Spacecraft Station-keeping on the Molniya Orbit Using Electric Propulsion

Paper number

IAC-05-C1.1.01

Author

Prof. Mikhail S. Konstantinov, Moscow Aviation Institute (MAI), Russia

Coauthor

Prof. Garri Popov, RIAME MAI, Russia

Coauthor

Dr. Vladimir Obukhov, RIAME MAI, Russia

Coauthor

Dr. Vyacheslav Petukhov, Khrunichev State Research & Production Space Center, Russia

Year

2005

Abstract

Orbital constellation on the Molniya orbits provides continuous coverage of the Northern Hemisphere. The typical orbital configuration consists of some number of spacecrafts (for example six). They are placed into some orbital planes. The spacecrafts moving should be synchronized. The requirements on time of passage of ascending node of an orbit, as well as on constancy of orbital trace and on some other requirements should be carried out
The problem of this constellation maintenance can be decomposed into problems of each spacecraft station-keeping. The purpose of the spacecraft orbit control is keeping of 3 parameters: right ascensions of ascending nodes (RAAN) deviation, argument of perigee, and longitude of ascending node. These parameters keeping for each spacecraft provides the constellation configuration keeping.
It is proposed the new spacecraft station-keeping strategy over long (7-10 years) time duration. Orbital parameters are controlled by 4 thrusting arcs placed in the apogee, perigee, ascending and descending branches of orbit. Thrust vector is pointed in the circumferential direction during apogee/perigee burns and thrust is orthogonal to orbital plane during ascending/descending burns. Apogee burn adjusts latus rectum, so it adjusts RAAN precession. Perigee burn controls orbital period, so it controls longitude of ascending node. Burns in the ascending and descending arcs adjust orbital inclination, so they adjust apsidal rotation. Centers of each thrusting arc have fixed values of eccentric anomaly, which correspond to maximal change of controlling parameters per unit velocity increment. Control parameters are lengths of thrusting arcs and thrust directions (positive or negative).
Two orbital propagation models are used for control synthesis. The first one is numerical high-precision orbital propagation model taking into account thrust, lunisolar perturbation, and earth gravity potential expansion of an arbitrary given order and degree. The second model is semi-analytical propagation model, based on averaging technique. This simplified model takes into account main secular terms due to thrust, lunisolar gravitation, and earth zonal harmonics.
All period of constellation lifetime is divided into subintervals having duration 1-6 months. For each subinterval it is solved a two-point boundary value problem (TPBVP) in the frame of simplified semi-analytical propagation model. Perigee burn compensates variations of orbital period while parameters of other burns are unknown TPBVP parameters. Namely there are thrusting arcs lengths and directions of thrust during these burns. Left boundary conditions correspond to the current orbital parameters of considered spacecraft and right boundary conditions corresponds to nullification of either controlled parameters or their rates. Controlled parameters are RAAN deviation and argument of perigee. The robust numerical homotopic technique is used to solve this TPBVP. After such computation of burning arcs parameter, spacecraft orbit is propagated using numerical high-precision propagator over considered subinterval. A simple feedback control is used to provide keeping of longitude of ascending node by perigee burns. As a result, spacecraft orbital parameters at the end of considered subinterval are obtained. These parameters are used as initial condition for next subinterval and so on, until covering whole lifetime.
Details of the technique realization and results of numerical analysis are discussed. It is shown that characteristic velocity consumption could be reduced to 50-70 m/s per year for station-keeping accuracy 0.5-1.0 degrees.

Abstract document

IAC-05-C1.1.01.pdf

Manuscript document

IAC-05-C1.1.01.pdf (🔒 authorized access only).

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