The Jacobi constant for a cometary orbiter
Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway e-mail: [eirik.mysen;kaare.aksnes]@astro.uio.no
Accepted: 29 July 2005
The Jacobi constant of a probe under the gravitational attraction of a rotating irregular body is rederived for excited, but free rigid rotation of the central mass. A related Tisserand-like quantity is found to be sufficiently conserved for it to qualify as a pseudo-integral. The quantity's near constancy is shown to imply that certain regions in the space of the probe's cometocentric orbital elements are forbidden. In particular, based solely on this analysis, it is seen how collision with the comet nucleus is best avoided if the initial probe velocity lies in the plane normal to the nucleus' rotational spin. A conclusion which is of relevance to the Rosetta mission where the lander Philae is to be delivered by Rosetta in a possibly close prograde, and therefore probably shape unstable, orbit. At the comet's heliocentric distance when the lander is delivered, radiation and radial outgassing pressure do not significantly affect these conclusions for a nominal target nucleus in a worst-case scenario. The latter effect is seen to somewhat decrease the impact risk of prograde trajectories, making the more stable retrograde orbits slightly less safe.
Key words: celestial mechanics / space vehicles / comets: general / comets: individual: 67P/Churyumov-Gerasimenko / methods: analytical / methods: numerical
© ESO, 2005