Analysis of a Station-Keeping Maneuver Strategy for Three Geostationary Satellites Collocation

Copyright © IFAC Automatic Control in Aerospace, Seoul, Korea, 1998

ANALYSIS OF A STATION-KEEPING MANEUVER STRATEGY FOR THREE GEOSTA TIONARY SATELLITES COLLOCATION

Byoung-Sun Lee l ,2,

Jeong-Sook Lee l and Kyu-Hong Choi 2

I Satellite Communications System Department, ETRI-Radio & Broadcasting Technology Laboratory Yusung P.OBox 106, Daejon 305-350, Korea 2Department ofAstronomy, Yonsei University Shinchon-Dong, Seoul 120-749, Korea

Abstract : A collocation strategy have been planned and analyzed for three geostationary satellites in the same longitude control box. The orbit determination error analysis is performed when only one ground station is used for the angle tracking and ranging. Based on the orbit determination errors, the station-keeping barids are allocated for 7-day EastlWest station-keeping maneuver cycle. The eccentricity control circle and inclination control box for individual satellite are allocated for the collocation. The eccentricity vector and inclination vector separation method is applied for the collocation, and the maneuver schedule is planned to minimize the operational load by avoiding simultaneous maneuvers. Total of eighty days of station-keeping maneuver simulations are performed for the three collocated satellites. The mutual distances between the satellites are monitored for avoiding collisions. Copyright © 1998 IFAC Keywords : Artificial satellites, Satellite control applications

services. Collocation strategy for the two satellites within ±0.1° such as TDF, BRAZILSAT, HISPASAT, and EUTELSAT have been analyzed by Dufor(l991), Fischer and Gautier(l993), Schulz and Andrade( 1994), Bassaler(l995), and Pattinson( 1996). The interferences such as the shadowing and disturbances of the communiCation link or attitude sensors between collocated satellites were studied by Harting(l991). The collocation strategy for three to six ASTRA constellation within ±0.1° longitude band for direct TV services have been planned by Wauthier and Francken(l994). In this paper, a station-keeping maneuver strategy is planned and analyzed for the three geostationary satellite collocation. Three satellites are assumed to be collocated in 1160 E ± 0.05 0 longitude, same as KOREA SAT 1 and 2. For developing stationkeeping maneuver strategy, orbit determination errors are analyzed first. Only one ground station is assumed for the angle tracking and ranging of the three satellites. Then station-keeping box is properly allocated. After that, a collocation strategy is set up and then the simulations are perfonned. The separations of the spacecraft are monitored during the collocation simulations of 80 days.

1. INTRODUCTION

The pOSItIOn of the geostationary communications satellite should be maintained within a certain band of the station-keeping box. Because of the growing number of the geostationary satellites and the limitation of the geostationary orbit arc, the satellite operator locates several satellites on the same geostationary orbit position. This is called collocation. In the past, the collocation of satellites in a same longitude control box was temporarily used for the transfer of services from a retiring satellite to a replacement satellite. The advantage of the collocation is that many collocated satellites are endurable for the malfunction of member satellites. On the other hand, the spacecraft operation is somewhat complicated because the radio interference and the physical collision between the satellites should be avoided. So, the proper strategy of the station-keeping maneuver opeartion for the collocated satellite is very important. Station-keeping of the collocated satellites within ±OJ o and ±0.1° longitude band were studied by Hubert and Swale(l984) for direct broadcasting

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should be allocated in East/West station-keeping maneuver band. The cross-track error component and the radial error component are very small compare to the along-track error. The cross-track error component affects the North/South stationkeeping. Fig. 2 shows the contributions of the major position error sources in covariance analysis. The azimuth angle measurement uncertainty clearly dominates in this case and it causes gradual increase of the alongtrack error component as shown in Fig. I. The elevation angle measurement uncertainty is the second dominant factor.

When there are no problems in collocation simulations, the collocation strategy can be applicable to the real spacecraft operation.

