Project-and-Ballistic Analysis of a Spacecraft Insertion into the Heliocentric Orbit with Thirty Degrees Inclination to the Solar Equator Plane

Аuthors

Konstantinov M. S.^*, Shevchenko V. V.^**

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

*e-mail: mkonst@bk.ru
**e-mail: vv.shevchenko5894@gmail.com

Abstract

The presented article deals with consideration of one of the possible trajectories for the Sun exploration from low heliocentric orbits with a given inclination of 30 degrees to the plane of the solar equator. The purpose of this analysis consists in the efficiency increasing of the space transportation systems while the interplanetary transfer realization by a series of passive gravity assist maneuvers near Earth and Venus.
For the  transportation system, consisting of a launch vehicle “Soyuz-2.1b”, chemical upper stage “Fregat” and a spacecraft (SC) equipped with an electric rocket propulsion based on a single engine “SPD-140D”, a solution to the problem of a spacecraft  insertion into the last working heliocentric orbit, was obtained within the framework of this study.
Characteristics of the SC insertion scheme were being found from the solution of the boundary value problem of the Pontryagin`s maximum principle, which allowed reducing the optimization problem to a boundary value problem for a system of ordinary differential equations. The SC mass launched into the last heliocentric orbit was considered as an optimization criterion.
The analyzed launch definition includes the following trajectory sections:
- the launch is performed from Baikonur Cosmodrome;
- the “Fregat” chemical upper stage ensures sufficient impulse of SC velocity for the of heliocentric Earth-to-Earth flight realization, on which the SC electric rocket propulsion activation is possible;
- the gravity assist maneuver near Earth is performed. It is considered passive, as well as all subsequent gravity assist maneuvers;
- on the heliocentric section of the Earth-to-Venus flight the SC thrust propulsion system turning on is possible as well;
- a series of four passive gravity assist maneuvers near Venus with the 1 : 1order of resonances  (the period of the Venus orbit is equal to the SC period). Heliocentric sections of the Venus-to Venus trajectory were considered passive;
- characteristics of the last gravity assist maneuver near Venus were selected in such a way as to satisfy the given inclination of the last working heliocentric orbit.
The launch date of November 7, 2031 (Julian date 2463177.979005602) turned out to be optimal for the considered launch epoch and the analyzed route. Other characteristics of the obtained trajectory are as follows:
1. At the SC launch from the Earth referenced orbit, the value of the chemical upper stage velocity impulse was equal to ∆V = 3468.293 m/s. It ensured the value of hyperbolic excess velocity at the launch from the Earth equal to V∞ =1305.019 m/s.
2. The maximum fuelling of the “Fregat” chemical upper stage was used. The SC mass after the separation of the “Fregat” chemical upper stage was 1865.983 kg.
3. At the heliocentric Earth-to-Earth section, the SC thruster propulsion system was switched on three times. Three active sections and three passive sections of the electric rocket propulsion operation were obtained. The Earth-to-Earth flight duration was 447.367 days. It required 366.66 kg of xenon.
4. The SC hyperbolic velocity excess near Earth was 8690,038 m/s. The SC mass after the gravity assist maneuver near Earth was 1499.3 kg.
5. The angle of rotation of the hyperbola asymptote during the gravity assist maneuver near Earth turned out to be equal to the maximum permissible angle of 51.96°.
6. The Earth-to-Venus flight duration is 49.45 days. The Earth-to-Venus flight is passive.
7. The value of the hyperbolic excess velocity when SC approaching Venus was of 15,901 km/s.
8. The maximum angle of rotation of the hyperbola asymptote near Venus is 19,119°. The gravity assist maneuver near Venus was realized at the minimum flyby altitude near the planet.
9. The SC mass near Venus was 1499.3 kg.
It was noted that while the SC launching scheme implementation, the final mass of the SC was 590 kg more than in the launching of the SC with the chemical propulsion system, and 169.5 days earlier the SC reached the specified inclination of 30 degrees to the plane of the solar equator.

