From: szabo@techbook.com (Nick Szabo)
Subject: Safety of flyby & aerobraking for large payloads at earth
Organization: TECHbooks --- Public Access UNIX --- (503) 220-0636
Date: Mon, 28 Sep 1992 06:15:17 GMT

What are the costs and benefits of using the earth
for gravity assist and aerobraking of large payloads?
What should be the policies concerning these flybies?

Here's how a gravity assist works. The planet is moving, 
so there's our energy source. The slingshot can be computed 
with the patched-conics approximation.  If we do a Hohmann 
ellipse to the planet in the inertial frame, the trajectory 
is a hyperbola in the frame of the planet.  The energy of 
the vehicle is the same at symmetric points on opposite sides 
of the hyperbola in the planet frame.  If we exit the rendezvous 
moving in the same direction as the planet, we gain velocity 
in that direction in the inertial frame.  If we exit the 
rendezvous moving opposite the direction of the planet, we lose 
inertial velocity.  Either gaining or losing velocity can
be useful, depending on where we're going.

Aerobraking is simpler to understand.  In layman's terms,
the air slows the spacecraft down, just like wind
resistance slows down a bicycle.  In orbital mechanics
terms, the spacecraft exchanges momentum with the particles
in the atmosphere.  An interesting variant, called cometary 
aerobraking, vaporizes a piece of ice a split second before 
it intercepts the spacecraft at high velocity.  The spacecraft 
uses the temporary cloud of gas to aerobrake, as if it were 
a planetary atmosphere.   

All these maneuvers allow us to tap into the energy
already stored in the orbits of the planets and minor
planets.  They can greatly reduce the mass of propellant
and tank needed for a mission; in the case of Galileo
the Venus-Earth-Earth-Jupiter trajectory saved it from
being cancelled when it had to substitute a smaller
upper stage for the powerful Centaur.

Very large payloads can benefit from these trajectories
for the same reason, especially at earth, which raises
the important question of safety.  We cannot tolerate 
bringing a dinosaur-killer sized asteroid anywhere near 
earth, or coming towards earth near an intercept trajectory.  
Reentry of c. 100 ton Shuttles is safely performed and 
tolerated towards inhabited areas, and natural fireballs 
and meteorites massing several tons each hit the earth 
harmlessly every year.  Somewhere between these two extremes, 
we need to figure out the margins of safety and enforce them.

There are several techniques for using earth to change the orbital 
trajectory of objects:

* fast aerobraking (eg Shuttle, Apollo)
* slow aerobraking (eg Hiten)
* gravity assist (eg Galileo)

All three of these can play important roles in reducing the costs of
capturing space materials from comet fragments and asteroids into 
various earth orbits.  The delta-v savings are roughly up to an order 
of magnitude for gravity flyby, and up to two orders of magnitude for
aerobraking.  

For gravity assist, the following need to be considered:

* what is the margin of error due to fringe atmospheric density,
  gravity anomaly and trajectory measurement error?
* how quickly and precisely can the on-board engines compensate for
  trajectory errors directly before and during the flyby?
* can the operation be timed so that a worst-case error will cause
  reentry over an uninhabited area (eg the ocean)?
* how much material on board is strongly toxic or radioactive?
* what is the worst-case scenario wrt the mass, composition, and
  worst-case error trajectory of the payload?

For slow aerobraking, we must also consider the above points, paying
close attention to the fringe atmospheric density, since that is what
we are using to change the trajectory. 

For fast aerobraking, we need to pay very close attention to upper 
atmospheric density at all levels.  The error margins are much less.  
Unless the worst-case scenario is trivial or the spacecraft is 
well-controlled aerodynamically, fast aerobraking is much more 
dangerous than slow aerobraking or gravity flyby.

Given these data points, we must then determine whether the project
is ethically and politically tolerable, and whether it can be insured.

For the sake of discussion, I make the following initial proposed rules
of thumb:

gravity assist & slow aerobrake 
	* <.0001% chance of trajectory error sufficiently large for reentry
	* if reentry, >98% chance it will occur over & towards 
	  uninhabited area
	* payload mass limits:
	  	solid metallic materials: 5,000 tons (no piece > 1 ton)
		stony materials: 10,000 tons (no piece > 5 tons)
		carbonaceous materials or loose regolith: 30,000 tons
		volatile ices w/pores: 50,000 tons
		strongly toxic or radioactive material: 
			(varies by material; 1 ton typical)
		
The shape and attitude of the container also play a major role.
For example a long, thin cylinder will be dispersed more widely 
than a sphere if it hits the atmosphere sideways instead of 
headlong.

fast aerobrake:
	* aerobrake must contain control surfaces sufficient to
	  give <.001% chance of reentry due to error
	* if reentry, >98% chance it will occur over & towards
	  uninhabited area
	* no strongly toxic or nuclear materials on board
	* mass limits:
solid metallic materials: 200 tons
all other materials: 400 tons (note: ceramic heat shield will
		be significant % of mass for any payload)

Significant amounts of simulation, study of real-life artificial 
and natural reentries, and benefit/risk analysis need to go into 
determining the actual safety margins.  Calculations like those 
done by Zdenek Sekanina, to predict the ability of comet material
to penetrate the earth's atmosphere, need to be perfected.

Privately financed insurance with unlimited liability
should be required for all such payloads.  If no insurance 
company is willing to underwrite the risk it is a good sign 
for the public that the maneuver is too risky and should be 
not be allowed.  On the other hand if the insurance industry
volunteers to take on the risk, this is a good sign that the
risks, financial and physical, are minimal, and that the payoff 
directly to the companies, and indirectly to mankind as a whole, 
are well worth it.



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