2. ORBIT DETERMINATION ERROR ANALYSIS

The orbit determination error analysis is important in operation of geostationary communications and broadcasting satellites. The position of the satellites should be carefully maintained within the allocated longitude and latitude band called station-keeping box. When the satellite is drifted out of the stationkeeping box, it may cause the radio interference or even physical interference to the neighboring satellites. So, the errors in orbit determination should be considered in station-keeping maneuver strategy. Covariance analysis is perfomied for estimating the errors in tracking and orbit determination process. The random measurement noise in tracking process and the mismodeling of measurement parameters and dynamical parameters in orbit determination process are considered. The multi-satellite error analysis program, ORAN is used for the covariance analysis(McCarthy, 1995). A single ground station tracking and ranging for the geostationary satellite is assumed. The key input parameters for orbit determination(OD) error covariance analysis are shown in Table I.

12000 10000

I

Values 36.0

Degrees North

Ground station longitude

127.5

Degrees East

:~"

6000

of

4000

Fig. I. Position error components in OD

10000

I

b t: w

58

Meters

Spacecraft longitude

116

Degrees East

Earth gravity model

4x4

Tracking data span

24

Hours

Orbit prediction span

72

Hours

Range measurement sigma

10.0

Meters

Range bias uncertainty

50.0

Meters

AzlEI measurement sigma

0.005

Degrees

AzlEI bias uncertainty

0.02

Degrees

Station time uncertainty

2.0

Seconds

STA·EL.E - - STA·AZI -

8000 6000

.'" 0 Q.

4000 2000

Ground station altitude

STA·TIM .••. STA·RAN--

.~

Units

Ground station latitude

8000

2000

Table J Input parameters for OD error analysis Parameters

g

w

-,-- --'

---

----

--- - --- --'

--- ----- --'

Fig. 2. Contributions of parameters in position error 3. STATION-KEEPING BOX ALLOCATION

A satellite in geostationary orbit is continuously perturbed by the forces due to the triaxiality of the Earth, luni-solar gravitational forces and solar radiation pressure. The geostationary satellite located at 116°E longitude tends to drifted west toward the stable point near 75° E longitude by the Earth's tesseral harmonics. The East/West StationKeeping(EWSK) maneuver burn direction is tangent to the orbit and adjusts the semi-major axis and eccentricity of the orbit to maintain the satellite within the station-keeping box. The station-keeping maneuver strategy should be designed to minimize spacecraft propellant usage and ground operational load. The orbit determination error in along-track direction, i.e., East/West direction was estimated about 5.5 km in covariance analysis of the previous section. The geostationary arc of 0.1° is converted to 73.6 km and the arc length of 5.5 km is converted

Fig. 1 shows the error components of the position in orbit determination error analysis. The radial(R), cross-track(C), along-track(A), and total(T) errors are shown in Fig. I. The along-track error component is overlapped by the total error and it is dominant in this case. After one day of tracking and ranging process, the orbit determination error in along-track direction is estimated about 5.5 km. The alongtrack errors are increased day after day. The alongtrack component in geostationary orbit is East/West direction. So, the orbit determination error margin

296

loaded on a spacecraft.

to 0.075°. The maneuver execution error of 0.025° would be added to the orbit determination errors and then the two guard bands of 0.01° in each side of the EWSK box are allocated. Two bands of 0.007° for the perturbations due to luni-solar gravitational effects are allocated as Hubert and Swale(l984). The remaining planning limit of about 0.066° must accommodate the diurnal longitude variation due to mean eccentricity, and secular drift due to the Earth's triaxiality. The maximum free drift time T is obtained from quadratic expressions of longitude motion due to triaxiality as a fwiction of time(Soop, 1994).

4. COLLOCATION STRATEGY SETUP The eccentricity vector e = (e %' ey) is defmed by e% = ecos(Q+m)

where e is the eccentricity, and Q specify the right ascension of ascending node and (J) is the argument of perigee. The magnitude of the eccentricity vector is equal to the eccentricity and the angle between the e-vector and the x-axis is equal to the right ascension of the perigee. The inclination vector i = (i%' i) is defmed by Y i% = i cos(Q) (3) iy = isin(Q) where i is the inclination of the orbit with respect to the equatorial plane. The angle between the i-vector and the x-axis is equal to the right ascension of the ascending node(Montenbruck, 1993). The eccentrIcIty and inclination(E&I) vector separation strategy is widly used for the collocation of the two satellites. When the differences between eccentricity vectors and inclination vectors are parallel, and the radial separation between the satellites is minimum, the North/South separation should be maximum. The collocation of the two Koreasat spacecraft using E&I vector strategy was monitored using analytical orbit propagator(Lee et aI., 1997). The relative distance between any two collocated satellites, projected onto the meridian plane is derived by Eckstein(l987).

