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Orbital evolution around irregular bodies
Earth, Planets and Space volume 51, pages1173–1180(1999)
The new profiles of the space missions aimed at asteroids and comets, moving from fly-bys to rendezvous and orbiting, call for new spaceflight dynamics tools capable of propagating orbits in an accurate way around these small irregular objects. Moreover, interesting celestial mechanics and planetary science problems, requiring the same sophisticated tools, have been raised by the first images of asteroids (Ida/Dactyl, Gaspra and Mathilde) taken by the Galileo and NEAR probes, and by the discovery that several near-Earth asteroids are probably binary. We have now developed two independent codes which can integrate numerically the orbits of test particles around irregularly shaped primary bodies. One is based on a representation of the central body in terms of “mascons” (discrete spherical masses), while the other one models the central body as a polyhedron with a variable number of triangular faces. To check the reliability and performances of these two codes we have performed a series of tests and compared their results. First we have used the two algorithms to calculate the gravitational potential around non-spherical bodies, and have checked that the results are similar to each other and to those of other, more common, approaches; the polyhedron model appears to be somewhat more accurate in representing the potential very close to the body’s surface. Then we have run a series of orbit propagation tests, integrating several different trajectories of a test particle around a sample ellipsoid. Again the two codes give results in fair agreement with each other. By comparing these numerical results to those predicted by classical perturbation formulae, we have noted that when the orbit of the test particle gets close to the surface of the primary, the analytical approximations break down and the corresponding predictions do not match the results of the numerical integrations. This is confirmed by the fact that the agreement gets better and better for orbits farther away from the primary. Finally, we have found that in terms of CPU time requirements, the performances of the two codes are quite similar, and that the optimal choice probably depends on the specific problem under study.
Broucke, R. A. and D. J. Scheeres, Computing orbits around an ellipsoid of revolution, paper AAS 94-161, in Advances in the AstronauticalSciences, Spaceflight Mechanics 1994, Vol. 87, Part I, pp. 423–440, 1994.
Chapman, C. R., J. Veverka, P. C. Thomas, K. Klaasen, M. J. S. Belton, A. Harch, A. McEwen, T. V. Johnson, P. Helfenstein, M. E. Davies, W. J. Merline, and T. Denk, Discovery and physical properties of Dactyl, a satellite of the asteroid 243 Ida, Nature, 374, 783–785, 1995.
Everhart, E., An efficient integrator that uses Gauss-Radau spacings, in Dynamics of Comets: Their Origin and Evolution, edited by A. Carusi and G. B. Valsecchi, pp. 185–202, Reidel, 1985.
Kellog, O. D., Foundations of Potential Theory, Dover, 1954.
Geissler, P., J.-M. Petit, D. Durda, R. Greenberg, W. Bottke, M. Nolan, and J. Moore, Erosion and ejecta reaccretion on 243 Ida and its moon, Icarus, 120, 140, 1997.
German, D. and A. L. Friedlander, A simulation of orbits around asteroids using potential field modelling, paper AAS 91-182, in Advances in the Astronautical Sciences, Spaceflight Mechanics 1991, Vol. 75, Part II, pp. 1183–1201, 1991.
Heiskanen, W. A. and H. Moritz, Physical Geodesy, Freeman and Co., 1967. Laplace, P. S., Oeuvres de Laplace†, Vol. 2, Chapter 1, 1782.
Petit, J.-M., D. D. Durda, R. Greenberg, T. A. Hurford, and P. E. Geissler, The long-term dynamics of Dactyl’s orbit, Icarus, 130, 177–197, 1997.
Pravec, P. and G. Hahn, Two-period lightcurve of 1994 AW1: Indication of a binary asteroid?, Icarus, 127, 431–440, 1997.
Pravec, P., M. Wolf, and L. Šarounovà, Occultation/eclipse events in binary asteroid 1991 VH, Icarus, 133, 79–88, 1998.
Rossi, A. and M. Fulchignoni, Study of the environment around the Rosetta candidate target asteroids, Planet. Space Sci., 47(6–7), 873–881, 1999.
Roy, A. E., Orbital Motion,Hilger, Bristol, 1982.
Scheeres, D. J., S. J. Ostro, R. S. Hudson, and R. A. Werner, Orbits close to asteroid 4769 Castalia, Icarus, 121, 67–87, 1996.
Scheeres, D. J., S. J. Ostro, R. S. Hudson, E. M. DeJong, and S. Suzuki, Dynamics of orbits close to asteroid 4179 Toutatis, Icarus, 132, 53–79, 1998a.
Scheeres, D. J., F. Marzari, L. Tomasella, and V. Vanzani, ROSETTA mission: Satellite orbits around a cometary nucleus, Planet. Space Sci., 46, 649–671, 1998b.
Werner, R. A., The gravitational potential of a homogeneous polyhedron, Celest. Mech. Dyn Astr., 59, 253–278, 1994.
Werner, R. A. and D. J. Scheeres, Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia, Celest. Mech. Dyn. Astr., 65, 313–344, 1997.
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Rossi, A., Marzari, F. & Farinella, P. Orbital evolution around irregular bodies. Earth Planet Sp 51, 1173–1180 (1999) doi:10.1186/BF03351592
- Test Particle
- Central Body
- Semimajor Axis
- Orbital Evolution
- Triaxial Ellipsoid