The Motion of Hyperion
Nikolai O. Kirsanov
KIRSANOV@ITA.SPB.SU
Institute for Theoretical Astronomy,
Kutuzova 10, St. Petersburg, Russia
The Saturn's seventh satellite---Hyperion---from the very moment of its
discovery is an interesting object for celestial mechanics due to the
peculiarities of the satellite's motion caused by the attraction of
Titan---the nearest to the Hyperion and the most massive satellite of
Saturn. These satellites are in resonance one with another.
This case of resonance motion in the Saturn System is used to test a
technique of obtaining the Newcomb polynomials both in algebraic and
numerical modes. The technique gives easily the results of the action
of the Newcomb polynomials on the Laplace coefficients in the analytical
as well as numerical form.
These polynomials are used to obtain a development of the perturbation
function of Titan to the motion of Hyperion with respect to the powers
of the eccentricities and mutual inclination. The fact that the
technique allows us to use an analytical mode of the perturbation
function simplifies the procedure of calculation of the derivatives of
the latter.
The technique has been used also for computing the perturbation function
of an asteroid from Jupiter for several commensurabilities. To test the
technique the equations representing conditions of existence of
Schwarzschild-type periodic solutions of the restricted three-body
problem has been constructed and solved for the both cases of resonance
motion.
To improve the osculating orbital elements of Hyperion and Titan 566
photographic astrometric observations are used. The observations are
represented with the mean accuracy 0.2 arc sec for Titan and 0.4 arc sec
for Hyperion. Using these elements a numerical integration covering
period March 1995 -- March 1996 was carried out. The numerical values
of the elements were averaged by using polynomials of the first or the
second degree with respect to time. The mean elements obtained in this
way can be used to calculate approximate ephemerides. The formulae for
computing such ephemerides are given. The accuracy of the approximate
ephemerides is near 2 arc sec in both right ascension and declination.