where, b"A. denotes half size of the free drift box and ..i denotes the mean drift-rate change,..i =-0. 198e-2 (deglday2) at 116°E. For the operational purpose, the station-keeping maneuver cycle is normally chosen on a weekly base. A 7-day cycle and a 14day cycle could be applicable to the satellite in 116 °E and the maneuver simulations were performed by Lee & Eun(l995). The 7-day EWSK cycle is chosen in this study for the collocation of three spacecraft within 1160 E ± 0.05 0 longitude. For the 7-day cycle, total deadband is calculated from eq.(l) as 0.012°. The remaining 0.054° will be used for diurnal longitude variation due to eccentricity. Table 2 shows the EWSK maneuver band allocation for a 7-day station-keeping cycle. The mean eccentricity limit driven by the allocation for eccentricity variation due to solar radiation pressure is also shown in Table 2. Fig. 3 shows the band allocations according to Table 2.

Prnin

=

{~e2 + M2 +(~e4 + M4 _ 2~e2 ~i2 cos2.9)

where R is the unperturbed geostationary semimajor axis(-42164.2 km) and .9 is the offset angle between the eccentricity vector difference and the inclination vector difference. This expression for the minimum distance shows that the Ell vector offsets · between any two satellites should be maximized when Ell vector offsets are parallel or anti-parallel. The eq.(4) becomes

Allocation 0.02 0.014 0.012 0.054 2.356 e-4

Prnin(.9 = 00r180) = R min{I ~ei, I ~il} . -0.05° -0.04° -0.033°

1/2}1I2 (4)

Table 2 EWSK band allocation for 7-Day Cycle Effect Guard band for OD and maneuver errors(O) Guard band for luni-solar perturbations(L) Allocation for drift and N/S coupling(O) Allocation for eccentricity due to solar radiation pressure(E) (Mean eccentricity limit)

(2)

ey = esin(Q+m)

·0.006° 116°E 0.006°

(5)

Fig. 4 shows the relative motion components in the meridian plane for parallel Ell vector offsets.

Fig. 3 EWSK band allocations for 7-day cycle The perturbations casued by the Sun and Moon are predominantly out-of-plane effects causing a change .in the inclination and in the right ascension of ascending node(Pocha, 1987). The North/South Station-Keeping(NSSK) maneuver burn is normal to the orbit and adjusts the inclination of the orbit to control the daily latitudinal excursions of the satellite. The NSSK maneuvers are very important because that normally spends over 90 % of the fuel

297

3 . ~-4

-----------,--------

(10····, . .

2.CE-4 -

,

..

:rCl>

O.OE+()

'

\

...

/~\

~--~ .

7

Earth

I"" '·

.~

i,

+

'i

\

.,.

.

~ ...

-1 .0E-4 ----'

'.

.

,

,'.

, .-

I

/

/

·2.0E-4 -

South

·3.0E-4

Fig. 4. Projection of the relative motion of two geostationary satellites for parallel offset

..J.0E.-4

KS2 770 IS.8

KS3 2800 S7.0

3.8394e-4

3.0767e-4

3.0S24e-4

l.lSe-4

l.lSe-4

l.lSe-4

O.OOe-O 1.20e-4

-I. 03924e-4 -6.00000e-S

1.03924e-4 -6.0000e-S

2.CE-4

3.CE-4

0.00 - - - - - - --- - - - - - - - -

l'

0.04

-1

0.02

~

0.00

- - ' - - - - -=====--

-0.04

-0.00

KS1

! -+-~_---~----'--

-0.00

-0.04

-0.02

0.00

0.02

0.04

0.00

i-x

Fig. 6. Inclination vector control box for three spacecraft collocation case Fig. 6 shows the inclination vector control box for the three satellites collocation case. The inclination vector should be controlled within the box allocated for each satellite. Following this strategy, the eccentricity vector differences and the inclination vector differences are parallel to each other so that the projection of the relative motion in Fig. 4 is satisfied. The station-keeping maneuver schedule for the three satellites should be planned to minimize the operational load in satellite control center by avoiding simultaneous maneuver of three spacecraft on the same day. Table 4 shows the collocation maneuver schedule for the simulation of the three collocated satellites. Table 4 Station-Keeping maneuyer cycle events for three spacecraft collocation

