig. 5-1. Photographs of Some Images on Prototype Holographic Message Plaque.
Fig, 5-1. Photographs of Some Images on Prototype Holographic Message Plaque.
E

III

I_

I:I OO

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(D

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or)

(D

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o.-

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rr

T--
Table V1.1-1 MSFC Space Environment. Team test Plan for Commercial

White-Light Holograms

Test Plan for Hologram Testing

1. Select 8 candidate materials

2. Identify samples to be exposed and set-aside control sheets of identical material

3. Cut samples to be exposed into squares 1.25 inch on a side

4. Perform thermo-optical measurements (alpha, emissivity, transmission)

5. Bakeout samples at 100 C for 48 hours under high vacuum

6. Perform thermo-optical measurements on baked-out samples

7. Take photographs of baked-out samples side-by-side with control samples

8. Mount 4 samples in exposure system

9. Expose samples to l_t radiation dose and UV.

10. Remove samples and perform thermo-optical measurements

11. Take phot%m'aphs of exposed samples side-by-side with control samples

12. Place remaining 4 samples in exposure chamber

13. Expose samples to 1st radiation dose and UV

14. Remove samples and perform thermo-optical measurements

15. Take photographs of exposed samples side-by-side with control samples

16. Place 4 new samples in exposure chamber

17. Expose to 2 _a radiation dose and UW

18. Remove samples and perform thermo-opticaI measurements

19. Take photographs of exposed samples side-by side with control samples

20. Place remaining 4 samples in exposure chamber

2 I. Expose to 2 _d radia_tion dose and LW

22. Remove samples and perform thermo-optical measurements

23. Take photographs of exposed samples side-by-side with control samples

24. Place 4 new samples in exposure chamber

25. Expose to 3 _ radiation dose and UW

26. Remove samples and perform thermo-optical measurements

27. Take photographs of exposed samples side-by-side with control samples

28. Place remaining 4 samples into exposure chamber

29. Expose to 3_ radiation dose and UV.

30. Remove samples and perform thermo-opticaI measurements

3 I. Take' photogaphs of exposed samples side-by side with control samples

32. Select best 4 samples t?_pes

33. Place 4 samples in test chamber and expose to bW for____hours at__ UV suns

34. Perform thermo-optical measurements

35. Take photogaphs
Vl.2 Radiation Test Quantifiable Ooti.c.al Results

After sample selection, preparation, and irradiation, a number of optical tests

were performed by Ryan Haggerty and the Space Environments team to quantify

radiation resistance of the samples selected. Control and irradiated samples were

tested for changes in fractional absorption to simulated solar electromagnetic (EM)

radiation (o_)and emittanCe (_ = emittd / absorbed solar EM).

Results are summarized in Table V1.2-1 and are described in greater detail in

Haggerty's forthcoming paper at STAIF-2001. Simulated solar-wind radiation between

10 and 100 Mrad has little or. no effect on-the fractional solar EM absorption and

emittance of the commercial white-light hologram samples tested.
m

mco

=,ul mm

14..

,.-E

oE

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:=¢J 0

0

13 II) m 0

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Vl.3 Effects of Space Radiation on Holoarams--Literature Search _

On June 13 and 14, 2001, C Bangs and G. Matloff followed the advice of H. J.

Caulfield of Fisk University and performed a literature search at the NASA Marshall

Spaceflight Center and Redstone Scientific and Technical Information Center (RSTIC),

both in Huntsville Alabama. the purpose of this search was to locate previous

references in the open literature that relate to the survival of holograms in the space

environment.

Three significant English-language studies were discovered. These include a

1988 paper in Optics Letters by J. P. Golden, G. P. Summers, and W. H. Carter, all of

the US Naval research Laboratory; a 1989 SPIE paper by A. McKay and J. White of

National Technical Systems, Inc., in Los Angeles, CA; and a 1993 report to the USAF

Rome Laboratory, Air Force Material Command, Griffiss Air Force Base, New York. The

Rome report was co-authored by S. P. Hotaling of Rome and G. Manivannan, R.

Changkakoti and R. A. Lessard, who were all affiliated with Laval University, in

Quebec, Canada.

Golden et al (1988) reported that holograms made in Polaroid DMP128

photopolymer can withstand a total dose of 2 Mrad of 63-MeV protons and 2-Mrad of

6OCo gamma rays without loss of diffraction efficiency. Diffraction efficiency was

defined by plotting incident-intensity fraction vs. diffraction angle in degrees from

normal before and after exposure. Separate exposures to protons and gamma rays

resulted in minimal degradation. Since a LEO satellite receives an electron /proton

dose in the neighborhood of 1 Mrad per year, this material seems to be sufficiently

hard for space holographic applications.

