Geodesic
Keeping a Solar Sail near the Triangular Libration
Russian journal of nonlinear dynamics, Tome 19 (2023) no. 4, pp. 521-532.

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The possibility of keeping a spacecraft with a solar sail near an unstable triangular libration point of a minor planet or a binary asteroid is studied under the assumption that only the gravitation and the solar radiation influence the spacecraft motion. The case where the solar sail orientation remains unchanged with respect to the frame of reference of the heliocentric orbit of the asteroid mass center is considered. This means that the angle between the solar sail normal and ecliptic, as well as the angle between this normal and the solar rays at the current point, does not change during the motion. The spacecraft equations of motion are deduced under assumptions of V.V. Beletsky’s generalized restricted circular problem of three bodies, but taking into account the Sun radiation. The existence of a manifold of initial conditions for which it is possible to choose the normal direction that guarantees the spacecraft bounded motion near the libration point is established. Moreover, the dimension of this manifold coincides with that of the phase space of the problem at which the libration point belongs to the manifold boundary. In addition, some proposals for stabilization of the spacecraft motions are formulated for trajectories beginning in the manifold.
Keywords: solar sail, libration point, binary asteroid, three-body problem 
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A. V. Rodnikov. Keeping a Solar Sail near the Triangular Libration. Russian journal of nonlinear dynamics, Tome 19 (2023) no. 4, pp. 521-532. http://geodesic.mathdoc.fr/item/ND_2023_19_4_a3/

[1] Anouar, A. and Bennani, M., “Gravitational Potential of Asteroids of Diverse Shapes”, Int. J. Astron. Astrophys., 11:4 (2021), 458–469 | DOI

[2] Aslanov, V. S., “Capture Trajectories into Vicinity of Collinear Libration Points by Variable Electrostatic Field”, J. Spacecraft Rockets, 59:3 (2022), 1039–1043 | DOI

[3] Kosmicheskie Issledovaniya, 45:5 (2007), 435–442 (Russian) | DOI

[4] Kosmicheskie Issledovaniya, 46:1 (2008), 42–50 (Russian) | DOI

[5] Burov, A. A. and Nikonov, V. I., “Libration Points inside a Spherical Cavity of a Uniformly Rotating Gravitating Ball”, Russian J. Nonlinear Dyn., 17:4 (2021), 413–427 | MR | Zbl

[6] Farrés, A., Heiligers, J., and Miguel, N., “Road Map to $L4/L5$ with a Solar Sail”, Aerosp. Sci. Technol., 95 (2019), 105458, 21 pp. | DOI

[7] http://www.isas.jaxa.jp/en/missions/spacecraft/current/ikaros.html

[8] https://en.wikipedia.org/wiki/List_of_minor_planets

[9] https://en.wikipedia.org/wiki/Minor-planet_moon#List_of_minor_planets_with_moons

[10] https://www.hayabusa2.jaxa.jp/en/

[11] https://www.planetary.org/explore/projects/lightsailsolar-sailing/#the-lightsail-2-mission

[12] Khabibullin, R. and Starinova, O., “Attitude and Orbit Control of a Solar Sail Spacecraft by Changing Reflectivity of Its Elements”, Math. Eng. Sci. Aerosp., 13:1 (2022), 73–84

[13] Prikl. Mat. Mekh., 49:1 (1985), 16–24 (Russian) | DOI | MR | Zbl

[14] Markeev, A. P., Libration Points in Celestial Mechanics and Space Dynamics, Nauka, Moscow, 1978, 312 pp. (Russian)

[15] McInnes, C. R., Solar Sailing: Technology, Dynamics and Mission Applications, Springer, New York, 2014, 328 pp.

[16] Vestn. Mashinostroen., 2013, no. 2, 43–46 (Russian) | DOI

[17] Polyakhova, E. N., Space Flight with a Solar Sail, Nauka, Moscow, 1986, 320 pp. (Russian)

[18] Rodnikov, A. V., “Coastal Navigation by a Solar Sail”, IOP Conf. Ser.: Mater. Sci. Eng., 868 (2020), 012021, 8 pp. | DOI

[19] Rozhkov, M. A., Starinova, O. L., and Chernyakina, I. V., “Influence of Optical Parameters on a Solar Sail Motion”, Adv. Space Res., 67:9 (2021), 2757–2766 | DOI

[20] Zhang, R., Wang, Y., Shi, Y., and Xu, Sh., “Libration Points and Periodic Orbit Families near a Binary Asteroid System with Different Shapes of the Secondary”, Acta Astronaut., 177 (2020), 15–29 | DOI

[21] Scheeres, D. J. and Bellerose, J., “The Restricted Hill Full $4$-Body Problem: Application to Spacecraft Motion about Binary Asteroids”, Dyn. Syst., 20:1 (2005), 23–44 | DOI | MR | Zbl

[22] Shymanchuk, D. V., Shmyrov, A. S., and Shmyrov, V. A., “Controlled Motion of a Solar Sail in the Vicinity of a Collinear Libration Point”, Astron. Lett., 46:3 (2020), 185–192 | DOI

[23] Szebehely, V. G., Theory of Orbits: The Restricted Problem of Three Bodies, Acad. Press, New York, 1967, 668 pp.

[24] Vulpetti, G., Johnson, L., and Matloff, G. L., Solar Sails: A Novel Approach to Interplanetary Travel, 2nd ed., Springer, New York, 2015, 301 pp.

[25] Woo, P. and Misra, A. K., “Bounded Trajectories of a Spacecraft near an Equilibrium Point of a Binary Asteroid System”, Acta Astronaut., 110 (2015), 313–323 | DOI

[26] Hou, X.-Y., Xin, X.-Sh., and Feng, J.-L., “Forced Motions around Triangular Libration Points by Solar Radiation Pressure in a Binary Asteroid System”, Astrodynamics, 4:1 (2020), 17–30 | DOI | MR

[27] Jiang, Y., “Equilibrium Points and Orbits around Asteroid with the Full Gravitational Potential Caused by the 3D Irregular Shape”, Astrodynamics, 2:4 (2018), 361–373 | DOI