To problem of spacecraft return to Earth using Moon's gravity

V.V.Ivashkin

Keldysh Institute of Applied Mathematics, RAS

Miusskaya Sq. 4, Moscow, 125047, RUSSIA

 

Geostationary satellites are practically fixed above some points at the Earth surface. These satellites are important to support the space communication and observation of the Earth. In a model of central Newtonian gravitational field, this satellite is known to move on the geostationary orbit (GSO) that is a circular equatorial one with a 24-h period of revolution, its radius is R>42164 km. To support operating these satellites, some problems in applied celestial mechanics have to be solved, a problem of launching spacecraft (SC) from the Earth to the GSO and a problem of the SC removal from the GSO, in particular.

Concerning the injection of the SC to the GSO using a chemical jet engine with a high thrust, analysis has shown that for a high enough latitude of a cosmodrome (more than about 28 degrees, this is satisfied for the Russian cosmodromes Baiconur and Plesetsk) "detour" scheme with initial flight to the Moon is better from energy point of view than usual "direct" scheme of flight. For this "detour" flight, a lunar gravity assist results in passive change of inclination and perigee radius of the SC orbit and only then the SC flies to the GSO. Because of importance of this result, this study was repeated later by the European scientists.

Another problem - a problem of the SC removal from the GSO that is a subject of our analysis - is originated first because the places on the GSO are very deficient. So, about 350 satellites are operating on the GSO now. Not to make space debris there, the SC has to be removed from the GSO after it ends to operate. Now the SC removal from the GSO is being performed by some increasing altitude of its orbit. But this method seems to be a temporary measure and soon in future the question will be to give better solution of the return problem.

The SC return from the GSO to the Earth can be taken for this solution. In this case, the SC destruction or its landing on the Earth surface will take place. The last variant can be necessary for example (and this is the second cause to study this problem) to return on the Earth some valuable equipment, results of scientific investigations or SC for inspection and service of the satellites at the GSO.

Main results of numerical and analytical analysis of the return problem on the base of chemical engine with a high thrust (an impulse approximation) are given in the paper. Necessary conditions to realize the "detour" scheme for the SC return from the GSO to the Earth are found. A set of these trajectories is constructed, and their characteristics are analyzed. It is shown that the "detour" trajectories using initial flight to the Moon for special lunar gravity assist and following flight to the Earth are better always from energy point of view than usual "direct" return trajectories.