McKay and White (1989) exposed dichromated gelatin holograms to a

simulated space environment including UV (ultraviolet) radiation, particle radiation

and vacuum effects. The vacuum corresponded to a 500-km altitude. In the vacuum

tests, a significant issue was the level of outgassing from holographic coatings.

Outgassing, which was ascertained by comparing sample weight before and after

exposure to vacuum conditions, amounted to only a few percdent of sample weight.

Most outgassing occurred during the first 24 hours of exposure and is probably do to

water vapor. Charged-particle exposure utilized 4 MeV protons at fluences simulating

the effects of 0.5-5 years exposure in the space environment, prior to exposure, testsample optical density varied 4.0-4.5. Exposure to 5 years of simulated space

charged-particle radiation resulted in a mean optical density loss of 1.6 and a mean

loss of 0.15. this was probably do to breaking of covalent bonds and resulting changes

in density and refractive index. The spectral peaks of the samples moved slightly

towards the blue by about 9 nm, from a pre-exposure spectral peak of 540-550 nm.

Ultraviolet effects were tested for 1104 simulated days of exposure to exoatmospheric sunlight. The peak wavelength decreased once agin by 6-20 nm for all

samples tested, for most samples tested, UV did not significantly effect optical density.

Hotaling et ai (1993) considered the survivability of dichromated (vinyl alcohol)

holograms in the space environment. Diffraction eficiency was used as the

degradation criterion and holographic thin-films were exposed to combinations of

ionizing radiation, temperature, and atomic oxygen simulating the LEO environment. A

VI-5
cobalt-60 gamma-ray source was varied to produce 0, 2.5, and 10 Mrads. Once again,

the combined effects resulted in no significant degradation to the optical performance

of the sample holograms.

The previous studies discussed in the last section utilize diffraction efficiency as

the operational parameter in considering radiation effects on holograms. Such an

approach requires monochromatic light sources of various wavelengths to be directed

upon the interference pattern that constitutes the hologram. The transmitted (or

reflected) light acts as though it has interacted with a diffraction grating. Difraction

efficiency considers the relative amount of output light from the hologram in the 0th,

1st, or 2nd order of the diffraction pattern from control and irradiated sample

holograms.

None of the studies cited in the previous section considers the replicability and

repeatability of the experimental results. This is not surprising, since diffraction

efficiency, by its very nature, has many possibilities for error, the small changes in the

performance of irradiated holograms in some of the cited studies should therefore not

be taken too seriously.

We therefore desired to develop a method of irradiated-hologram evaluation

that would be less susceptible to experimental error and would have replicability that

could be determined by experiment. The following procedure was proposed by the PI,

after discussions with C Bangs and two Brooklyn, NY based artists who assisted with

preparation of the prototype holographic message plaque described in Chapter V--

David Wister Lamb and Lajos Szobozlai. After discussions, the procedure was

approved and implemented by Dr. David Edwards, team leader of the MSFC Space

Environments Team.

After baking and irradiation, control and irradiated hologram samples were

transferred (care being taken to avoid contact with human hands and other impurities)

to the tray of a scanner connected to a PC (Personal Computer). The computer was

equipped with Adobe PhotoshopTM, a software package designed for commercial and

artistic image processing application.

After images of the hologram samples were scanned into Photoshop, the Image

Histogram utility of the software package was activated. This allows the utility to

ascertain image quality in three primary colors, R (red), B(blue), abd G (green). Image

quality in a selected color is quantified by the relative number of image pixels in that

color. Because of the relative nature of the histogram output, it was decided to define

image quality (iq) in the three primary colors as follows :

R B G

, B;-- G= ,,

q R+ B+ G ' q R+B+G ' 'q R+B+G (6-1)

where R, B, and G here refer to the histogram pixel counts in the various colors.

VI-6
lnconsidering experimental repeatability, consideration revealed that there are

two readily identifiabie sources of error. Because of variations in electrical line power

in the MSFC Space Environments facility, scanned-image histogram data might be

slightly different from one experimental run to the next. Also, different portions of the

scanner surface might have different spectral sensitivity.