Keywords:

design-and-ballistic analysis, electric propulsion system, passive gravity maneuver, working heliocentric orbits

References

1. Kuznetsov V.D. Mekhanika, Upravlenie i Informatika, 2012, no. 6(12), pp. 5–14.
2.  Leb Kh.V., Petukhov V.G., Popov G.A. Trudy MAI, 2011, no. 42. URL: https://trudymai.ru/eng/published.php?ID=24275
3.  Kasper J.C., Klein K., Lichko E. et al. Parker Solar Probe Enters the Magnetically Dominated Solar Corona. Physical Review Letters, 2021, vol. 127, no. 25: 255101. DOI:10.1103/PhysRevLett.127.255101
4.  Müller D., Marsden R.G., St. Cyr O.C. et al. Solar Orbiter: Exploring the Sun-heliosphere connection. Solar Physics, 2013, vol. 285, pp. 25-70. DOI: 10.1007/s11207-012-0085-7
5.  Buckley M. NASA’s Parker Solar Probe Completes 18th Close Approach to the Sun. Johns Hopkins Applied Physics Laboratory, 2024. URL: https://blogs.nasa.gov/parkersolarprobe/
6.  Elnikov R.V. The analysis of a transfer Earth Mars with a lunar gravity assist maneuver and use of a small thrust. Aerospace MAI Journal, 2012, vol. 19, no. 5, pp. 38-44.
7.  Elnikov R.V. Trudy MAI, 2012, no. 50. URL: https://trudymai.ru/eng/published.php?ID=27613
8.  Sotskov I.A. The upper stage project parameters selection while its experimental work-out. Aerospace MAI Journal, 2023, vol. 30, no. 2, pp. 62-69. DOI: 10.34759/vst-2023-2-62-69
9.  Martynov M.B., Petukhov V.G. Vestnik FGUP “NPO im. S.A. Lavochkina”, 2011, no. 2, pp. 3-11.
10.  Gnizdor R.Yu., Pyatykh I.N., Kaplin M.A., Rumyantsev A.V. Development and characteristics studying of the xenon and krypton operating SPD-70M thruster engineering model. Aerospace MAI Journal, 2023, vol. 30, no. 2, pp. 106-115. DOI: 10.34759/vst-2023-2-106-115
11.  Sinitsin A.A. Effektivnost' primeneniya elektroraketnykh dvigatel'nykh ustanovok v transportnoi operatsii vyvedeniya kosmicheskikh apparatov na geostatsionarnuyu orbitu (The effectiveness of the use of electric rocket propulsion systems in the transport operation of launching spacecraft into geostationary orbit), Doctor’s thesis, Moscow, Issledovatel'skii tsentr im. M.V. Keldysha, 2009, 160 p.
12.  Konstantinov M.S. Kosmicheskie issledovaniya, 2019, vol. 57, no. 5, pp. 347-360. DOI: 10.1134/s0023420619050042
13.  Nikolichev I.A. Optimization of the multirevolutional non-coplanar low-thrust orbital transfers. Aerospace MAI Journal, 2013, vol. 20, no. 5, pp. 66-76.
14.  Petukhov V.G., Paing S.T.U. Izvestiya RAN, Energetika, 2019, no. 3, pp. 140–154.
15.  Konstantinov M.S., Min T. Trudy MAI, 2013, no. 67. URL: https://trudymai.ru/eng/published.php?ID=41510
16.  The SOFA Software Libraries. International Astronomical Union. Division 1: Fundamental Astronomy, Commission 19: Rotation of the Earth, Standards of Fundamental Astronomy Board. 2013. URL: www.iausofa.org
17.  Li B.L., El'nikov R.V. Materialy XLVI Mezhdunarodnoi molodezhnoi nauchnoi konferentsii “Gagarinskie chteniya – 2020” (14-17 April 2020; Moscow). Moscow, MAI, 2020, pp. 701-702.
18.  Konstantinov M.S., Thein M. Method of Interplanetary Trajectory Optimization for the Spacecraft with Low Thrust and Swing-bys. Acta Astronautica, 2017, vol 136, pp. 297-311. DOI: 10.1016/j.actaastro.2017.02.018
19.  Casalino L., Colasurdo G., Pastrone D. Optimization Procedure for Preliminary Design of Opposition-Class Mars Missions. Journal of Guidance, Control, and Dynamics, 1998, vol. 21, no. 1, pp. 134-140. DOI:10.2514/2.4209
20.  Konstantinov M.S., Shevchenko V.V. Ballistic Design of a Solar Probe into a Heliocentric Orbit with a Large Inclination to the Solar Equator. AIP Conference Proceeding, 2023, vol. 2549, no. 1: 120004. DOI: 10.1063/5.0107997