Astronomy and Astrophysics – Astronomy
Scientific paper
Nov 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999cemda..75..185s&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, v. 75, Issue 3, p. 185-200 (1999).
Astronomy and Astrophysics
Astronomy
1
Resonance, Periodic Orbit, Saturn Satellites
Scientific paper
The motion of Hyperion is an almost perfect application of second kind and second genius orbit, according to Poincaré’s classification. In order to construct such an orbit, we suppose that Titan’s motion is an elliptical one and that the observed frequencies are such that 4n H-3n T+3n ω=0, where n H, n T are the mean motions of Hyperion and Titan, n ω is the rate of rotation of Hyperion’s pericenter. We admit that the observed motion of Hyperion is a kbar T periodic motion ( {bar T = 2π /bar n} ) such as n_{H} = N_{H} \cdot bar n/k;{3n_{T} = N_{T} \cdot bar n/k;n_ω = - bar n/k . Then, (4N_{H} - N_{T} - 3)bar n/k = 0 .N H, N T, k∈ N +. With that hypothesis we show that Hyperion’s orbit tends to a particular periodic solution among the periodic solutions of the Keplerian problem, when Titan’s mass tends to zero. The condition of periodicity allows us to construct this orbit which represents the real motion with a very good approximation.
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