Vl.5 Effects_ofS__Sp_.__e_R_adiation..onHolograms,- Expe...riments..and Repeatability

Holographic samples were prepared for scanning by Ryan Haggerty and the

MSFC Space Environments team in late June 2001. in early July, the samples were

scanned by C Bangs; results were evaluated by the C Bangs and the PI using the

Photoshop software package. Figure 6-1 presents printouts of the scanned images of

control and irradiated holograms

Fig. 6-1. Scanned images of Some Control and Irradiated Commercial Holograms

Variety .Control

Hyperplaid

_1_00Mr.a.d Expo_sure

Rain

!

_i iI

:(ill!

i ii ,!

Ripple

Sparkle

. _,_,_'z,. ,_

, _ . . , _' _- -

•, _ _ -, ._ .. _ ,,

' __ ___ :M, N

VI-7
The indentations on the upper left of some of the samples in Fig. 6-1 were for

alignment purposes. The eye is not sensitive enough to discern differences between

the control and irradiated commercial hologram samples in this figure.

• After printing out the scans presented in Fig. 6-1, these scans were evaluated

using the formalism presented in Section Vl.4 of this chapter. Results are presnted as

fig. 6-2, where U - unbaked, C = control, 1 - 10 Mrad exposure, 2 - 50 Mrad exposure

and 3 = 100 mrad exposure.

Fig. 6-2. Holographic Sample Color-Quality Variation with Irradiation

Hyperplaid

Rain

Ripple

R / (R+B+G)-___ O

G / (R+B+G_

B / (R+B+G)-- _,-_

sparkle

U C 1 2 3

Sample Status (U=unbaked,C = control ;1,2,3= 10, 50,100 Mrad))

V/-8
Color-quality variations with irradiation are almost always less than about 7%

for the samples tested Before considering the significance of the small variations in

this quantity presented in Fig. 6-2 by repaeatability investigations, we also prepared

plots of mean luminosity vs. irradiation. Mean luminosity is essentially the sum of R, B,

and G pixeis listed in the Photoshop TM histogram. Luminosity increased with baking

for Rain and Hyperplaid, and decreased with baking for Ripple and Sparkle. In all

cases, small amount of electron irradiation increased luminosity. For Ripple, higher

dosages had little effect on mean luminosity. Luminosity decreased with increasing

irradiation for the other three samples.

We next evaluated the repeatability of this experimental procedure. This was

done in two ways. First, a holographic sample was placed in a fixed location on the

scanner. Power to the equipment was turned on, the sample was scanned and

histogram results recorded. Power was then turned off and the procedure was

repeated without moving the sample. In the Second repeatability test, power was to

the PC and scanner were left on and the sample was repeatedly scanned at different

portions of the scanner surface. Results are summarized in Table Vi.5-1.

Table VI.5-1. Scanned Hologram Repeatability Tests.

.Test1 • Power off/on. Hologram variety' Rain. Samole Iocatbn • mid-.ce,n,ter of scanner,_

Trial Sample Mean Luminosity Mean Red(R) Mean Green (G) Mean Blue (B)

1 Rain C 185.54 210.10 173.81 181.37

2 (control) 196.38 217.49 190.21 171.95

3 197,82 218.14 191.94 173.98

1 Rain 2 182.87 202.64 173.66 178.32

2 (50 Mrad) 197.82 218.14 191.94 173.98

Test 2 Power on. Holoaram sample • Rain control (C): various scanner locations

Scanner Location Mea.n Luminosity Mean Red(R) Mean Green,(.(3.) Mean Blue (B)

mid-center 196.38 217,49 190.21 171.95

top-right 174.22 196.03 163.80 170.65

bottom-right 194.92 219.98 185.64 176.42

mid-left 212.84 224.23 210.13 195.82

bottom-left 221.22 231.61 220.49 196.80

top-left 174.22 196.03 163.80 170.65

mid-right 214.49 224.98 213.80 189.51

top-tight 174.22 196.03 163.80 170.65

V/-9
Power on-off tests (Test 1 in Table VI.5-1 results in maximum experimental

errors in the vicinity of 7% in R, B, and G pixel counts. Variations in sample location on

the scanner results in R. B. and G experimental errore of about the same magnitude.

Care. was taken in the performing the operational scans that resulted in Fig. 6-2

to keep the experimental sample as close to the center of the scanner as possible.

Even so, the maximum precision of the data obtained using this technique is about

7%.

Therefore, the small variations in hologram color quality with irradiation

presented in Fig. 6-2 must be considered to be insignificant. Our results are therefore

in agreement with those of the cited studies from the literature. Simulated solar-wind

irradiation, at least up to 10o Mrads, has little or no effect upon the quality of a

commercial white-light hologram. We may reasonably expect that space-qualified

holograms will do well even under much higher levels of irradiation.

