Optimization of spacecraft trajectory onto the heliocentric orbit

Space technologies


Аuthors

Konstantinov M. S.*, Min T. **

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: mkonst@bk.ru
**e-mail: minnntheino@gmail.com

Abstract

The main subject of this study is an interplanetary trajectory of spacecrafts with electric propulsion. The paper is devoted to the optimization of the spacecraft trajectory with electric propulsion into working heliocentric orbit. The purpose of this article is the analysis of the optimal directinsertion trajectory of the spacecraft with electric propulsion into the working heliocentric orbit with low perihelionand high inclination as well as the analysis of the possible types of extremals.
The trajectory optimization problem of spacecraft with electric propulsion into working heliocentric orbit with a given perihelion radius, a phelionradius and inclination to the ecliptic plane for the fixed time is carried out by usingthe Pontryagin’s maximum principle. The compliance with the transversality conditions for solving the boundary value problem was ensured.
The analysis of the possible types of extremals of the optimal directinsertion trajectories of the spacecraft with electric propulsion into the working heliocentric orbit with low perihelionand high inclination was carried out. As a result of this work the characteristics ofthe optimal direct insertion trajectory of the spacecraft into the target heliocentric orbit for space transportation system on the basis ofthe launch vehicle "Soyuz-2," the chemical upper stage "Fregat" and the electric propulsion type “RIT 22” are obtained. The analysis of multiple types of extremals is presented. Seven types of extremals are shown and their propertiesare analyzed.
These results can be used during the development of space research programs with using the heliocentric trajectories. For example, to study the inner heliosphere of the Sun from close distances and positions of outer ecliptic plane.
By using the space transportation system based on the launch vehicle "Soyuz-2," the chemical upper stage "Fregat" and the electric propulsion system type «RIT-22", we can insert the spacecraft with the mass more than1350 kg into the heliocentric orbit with a low perihelion and inclination to the ecliptic plane equal to 30 degrees. In this case, the required mass of xenonis 640...650 kg.
The essential optimal conditions for spacecraft insertion into the heliocentric orbit are obtained and ensuring compliance with these conditions in the solution of the boundary value problem are carried out.

Keywords:

spacecraft, optimal trajectory, Sun exploration, Pontryagin’s maximum principle, transversality conditions, ion thrusters

References

  1. Leb H.V., Petukhov V.G., Popov G.A. Elektronnyi zhurnal “Trudy MAI”, 2011, no. 42, available at http://www.mai.ru/science/trudy/published.php?ID=24275 (18.02.2011)
  2. The official website of Lavochkin Research and Production Association, available at http://www.laspace.ru/rus/fregat_construction.php
  3. The official website of EADSASTRIUM, available at http://cs.astrium.eads.net/sp/spacecraft-propulsion/ion-propulsion/index.html
  4. Pontryagin L.S., Boltyanskiy V.G., Gamkrelidze R.V., Mishchenko E.F. Matematicheskaya teoriya optimalnyh protsessov (Mathematical theory of optimal processes). Moscow, “Nauka”, 1983, 393 p.
  5. Grodzovskiy G.L., IvanovYu.N., Tokarev V.V. Mehanika kosmicheskogo polyota (problem optimizatsii) (Mechanics of the space flight (optimization problems), Moscow, “Nauka”, 1975 702, p.
  6. Konstantinov M.S., Kamenkov E.F., Perelygin B.P., Bezverbyi V.K. Mehanika kosmicheskogo polyota (Mechanics of the space flight), Moscow, “Mashinostroyeniye”, 1989, 408 p.

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