SIMULATION AND ANALYSIS OF A 

GEOPOTENTIAL RESEARCH MISSION 

SEMI-ANNUAL STATUS REPORT 

GRANT NAG5-528 

(bASA-C&-16C6SS) SIWULA'I'ICL BAL ANALYSIS CP N 8 7-2 4 04 2 

A GECEOIEt4IIAL frE,CEAfiCE MI,C$J(E Zeniannual 

Stataa EeFoEt ('lcras Uriv.) 19 p Avail: 

LSfS EC A02/tE A01 CSCL O&?E Unclas 

G3/46 007685 7 

Principal Investigator: 

B. E. Schutz 

The University of Texas at Austin 

Center for Space Research 

Austin, Texas 787 12 

(512) 471-4267 

June 1987 
Major Events 

1. Research results for the first simulation of GRM (8508) were published in manuscripta geodaetica , 

Vol. 12, pp. 51-63, 1987. A copy of this report was submitted with the previous semi-annual report. 

This represents the completion of the first-year efforts. 

2. A presentatioil of current research results pertaining to GRM was made at the American Geophysical 

Union Spring Meeting in Baltimore on May 18, 1987. The presentation consisted of a 15 minute oral 

presentation. A copy of the abstract and slides presented at the meeting are enclosed. 

3. The current research results are being prepared for publication in a refereed journal. The manuscript 

is in preparation and will be forwarded as soon as possible, Publication of this paper will mark the 

completion of the second-year efforts. 

Present Research Activities 

Recent efforts have centered on : 

1. the production of the second GRM simulation (S8703), 

2. studies of the selection of initial conditions to meet the ground track and relative drift requirements 

of the mission, 

studies of the orbit adjustments required to compensate for orbital insertion and mission planning 

uncertain ties, 

4. studies of the procedures to meet the orbit determination requirements of the mission, and 

5. studies of the drag compensation mechanism and the subsequent implications for GRM. 

3. 

The results for item 1 are being prepared for publication in a refereed journal. The results for items 2, 3, 

and 4 are being prepared as part a doctoral dissertation that should be completed this summer. The results 

for item 5 are being prepared as part of a masters thesis that should be completed this fall. 

In preparation for the third-year efforts, plans are underway to implement studies into: 

1. possible tracking systems for GRM, 

2. the recovery of the geopotential coefficients using classical techniques, 

3. the production of a GRM simulation with gravity gradiometer measurements, and 

4. including additional, time varying components of the force field in the simulation of GRM. 
OF PO02 QUALITY 

RECENT DEVELOPhiENTS IN THE SMULATION OF 

iI GEOPOTENTIAL RESEAEiCH MISSION 

J. 13. LundberR (Center for Space Research, The University 

of Texas at Austin. Austin. TX 78712) 

B. E. Schutz. B. D. Tapley, L. White, mdP. Antreasian 

Computer simulations have been performed for a 

Gcopotential Research iMission (GRM) to enable the study 

of the gravitational sensitivity of the range-rate 

measurements between the two satellites and to provide a 

set of simulated measurements to assist in the evaluation of 

techniques developed for the determination of the gravity 

field. The simulations were conducted with two satellites 

in near-circular, frozen orbits at 160 km altitudes separated 

by 300 km. High precision numerical integration of the 

polar orbits was used with a gravitational field complete to 

degree and order 360. The set of simulated data for a 

mission duration of about 32 days was generated on a Cray 

X-MP computer. The results presented in this repon cover 

the most recent simulation, S8703, and includes a summvy 

of the numerical integration of the simulated trajectories, a 

summary of the requirements to compute nominal 

reference trajectories to meet the initial orbit determination 

requirements for the recovery of the geopotentid, an 

;malysis of the nature of the one-way integrated doppler 

measurements associated with the simulation. and a 

~~ ~__ 

discussion of the data set to be made available. 

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1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

1987 Spring Meeting 

SCKU027799 

Dr. B. E. Schua 

Center for Space Research 

The University of Texas at Austin 

Austin,TX 78712 

(512) 4714267 

G 

0 

0% 

Ms. Susie Y. Thorn 

Center for Space Research 

The University of Texas at Austin 

Austin.TX 78712 

C 
RECENT DEVELOPMENTS IN THE 

SIMULATION OF A 

GEOPOTENTIAL RESEARCH MISSION 

J. B. LUNDBERG, B. E. SCHUTZ, B. D. TAPLEY 

L. K. WHITE, and P. ANTREASIAN 

Center for Space Research 

The University of Texas at Austin 

Austin, Texas 78712 

Presented at the 

American Geophysical Union 

Spring 1987 Meeting 

Baltimore, Maryland 

May 18, 1987 
r 

i ! 