VI.6 Effects of Space Radiation on Holoarams-- Photoqraphic Tests

_ _

A final investigation of simulated solar-wind radiation effects on commercial

white light holograms was performed by NASA / MSFC photographer Emmett Given.

Control and 100 MRad samples of the holographic varieties tested were

photographed side-by-side using a high resolution camera and direct, overhead

lighting, the results are presented as Fig. 6-3.

The photographer reported to us that control, and irradiated samples are

essentially identical. The small differences between control and irradiated samples in

the photographs are due to positioning of camera and lights.

Cha#ter 6 References

J. P. Golden, G. P. Summers, and W. H. Carter, "Resistance of Holograms made in

Polaroid DMP128 Photopolymer to Ionizing Radiation Damage," Optics Letters, 13,

949-951 (1988).

A. McKay and J. White, "Effects of Simulated Space Environments on Dichromated

Gelatin Holograms," SPIE, 1044, 269-276 (1989).

S, P. Hotaling, G. Manivannan, R. Changkakoti and R. A. Lessard, "The Performanceand Survivability of Dichromated Poly (Vinyl Alcohol) Holograms for Space-Based

Photonic Applications, RL-TR-93-131, Rome Laboratory, Griffiss Air Force Base, Rome,

NY (July 1993).

VI-I O
Fig. 6.3b Photographs of Control (Top) and l O0-Mrad Irradiated "Rain"

W-12

,%.

.o°

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Fig. 8.3d Photographs of Control (Top) and !O0-Mrad irradiated"Sparkle"

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BIBLIOGRAPHY

A. Bond and A. R. Martin, "World Ships -- An Assessment of the Engineering

Feasibility," JBIS, 37, .254-266 (1984).

H. J. Cauifield ed., Handbook of Optical Holography, Academic, NY (1979).

F. Dyson, "Interstellar Transport," Physics Today, 21, No. 10, 41-45 (October, 1968).

R. L. Forward, "Solar Photon Thruster," J. Spacecraft, 27, 411-416 (1990).

G. Genta and E. Brusca, The Aurora Project" A New Sail Layout • Acta Astronautica,

44, 141 146 (1999).

R. Haggerty and T. Stanaland, "Application of Holographic Film in Solar Sails," to be

delivered, STAIF-2002, Albuquerque, NM 9Feb. 3-7, 2002).

J. Heidmann and C. Maccone, "ASTROsaii and SETlsail • Two Extrasolar System

Missions to the Sun's Gravitational Focus," Acta Astronautica, 37, 409-410 (1994).

L. D. Jaffe, C. Ivie, J. C. Lewis, R. Lipes, H. N. Norton, J. W. Sterns, L. D. Stimpson, and

P. Weissman, "An interstellar Precursor Mission," JBIS, 33, 3-26 (1980).

L. Johnson, "Options for Interstellar Probe," private communication, June, 2001

L. Johnson and S. Leifer, "Propulsion Options for Interstellar Exploration," AIAA-2000-

3334.

P. C. Liewer, R. A. Mewaldt, J. A. Ayon, C. Garner, S. Gavitt, and R. A. Wallace,

"interstellar,Probe using a Solar Sail: Conceptual Design and Technological

Challenges, presented at COSPAR Colloquium, The Outer Heliosphere : The Next

Frontier, Potsdam, Germany, July 24-28, 2000.

C. Maccone, "Sun-Lensing the Cosmic Microwave Background from 763 AU by Virtue

of NASA's Interstellar Probe," in Missions to the Outer Solar System and Beyond :

Third IAA Symposium on Realistic Near-Term Advanced Scientific Space Missions,

Aosta, Italy, July 3-5, 2000, ed. G. Genta, Levrotto & Bella, Torino, Italy (2000).

E. Mallove and G. L. Matloff, The Starflight Handbook, Wiley, NY (1989).

A. R. Martin, ed., "Project Daedalus "The Final Report on the BIS Starship Study,"

supplement to JBtS (1978).

A. R. Martin, "World Ships--Concept, Cause, Cost, construction, and Colonization,"

JBIS, 37, 243-253 (1984).

B-1
G. L. Matioff, "Interstellar Solar Sails "Consideration of Real and Projected Sail

Materials," JBIS, 37, 135-141 (1984).

