Abstract
The beta angle, an angle formed by the sunlight and a spacecraft orbital plane, is an important parameter for science orbit design of orbiter missions. This angle defines lighting conditions and eclipse occurrences, and is used for science observation planning. Not only is this parameter perturbed by the irregular gravity field of the primary body, it varies with the body’s motion around the Sun. Investigating the evolution of the beta angle is therefore critical for science orbit design. This paper analyzes the J2-perturbed beta angle evolution via orbit averaging and year averaging, and derives conditions to constrain the short- and long-term evolutions of the beta angle. The orbit averaging analysis is further extended to provide a relaxed orbit condition that allows flexible science orbit design while naturally maintaining the beta angle evolution within science requirements. These analyses are carried out for an arbitrary rotation pole direction as it defines the orientation of the irregular gravity field seen in an inertial frame. The analytical work is numerically demonstrated with science orbit design for the Psyche mission, a recently selected mission of the NASA’s Discovery Program.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Boain, R.J.: A-B-Cs of sun-synchronous orbit mission design. In: 14th AAS/AIAA Space Flight Mechanics Conference, Maui, HI (2004)
Broschart, S.B., Lantoine, G., Grebow, D.J.: Quasi-terminator orbits near primitive bodies. Celest. Mech. Dyn. Astron. 120(2), 195–215 (2014). https://doi.org/10.1007/s10569-014-9574-3
Byram, S.M., Scheeres, D.J.: Stability of sun-synchronous orbits in the vicinity of a comet. J. Guidance Control Dyn. 32(5), 1550–1559 (2009). https://doi.org/10.2514/1.41655
Chappaz, L., Broschart, S.B., Lantoine, G., Howell, K.: Orbital perturbation analysis near binary asteroid systems. In: AAS/AIAA Space Flight Mechanics Meeting, Williamsburg, VA (2015)
Cinelli, M., Circi, C., Ortore, E.: Polynomial equations for science orbits around Europa. Celest. Mech. Dyn. Astron. 122(3), 199–212 (2015). https://doi.org/10.1007/s10569-015-9616-5
Circi, C., Ortore, E., Bunkheila, F., Ulivieri, C.: Elliptical multi-sun-synchronous orbits for Mars exploration. Celest. Mech. Dyn. Astron. 114(3), 215–227 (2012). https://doi.org/10.1007/s10569-012-9432-0
Dankowicz, H.: Some special orbits in the two-body problem with radiation pressure. Celest. Mech. Dyn. Astron. 58(4), 353–370 (1994). https://doi.org/10.1007/BF00692010
Fujiwara, A., Kawaguchi, J., Yeomans, D.K., Abe, M., Mukai, T., Okada, T., et al.: The Rubble-Pile Asteroid Itokawa as Observed by Hayabusa. Science 312(5778), 1330–1334 (2006). https://doi.org/10.1126/science.1125841
Han, D.: Orbit Transfers for Dawn’s Vesta Operations: Navigation and Mission Design Experience. In: 23rd International Symposium on Space Flight Dynamics, Pasadena, CA (2012)
Han, D., Smith, J.C., Kennedy, B.M., Mastrodemos, N., Whiffen, G.J.: Orbit Transfers for Dawn’s Ceres Operations: Navigation and Mission Design Experience at a Dwarf Planet. In: 14th International Conference on Space Operations, Daejeon, Korea, (2016). https://doi.org/10.2514/6.2016-2427
Hanuš, J., Ďurech, J., Brož, M., Warner, B.D., Pilcher, F., Stephens, R. et al. : A study of asteroid pole-latitude distribution based on an extended set of shape models derived by the lightcurve inversion method. Astronomy and Astrophysics 530(A134), (2011). https://doi.org/10.1051/0004-6361/201116738, arXiv:1104.4114v1
Hart, W., Brown, G.M., Collins, S.M., De Soria-Santacruz, Pich, M., Fieseler, P. et al.: Overview of the Spacecraft Design for the Psyche Mission Concept. In: IEEE Aerospace Conference. IEEE, Big Sky, MT, (2018). https://doi.org/10.1109/AERO.2018.8396444
Hu, W., Scheeres, D.J.: Spacecraft motion about slowly rotating asteroids. J. Guidance Control Dyn. 25(4), 765–775 (2002). https://doi.org/10.2514/2.4944
Kikuchi, S., Tsuda, Y., Kawaguchi, J.: Delta-V assisted periodic orbits around small bodies. J. Guidance Control Dyn. 40(1), 150–163 (2017). https://doi.org/10.2514/1.G000696
Konopliv, A.S., Asmar, S.W., Park, R.S., Bills, B.G., Centinello, F., Chamberlin, A.B., et al.: The Vesta gravity field, spin pole and rotation period, landmark positions, and ephemeris from the Dawn tracking and optical data. Icarus 240, 103–117 (2014). https://doi.org/10.1016/j.icarus.2013.09.005
Konopliv, A.S., Park, R.S., Vaughan, A.T., Bills, B.G., Asmar, S.W., Ermakov, A.I., et al.: The Ceres gravity field, spin pole, rotation period and orbit from the Dawn radiometric tracking and optical data. Icarus 299, 411–429 (2018). https://doi.org/10.1016/j.icarus.2017.08.005
Lantukh, D., Russell, R.P., Broschart, S.: Heliotropic orbits at oblate asteroids: balancing solar radiation pressure and J2 perturbations. Celest. Mech. Dyn. Astron. 121(2), 171–190 (2015). https://doi.org/10.1007/s10569-014-9596-x