1; 

q.! 
REVIEW OF SIMULATIONS 

Objective: The creation of a simulated GRM data set: 

to study the gravitational sensitivity of 

range-rate measurements between two 

satellites 

for the evaluation of techniques developed 

for gravity recovery from range-rate 

measurements 
OUTLINE OF GRM SIMULATION 8505 

9 32 sidereal days 

Geopotentiai field complete to degree and order 180 

plus orders 0 through 10 to degree 300 (Rapp, OSU) 

GM = 3.986013 x IO5 km3/sec2 

ae = 6378.155 km 

Constant Earth angular velocity vector 

Tides and luni-solar effects not included 

0 Nongravitational effects not included 

Instantaneous range and range-rate measurements at 

5-second intervals 

Nominal ephemeris based upon GEM-I06 
OUTLINE OF GRM SIMULATION S8703 

32 sidereal days 

Geopotential field complete to degree and order 360 

WPP, OSU) 

GM = 3.9860044 x IO5 km3/sec2 

a, = 6378.137 km 

Constant Earth angular velocity vector 

Tides and luni-solar effects not included 

Nongravitational effects not included 

Integrated, one-way doppler measurements as 

measured at each satellite at 4-second intervals 

Nominal ephemeris based upon GEM-I06 
COMPUTATION OF EPHEMERIDES 

Method 

e 

e 

e 

Encke formulation of the equations of motion 

Class 2, fixed-mesh, multistep algorithm of 

order 10 

CRAY WMP-24 

Comparison 

S8508 

I Stepsize (sec) 

Cost per function 

evaluation (msec) 

I Run time (ht) 

G ro u nd track 

closure after 

32 days (km) 

5 

8.3 

5.6 

-2 km 

S8703 

4 

23.6 

19.2 

-2 km 
FIT OF NOMINAL REFERENCE ORBIT TO S8703 

Direction 

Mission requirements for nominal orbit: 

RMS 

(m) 

Radial position errors (30): 

Along-track position errors (30): 

Cross-track position errors (30): 

100 m 

300 m 

100 m 

Max Error 

64 

206 

69 

(m) 

Fitting GEM-I06 ephemeris to S8703 resulted in 

RMS differences of several kilometers 

RMS Max Error 

(m) (m) 

18 64 

61 209 

17 72 

0 To meet mission requirements, gravitational 

coefficients based upon GEM-I OB were adjusted: 

J,, J, and two pairs of resonant coefficients 

at orders 16, 17, 33, 49, 82, 164 

Radial 

Along-track 

Cross-track 

Comparison of the final nominal orbit to S8703 

I I SAT #I 1 SAT #2 

18 

61 

17 

I I 
TIME ’OF FLIGHT VS. TIME FOR 

THE RECEPTION OF SATELLITE TWO 

u d 2 

i 

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i 

f 

! 

I 

i 

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j 

i 

I 

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1 1 1 I 1 1 1 

6.0 12.0 10.0 24. 0 30. 0 36.0 

TIME (DAYS) 
0 

csl 

.- 

c0 

OD 

0 

.- 

0 

THE AVERAGE RANGE-RATE OF THE TWO DOPPLER 

MEASUREMENTS VS. TIME 

I rvE 

' 0:o 6: 0 12.0 18.0 24.0 

TIME (DAYS) 

30.0 36.0 
RESIDUALS BETWEEN FULL FIELD AND 

GMIOB 36x36 PLUS SELECTED HARMONICS FOR SAT 1 

0 

04 I .I 

kl 

0 

z 

w 

tY 

w 

LL 

LL 

H 

n 

J 

6 

H 

4 

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n 

0 'I d ' 

I t I I I 

TO.'O 6. 0 12.0 18.0 24.0 30.0 36.0 

J 

TIME ( DAYS ) 
RESIDUALS BETWEEN FULL FIELD AND 

GMIOB 36x36 PLUS SELECTED HARMONICS FOR SAT 1 

0 

0 * 

"I 

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z 

to 

c i? I/ I 

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RESIDUALS BETNEEN FULL FIELD AND 

GMIOB 36x36 PLUS SELECTED HARMONICS FOR SAT 1 

0 

Nc 

1 

1 1 I I I -7 ' 0.0 6.0 12.0 18. 0 24. 0 30. 0 36.0 

TIME ( DAYS ) 
RESIDUALS BETWEEN FULL FIELD AND 

GMIOB 36x36 PLUS SELECTED HARMONICS FOR SAT 2 

0 I 1 I 1 I I 

40 6.0 12.0 18.0 24.0 30. 0 36.0 
RESIDUALS BETWEEN FULL FIELD AND 

GMIOB 36x36 PLUS SELECTED HARMONICS FOR SAT 2 

I 1 I I I I I 

.o 6.0 12.0 18.0 24.0 30.0 36. 

0 

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u) 

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.- 

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w 

z 

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(La 

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RESIDUALS BETWEEN FULL FIELD AND 

GMlOB 36x36 PLUS SELECTED HARMONICS FOR SAT 2 

0 

N0 

0 

m 

0- 

I I I I I 1 ' o.'o 6. 0 12.0 18. 0 24. 0 30. 0 36.0 

TIME ( DAYS ) 
DATA SET TO BE DISTRIBUTED 

At four-second intervals: 

t time tag 

4n,i integrated one-way doppler measurements 

along the nominal orbit received at 

satellite i 

4,i integrated one-way doppler measurements 

along the simulated orbit received at 

satellite i 

Ei pseudo-noise parameter . rn,Tn)i position and velocity vectors of the nominal 

orbit for satellite i 

Nominal gravity field 

True gravity field