G. L. Matloff, "interstellar Solar Sails • Projected Performance of Partially Transmissive

Sail Films," IAA-97-1AA.4.1.04

G. L. Matioff, Deep-Space Probes, Springer-Praxis, Chichester, UK (2000).

G. L. Matloff and K. Parks, "Hyperthin and Perforated Solar Sails in Low Earth Orbit

(LEO) ' A Step to the Moon, Mars, and Beyond.," AIAA-89-2442

G. L. Matloff and E. Mallove, "Solar Sail Starships "the Clipper Ships of the Galaxy,"

JBIS, 34, 371-380 (1981 ).

G. L. Matloff and E. Mallove, "The Interstellar Solar Sail • Optimization and Further

Analysis," JBIS, 36, 201-209 (1983).

C. R. Mclnnes, Solar Sailing -- Technology, Dynamics, and Mission Applications,

Springer-Praxis, Chichester, UK (1999).

R. A. Mewaldt and P. C. Liewer, "An Interstellar Probe Mission to the Boundaries of the

Heliosphere and Nearby Interstellar Space, presented at Space 2000, Sept. 19-21,

2000, Long Beach, CA.

C. Sagan, The Cosmic Connection, Dell, NY (1975).

G. Saxby, Practical Holography, Prentice-Hall, NY (1988).

S. Scaglione and G. Vulpetti, "The AURORA Project • Removal of Plastic substrate to

Obtain an All-Metal Solar Sail," Acta Astronautic& 44, 147-150 (1999).

W K. Stuckey and M. J. Meshishnek, "Solar Ultraviolet and Space Radiation Effects

on Inflatable Material," Aerospace Report TR-2000 (8565)-9, August 20, 2000. ..

G. Vulpetti, "The Aurora Project" Flight Design of a Technology Demonstration

Mission," in Missions to the Outer Solar System and Beyond, 1st IAA Symposium on

Realistic, Near-Term Scientific Space Missions, ed. G. Genta, Levrotto & Bella, Turin,

Italy (1996), pp 1 -16.

G. Vulpeti, "3D High-Speed Escape Heliocentric Trajectories by All-Metal Sail, LowMass Sailcraft," Acta Astronautic& 39, 161-170 (1996).
G. Vuipetti, "Saiicraft at High Speed by Orbital Angular Momentum Reversal," Acta

Astronautica, 40, 733-758 (1997).

G. Vulpetti, "General 3D H-Reversal Trajectories for High-Speed Sailcraft, Acta

Astronautica, 44, 67-73 (1999).

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Astronautica, 44, 123-132 (1999).

G. Vulpetti, "Sailcraft-Based Mission to the Solar Gravitational Lens," STAIF-2000,

Albuquerque, NM, Jan. 30-Feb. 3, 2000.

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Test Report, Work Request WR-ED 32-243, .August 2000.

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version 40 (Feb. 2001) http//www. SRIM.org

SA,I LS

The following pages present use of the solar photon thruster (a multi-sail solar

sail that can redirect the reflected photon vector) with holographic optical elements to

allow solar-sail operation between low Earth orbit (LEO) abd higher drag-free orbits.

the color graphic was prepared for the P! by NASA / MSFC artist Bruce Shelton, senior

media developer with Computer Sciences Corporation, in consultation with C Bangs.

• A number of presentations at NASA / MSFC and NSSTC during the summer of

2001 featured the following pages. The audiences included Randy Baggett, Helen

Cole, John Cole, Les Johnson and Jonathan Jones of NASA / MSFC and John

Caulfieid of Fiske University.

Jonathan jones pointed out a dynamical issue with the solar-photon thruster as

configured here, utilized in the high-atmospheric-drag environment of LEO, about 500

km above Earth's surface. Namely, the reflected photon radiation-pressure and

atmospheric-drag vectors do not operate along the same line. this would result in a

torque.

One way of correcting this problem would be to incorporate additional reflectors

such that the photon exhaust is co-planar with the sail. This would introduce additional

complexity and slightly degrade projected performance.

Figure AP-1 presents another possibility, as suggested by John Caulfieid.

Holographic images of corner-cube reflectors could be incorporated in a holographic

main sail. These could, in principle, rotate the photon stream by 90 degrees within the

main sail, removing the necessity for additional thruster elecments.

Figure AP-1 was prepared by the Pi. With the exception of the color graphic, all

other Appendix figures were created by C Bangs or with the assistance of C Bangs

AP-1
APm_2
The Holographic Solar-Photon Thruster

Dr. Greg Matloff, summer 2001 MSFC /ASEE Faculty Fellow

Original solar-photon thruster idea was proposed by Forward (see Ref. 1)

Rainbow Holograms are white-light transmission holograms.