Table 3 Parameters for three satellites collocation KSI 660 16.9

1 . CE~

O.OE+o

Fig. 5. Mean eccentricity vector control circle for three spacecraft collocation case

For collocating three satellites in 116 E ± 0.05 longitude, the eccentricity vector control circle and the inclination vector control box for each satellite should be defmed. The radius of the total eccentricity vector limit for 7-day EWSK strategy was calculated as 2.356e-4 in Table 2. The eccentricity control circle for three individual satellite should be coordinated in the total The proposed eccentricity circle of 2.356e-4. strategy for eccentricity vector control is that the mean eccentricity vector follows the limit circle such that the mean eccentricity vector difference between three satellites make the trianglular shape as shown in Fig. 5. Fig. 5 shows the eccentricity limit circles for the three individual satellites. The EWSK maneuver should be performed such that the mean eccentricity vector follows the limit circle. The mean eccentricity vector points the direction of the Sun such as the Sun-pointing perigee strategy by Kamel and Wagner(l982). Unlike the Sun-pointing perigee strategy, two-part EWSK maneuvers are required in this case because the natural steady state eccentricty evolution exceeds the eccentricity control limit circle. The triangular shape in Fig. 5 shows the configuration at Summar solstice. The eccentricity vector offsets are about 2.07846e-4 and it can be converted to the distance of 8.76 km. The minimum distance of 8.76 km is guranteed using this strategy. Table 3 shows the key parameters for the eccentricity vector control. The radius of steady state eccentricity for the satellite is calculated based on the area-to-mass ratio. Two part EWSK maneuvers are required in this case because the radius of steady state eccentricity is bigger than that of planned eccentricity.

Mass(kg) Area(m2) Steady State Eccentricity Radius Planned Eccentricity Radius X of circle center Y of circle center

-1 .0E-4

e-x

0

0

-2.0E~

First Week (I -7)

KSI KS2 KS3

M EW TR M EW

T

W

T

NS TR T

TR NS W

EW TR T

F TR

S NS

S TR

EW F

S

S

Second KSI Week KS2 TR EW (8 -14) KS3 TR EW TR : Tracking and Ranging, EW : EWSK, NS : NSSK

298

5. COLLOCATION SIMULATIONS

Fig. 9 shows the distance between the KS 1 and KS2 during the simulation period. Fig. 9 also shows the radius and latitude of the KSl and KS2. The state vector updates and maneuvers are shown in the bottom. Fig. 10 shows the same parameters as in Fig. 9 for the KS 1 and KS3 . As pointed out in the earlier paragraph, the distance between the KS 1 and KS3 is greater than that of KS 1 and KS2 because the inclination vector of KS 1 is somewhat shifted to the left. Fig. 11 shows the same parameters for the KS2 and KS3. The distances between three satellites are kept greater than 10 km to avoid the collisions between the satellites.

The collocation simulation for the three satellites in the longitude control box of 116° E ± 0.05° is performed to evaluate the strategy. The EWSK and NSSK maneuvers are performed for 80-days period according to the maneuver schedule in Table 4. Geo-Control program is used for the simulations(Montenbruck et al., 1992). Fig. 7 shows the mean eccentricity vectors history of the three satellites. The mean eccentricity vectors of the individual satellites followed the eccentricity control circles shown in Fig. 5. The epoch of the simulation is set to September 12, 1999. So, the mean eccentricity vectors evolve downward to follow the revolution of the Sun. Fig. 8 shows the inclination vectors history of the three satellites for the same period. The inclination vectors of the individual satellites are changed within the inclination control boxes shown in Fig. 6. The inclination vectors of the KS 1 show a little bias to the left side of the control box. So, the distances between the KS 1 and KS2 will be shorter than that of KSI and KS3 . .. y

Fig. 9. Collocation monitoring for KSl and KS2

4

2

·2

Fig. 10. Collocation monitoring for KSl and KS3

·2

Fig. 7.

2

4

...

Mean eccentricity vectors history r.~"0II

Vf£JD< (d'tl

. 0.10 ,.y 0.08 0.06 0.04 0.02 0.00 ·0.02 ·0.04

~I

Fig. 11 . Collocation monitoring for KS2 and KS3

6. CONCLUSION

+

~ ~

A collocation strategy has been planned and analyzed for the three geostationary satellites within ±0.05° control box of 1160 E longitude. The orbit determination error analysis was performed for the station-keeping band allocation. Seven-day EastlWest station-keeping and fourteen-day North/South station-keeping maneuver cycle were applied for the collocation strategy. The collocation simulation was performed for 80-days period.