Lauretta, D.S., Balram-Knutson, S.S., Beshore, E., Boynton, W.V., Drouet d’Aubigny, C., DellaGiustina, D.N., et al.: OSIRIS-REx: sample return from asteroid (101955) bennu. Space Sci. Rev. 212(1–2), 925–984 (2017). https://doi.org/10.1007/s11214-017-0405-1
Li, J.Y., Le Corre, L., Schröder, S.E., Reddy, V., Denevi, B.W., Buratti, B.J., et al.: Global photometric properties of asteroid (4) Vesta observed with Dawn framing camera. Icarus 226(2), 1252–1274 (2013). https://doi.org/10.1016/j.icarus.2013.08.011. arXiv:1310.4165
Miller, J., Konopliv, A., Antreasian, P., Bordi, J., Chesley, S., Helfrich, C., et al.: Determination of shape, gravity, and rotational state of asteroid 433 Eros. Icarus 155(1), 3–17 (2002). https://doi.org/10.1006/icar.2001.6753
Morrow, E., Scheeres, D.J., Lubin, D.: Solar sail orbit operations at asteroids. J. Spacecr. Rockets 38(2), 279–286 (2001). https://doi.org/10.2514/2.3682
Oh, D.Y., Collins, S., Goebel, D., Hart, B., Lantoine, G., Snyder, S., et al.: Development of the Psyche Mission for NASA’s Discovery Program. In: International Electric Propulsion Conference, Atlanta, GA (2017)
Ortore, E., Circi, C., Cinelli, M.: Optimal orbits around Ganymede for the JUICE mission. Aerosp. Sci. Technol. 46, 282–286 (2015). https://doi.org/10.1016/j.ast.2015.07.021
Russell, C., Raymond, C. (eds.): The Dawn Mission to Minor Planets 4 Vesta and 1 Ceres. Springer, New York, New York, NY, (2012). https://doi.org/10.1007/978-1-4614-4903-4
Russell, C.T., Capaccioni, F., Coradini, A., De Sanctis, M.C., Feldman, W.C., Jaumann, R., et al.: Dawn mission to vesta and ceres. Earth Moon Planets 101(1–2), 65–91 (2007). https://doi.org/10.1007/s11038-007-9151-9
Russell, R.: Survey of spacecraft Trajectory design in strongly perturbed environments. J. Guidance Control Dyn. 35(3), 705–720 (2012). https://doi.org/10.2514/1.56813
Russell, R.P., Lantukh, D., Broschart, S.B.: Heliotropic orbits with zonal gravity and shadow perturbations: application at Bennu. J. Guidance Control Dyn. 39(9), 1925–1933 (2016). https://doi.org/10.2514/1.G001279
Scheeres, D.: The effect of C 22 on orbit energy and angular momentum. Int. Astron. Union Colloq. 172, 339–348 (1999). https://doi.org/10.1017/S0252921100072699
Scheeres, D.: Orbit mechanics about asteroids and comets. J. Guidance Control Dyn. 35(3), 987–997 (2012a). https://doi.org/10.2514/1.57247
Scheeres, D.: Orbital mechanics about small bodies. Acta Astron. 72, 1–14 (2012b). https://doi.org/10.1016/j.actaastro.2011.10.021
Scheeres, D., Ostro, S., Hudson, R., Werner, R.: Orbits close to asteroid 4769 castalia. Icarus 121(1), 67–87 (1996). https://doi.org/10.1006/icar.1996.0072
Scheeres, D., Ostro, S., Hudson, R., DeJong, E., Suzuki, S.: Dynamics of orbits close to asteroid 4179 toutatis. Icarus 132(1), 53–79 (1998). https://doi.org/10.1006/icar.1997.5870
Scheeres, D.J.: Satellite dynamics about asteroids. Adv. Astron. Sci. 87(1), 275–292 (1994)
Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer, Berlin (2012c). https://doi.org/10.1007/978-3-642-03256-1
Scheeres, D.J., Hu, W.: Secular motion in a 2nd degree and order-gravity field with no rotation. Celest. Mech. Dyn. Astron. 79(3), 183–200 (2001). https://doi.org/10.1023/A:1017555005699
Scheeres, D.J., Williams, B.G., Miller, J.K.: Evaluation of the dynamic environment of an asteroid: applications to 433 eros. J. Guidance Control Dyn. 23(3), 466–475 (1999). https://doi.org/10.2514/2.4552
Shepard, M.K., Richardson, J., Taylor, P.A., Rodriguez-Ford, L.A., Conrad, A., de Pater, I., et al.: Radar observations and shape model of asteroid 16 Psyche. Icarus 281, 388–403 (2017). https://doi.org/10.1016/j.icarus.2016.08.011
Vallado, D.A.: Fundamentals of Astrodynamics and Applications, 3rd edn. Springer, New York (2001)
Yamaguchi, T., Saiki, T., Tanaka, S., Takei, Y., Okada, T., Takahashi, T., et al.: Hayabusa2-Ryugu proximity operation planning and landing site selection. Acta Astron. 151(May), 217–227 (2018). https://doi.org/10.1016/j.actaastro.2018.05.032
Acknowledgements
The work described in this paper was carried out in part at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. The authors would like to thank the Psyche project members for their advice and discussion. The authors are also grateful for the suggestions and comments from the editor and reviewers, which greatly improved the quality of the paper. K. Oguri acknowledges financial support for part of his Ph.D. study from Nakajima foundation and Masason foundation.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Oguri, K., Lantoine, G., Hart, W. et al. Science orbit design with a quasi-frozen beta angle: effects of body obliquity on J2-perturbed dynamics. Celest Mech Dyn Astr 132, 48 (2020). https://doi.org/10.1007/s10569-020-09987-z
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10569-020-09987-z