This means that the reconstruction beam is on sideof plate opposite viewer.

Holographic images can be very reflective, highly radiation resistant, and of micron

thickness

Many holographic images can be stored on a single plate. This means that an

angular shift of a few degrees relative to the light source can dramatically alter

optical properties.

SPACE APPLICATIONS :

1. Attitude Control: steering vanes affected by solar radiation pressure that change

re flectivity when slightly rotated

Example • absorptive hologram changes to reflective after a 5 degree rotation.

Photons off reflective vane transfer as much as 2X momentum than those off

absorptive vane.

2. Primary propulsion" sail can be used to implement Trailblazer mission

(effectively unfurl rapidly near Sun) or for LEO--GEO orbit raising if

configured as a solar-photon-thruster (SPT). In LEO (about 500 km), a primary

parabolic reflector focuses light on a much smaller thruster element, which

allows for a tangential thrust component. The thruster element would be

holographic, so that a small rotation could change refelection to transmission. As

well as curvature, holographic Fresnel Lenses could be used to focus light on

thruster element. To reduce atmospheric drag, main sail would be normal to

direction to earth center. Top of main sail would be emissive, bottom reflective

to visual and IR. This reduces direct solar back pressure and increases

acceleration by reflected Earthlight and reradiat ed solar energy absorbed by

the Earth

AP-3
HOLOGRAPHIC SOLAR PHOTON THRUSTER :

(Alternative Configuration)

Near Parabolic

Main Sail

Cable

Cable

Tangential Reflected Sunlight

|

Holographic Thruster

(alter from reflective

to transmissive by

changing angle)

L

,_ ..........

i Ill II II I _ _ _ll I _

Payload

AP-4

Sunlight

(or reflected Earthlight

radiated Earth IR)
Direct insolation

(zenith Sun)

i/

_>

Reflected by La

Thruster

\

\

\

Dark emissive layer on main sail top

Reflective

holographic thruster

reflected &

reradiated

Earthlight

I

I

I

Payloadi !

transmitted

//'

Spacecraft velocity and tangential

acceleration

Transmissive holographic

Thruster

Reflective (lower)

Main sail layer &

holographic Fresnel

lenses

_ololzraphic Solar-Photon Thruster

i i i i
SPT Operation Between LEO and GEO" A Comm-Sat Tug"

THREE ORBITAL POSITIONS, Three photon streams (P)

PI = S = direct solar insolation (solar constant) = 1368 watt/m 2

P2 - A_S - Earth-reflected sunlight, A. = Earth albedo

P3 = (1-A.) S = solar radiation absorbed by Earth and later reradiated as IR

K_ - reflectivity of emissive, upper main sail to direct solar insolation

K2 - reflectivity of lower reflectivemain sail to P2

Ka = reflectivity of lower reflective main sail to P3

RF - radial force on main sail

TF - tangential force on thruster (90% reflective, 45 degree angle)

c = speed of fight, A_ = area of main sail

Position I • Zenith Sun

Turn thruster off

to reduce downward

radial force

Position 2" Nadir Sun Position 3/4" Dawn/Dusk Sun

mm m mn mm mmmmm mmm m mm m mm m mmmm mlml mm m m mm

mmmmm

No direct sunlight

since it' s night

Turn thruster off

to reduce net

downward radial

force on thruster

(0.7RF)

No direct sunlight on

main sail

Dawn direct Sun on

thruster cancels dusk

direct Sun on thruster

RF= [-(I+K0 +

Ae (l+K2) +

(1-A_) (I+K3)]SAJc

RF _

_I-A_) (I+K3)_SAJc

RF = [A_/2 (1+K2) +

(l-A0 (I+K3)]SAJc

AP-6
SPT Operation Between LEO and GEO : A Comm-Sat Tug :

THREE ORBITAL POSITIONS, Three photon streams (P)

P_ = S = direct solar insolation (solar constant)= 1368 watt/m 2

P2 - A,S -- Earth-reflected smdight, A, - Earth albedo

P3= (1-A_) S = solar radiation absorbed by Earth and later reradiated as IR

Kx - reflectivity of elmssive, upper mare sail to direct mlar insolation

K2 - reflectivity of lower reflectivemain sail to P2

K3 - reflectivity of lower reflective main sail to P3

RF = radial force on main sail

TF -tangential force on thruster (90% reflective, 45 degree angle)

c - speed of light, A, - area of main sail

i

i

Position 1 : Zenith Sun

-- | nl nil n om,,-| m| | | | | |nil ul,. m |.. | | nil | | | i |!