·0.06 ·0.08 ·0.10 '-----'-_-'----'-_-'-_'---'-_-'----'-_-'----' ·0.10 · 008 ·0.06 ·0.04 ·0.02 0.00 0.02 004 0.06 0.08 0.10

i·x

Fig. 8.

Inclination vectors history

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Satellites. Second International Symposium Ground Data Systems for Space Mission Operations, Pasadena, California. pp.I-6. Montenbruck, O. (1993). General Description of the MAPLA Maneuver Planning Program, DLRlGSOC. pp. 3- 8. Pattinson, L. (1996). Eutelsat Satellite Collocation, paper no. AIAA96-1187-CP, 557-565. Pocha, J. J. (1987). An Introduction to Mission Design for Geostationary Satellites, D. Reidel, Dordrecht. pp. 103 - Ill. Schulz, W. and E. P. Andrade (1994). Colocation of Geostationary Satellites. RBCM- J. of the Braz. Soc. Mechanical Sciences, XVI, 158-162. Soop, E. M. (1994). Handbook of Geostationary Orbits, Kluwer, Dordrecht. pp. 79-82. Wauthier, P. and P . Francken (1994). The ASTRA co-location strategy for three to six satellites. RBCM-J. of the Braz. Soc. Mechanical Sciences, XVI,163-170.

Simultaneous maneuvers were avoided to minimize the satellite operation load. The applied collocation strategy was found to maintain the mutual distances of the satellites over 10 km. The study verified that the three satellites would be collocated safely in 116°E ±0.05°. For the operational purpose, the contingency operations of the collocated satellites should be planned and analyzed when the station-keeping maneuvers for individual satellite could not be performed according to the schedule by accident. Automatic simulation program including sequential station-keeping maneuvers and orbit propagation for the collocated satellites are useful for many satellites collocation case. Collocation strategy for the four satellites in 116° E ±0.05° box will be performed as a further study.

REFERENCES Bassaler, P.(1995). Colocation Strategy in G.E.O. Orbit For Both Eutelsats Satellites FMl & FM6. International Symposium Space Flight Dyanamics, Toulouse, France. MS95/027, pp. 503-518. Dufor, F. (1991). One Year of Co-location at 19 degrees west with TDF-l and TDF-2 Spacecrafts. ESA Symposium on Spacecraft Flight Dynamics" Darmstadt, Germany. ESA SP-326, pp.23-25. Eckstein, M. C. (1987). On the Separation of Colocated Geostationary Satellites, DFVLRlGSOC, TN87-20. Fischer, J. and H. Gautier (1993). Colocation Strategy for the HISPASA T Satellites. AASIGSFC International Symposium on Space Dynamics, Greenbelt, Maryland. AAS-93-288 Harting, A. (1991). Approach to the Evaluation of Interferences between Co-Iocateed Geostationary Spacecraft. ESA Symposium on Spacecraft Flight Dynamics, Darmstadt, Germany. ESA SP-326, pp.1l-16. Hubert, S. and J. Swale (1984). Stationkeeping of a Constellation of Geostationary Communications Satellites, AIAAlAAS Astrodynamics Conference, Seattle, Washington. paper no. AIAA-84-2042. Kamel, A. A. and C. A. Wagner (1982). On The Orbital Eccentricity Control of Synchronous Satellites. J. Astronautical Sciences, XXX, 61-73 . Lee, B.-S., J.-S. Lee, J.-c. Yoon, and K.-H . Choi (1997). A New Analytical Ephemeris Solution For the Geostationary Satellite and Its Application to KOREASAT. Space Technology, 17,299-309. Lee, B.-S and J. W. Eun (1995). Station-Keeping Maneuver Simulation for the KOREA SAT Spacecraft Using Mission Analysis Software. J. ofAstronomy and Space Sci., 12, 102-111. McCarthy, J. (1995). The Operational Manualfor the ORAN Multi-Satellite Error Analysis Program, Hughes STX, Maryland. pp. 1-52. Montenbruck, 0., M. C. Eckstein, and J. Gonner (1992). The Geo-Control System for Station Keeping and Colocation of Geostationary

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