Turn thruster off

to reduce downward

radial force

Position 2 : Nadir Sun Position 3 /4: Dawn/DuskSun

No direct sunlight

since it's night

Turn thruster off

to reduce net

downward radial

force on thruster

(0.7RF)

No direct sunlight on

main sail

Dawn direct Sun on

thruster cancels dusk

direct Sun on thruster

RF= [-(I+K1) +

Ae (l+K2) +

(1-A_) (I+K3)]SAJc

RF _

[ (1-A_) ( I+K3)]SAJc

RF ffi [A_/2 (l+K2) +

(1-A_) (I+K3)]SAJc

AP-7
ESTIMATING RADIAL FORC E, let K_=0.5, K2=K3=0.9, A_ - 0.4, 1-A_-0.6

Radial Force (RF) on thruster = - 0.7 Radial Force on main sail from reflected and

reradiated Eartl_ght, for 45 degree angle

(Actualy slightly smaller if thruster is 90% reflective)

POSITION 1: RF_ - [SAJc] [-1.5 + 0.4 (1.9) + 0.6 (1.9) - 0.4 SAs/c {ZENITH SUN}

If thruster is on, net radial force on _e = -0.7 SAJe

POSITION 2 : RF2 = 0.6 (1.9) SAJc = 1.14 SAJc. If thruster is on, RF_2 = 0.3 SAJc

POSITION 3/4 : RFnet,3 - 0.3 [0.2 (1.9) +0.6(1.9)] - 0.5 SAJe

If thruster is off in POSITIONS 1 and 2, average RF for an orbit is about 0.43 SAJc

If tlm_ter is always on, average RF for an orbit is about 0.17 SAJ¢.

TANGENTIAL FORCE = cos(degrees) X average radial force from P2 & P3.

Average tangential force per orbit-average for positions 1,2,3,4

Average tangential force per orbit is about SAJc

Average Tangential Acceleration is about SAJ( M_ c), where M_ is spacecraft

mass.

_l'hree Possible SPT Configurations-all with sail mass = 1/3 s/c mass, s/c areal mass

thickness - 6 grams per square meter

CASE 1 : DEMO flight---10 kg payload, 5 kg, sail-radius = 16 m

CASE 2 : Micro_t - 500 _ payload mass, 250 kg sail mass, sail radius - 115 m

CASE 3 : Large Com Sat 10000 kg payload, 5000 kg sail mass, sail radius = 515 m

If Fresnel Lenses are not used, we require a parabolic main sail--

Focal length - 0.5 (radius of curvature).

ATMOSPHERIC DRAG ESTIMATE IN LEO

Assume 500-m sail diameter. Use spherical approximation for sail shape. Assume 2

km sail-thruster distance.

0/2 = 0.25/2=0.125 radians = about 7.2 degrees

cos (0/2) = x/2000, x = 1984 m, h = 16 m

cross-sectional area (A_r) seen by Earth's

atmosphere is approximately 0.5 (16) (500) or

4000 m 2 .

AP-8
From Ref. 2, LEO atmospheric-drag deceleration is -0.5 Cd Acr OVs2 /M_/_,

where p is atmospheric density, Ca is drag coefficient (2---2.3) and V_ is

spacecraft orbital velocity. We assume a 500-km minimum SPT operational orbital

height, the maximum Shuttle orbit. At 500 l_, is about 10 "_2l_m 2 (From Ref. 1

and TRW Space Data. Drag deceleration is about 10 -4 m/sec 2, since s/c orbital

velocity is about 8 l_/sec. Asstmdn_ a 3,500 k_ spacecraft mass, drag deceleration is

about 1/3 orbitally-averaged tangential acceleration.

Spacecraft requires about 200 days to go from LEO orbital velocity to Earth-escape

velocity. This is an overestimate because at orbital heights greater than 1000 km or

so, atmospheric drag becomes minimal. Sail can be rotated to use direct insolation

for acceleration at these heights.

.THERMAL LIMITATIONS ON THRUSTER SIZE

From Chap. 2 of Ref. 3, solar power per unit area absorbed by the thruster is

S (A_ l Ath ) .{1-Rth}, where S is the solar constant, A_ is sail area, Ath is thruster area,

and Rth is thruster reflectivity. Remembering that solar flux absorbed by the sail is

absorbed by one sail tace but emRted by two and applying blackbody theory, the

thruster blackbody temperature can be expressed:

Tth = {[S/(2o)] (As/Ata ) {1-Rta}]} °'2s degrees Kelvin

Where o is the Stefan-Boltzmann Constant = 5.67 X 10 .8 watt/m2-K 4

If the sail/thruster area ratio is 10, 100, 1000, 10000, and 100000, the maximum

thruster blackbody temperature is respectively 330, 588, 1045, 1860, and 3307

degrees Kelvin..For an aluminum thruster, maximum sail/thruster area is about

100. For an advanced thruster made out of 3000 degree Kelvin material, maximum

sail/thruster area is about 100,000.

REFERENCES

1. R.L. Forward, "Solar Photon Thruster," J. Spacecraft, 27, 411-416 (1990).

2. G.L. Matloff and K. Parks, "Hypertl_n and Perforated Solar Sails in Low Earth

Orbit (LEO) • A Step to the Moon, Mars, and Beyond," AIAA-89-2442.

3. G.L. Matloff, Deep-Space Probes, Springer-Praxis, Cldchester, UK (2000).

AP- 9
A POSSIBLE SPT ORIENTATION, for ORBITAL HEIGHT > 1000 KM

Above orbital heights 1000 km, SPT atmospheric drag becomes minimal. One way

to accelerate the spacecraft tangentially is to turn off the thruster and rotate main

sail so that the reflective side is always normal to the Sun, for every orbital

"afternoon", as shown. Since the spacecraft spends half its time in daylight and

positive-energy tangential solar radiation pressure acceleration is possible for half of

every daylight pass, the tangential acceleration averaged over every orbit is

approximately

(l+K2) S A_/(4 c M _),

or about 2.17 X 10 _ A_/M _ meters per second squared. If the thruster is

actvated for part of the orbit, the average acceleration will be increased. For

heights not much greater than a few thousand kilometers, reflected and reradiated

Earthshine will provide some additional positive tangential acceleration possibilities

for the SPT.

Sunlight

AP-10
Fig. AP-1. Use of a Holographic Main Sail to Redirect Photon Radiation-Pressure Vector

Main sail (about 1-micron thick)

ca

payload

Incident light

J_

output light (redirected by

holographic images of

corner-cube reflectors in

main-sail)

f

f

Earth

-..,,

.-,&£-11
_oorm Approved

REPORT DOCUMENTATION PAGE I OMB No. 0704-0188

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1. AGENCY USE ONLY (Leave Blank) ! 2. REPORT DATE

• I June 2002

4. I-iiLE AND SUBTITLE

The Interstellar Probe (ISP)" Pre-Perihelion

Trajectories and Application of Holography

3. REPORT Contractor TYPE AND DATESReport COVERED (Final)

5. FUNDING NUMBERS

6. AUTHORS

G.L. Matloff,* G. Vulpetti,** C. Bangs,*** and R. Haggerty*

7. PERFORMING ORGANIZATION NAMES(S) AND ADDRESS(ES)

Pace University

l Pace Plaza

New York, New York 10038

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

George C. Marshall Space Right Center

Marshall Space Flight Center, AL 35812

H-29712D

8. PERFORMING ORGANIZATION

REPORT NUMBER

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA/CR-- 2002-211730

11. SUPPLEMENTARYNOTES

Prepared for Space Transportation Directorate

*Pace University, **Telespazio Company, ***Art Resource Transfer, Inc.

Technical Monitor: L. Johnson

12a. DISTHIBUTION/AVAILABILIIY STATEMENT

Unclassified-Unlimited

Subject Category 16

Standard Distribution

12b. DISTRIBUTION CODE

13. ABSTHACT (Maximum 200 words)

Between February and September 2001, a number of aspects of the solar-sail-launched Interstellar probe

(ISP), which is under consideration by NASA for launch in the 2010-2015 timeframe, were researched.

The effort was conducted in New York City (NYC) February-May, at Marshall Space Flight Center

(MSFC) May-July (when the PI served as a NASA Summer 2001 Faculty Fellow), and in NYC

August-September. In addition to the people listed on the title sheet, many people in NYC and at MSFC

participated in this research.

14.SUBJECTTERMS

solar sail, in-space propulsion, space transportation, holography

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OF REPORT

Unclassified I

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Unclassified 19. SECURITY CLASSIFICATION

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Unclassified

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88

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