Other
Scientific paper
Sep 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987phdt........72h&link_type=abstract
Thesis (PH.D.)--UNIVERSITY OF LIVERPOOL (UNITED KINGDOM), 1987.Source: Dissertation Abstracts International, Volume: 50-10, Sec
Other
3
Scientific paper
Available from UMI in association with The British Library. In this work we aim to investigate the dynamics of the satellites Titan, Hyperion and Iapetus using both numerical and analytical methods. We wish to develop dynamical models which accurately represent the real satellite system and therefore we place emphasis upon comparison with observations and with other dynamical models. The thesis is in four parts: (1) Revision of Sinclair's (1974) theory of Iapetus. Sinclair's theory is compared with Sinclair and Taylor's (1985) numerical integration. Several important terms are found to be missing from the theory. These are Solar perturbations in the node and inclination with periods of 10 and 29 years. Rapaport's (1978) work on perturbations in the mean longitude by Titan due to a 5:1 near-commensurability is also examined and we show that he has overestimated the size of these terms. (2) Long-period motion of the orbit plane of Iapetus. We develop an analytical theory of the motion of Iapetus' orbit plane under the influence of Solar, Titan and oblateness perturbations using the device of the Laplacian plane. The theory is compared with observed values of the node and inclination over a period of 200 years, and the mass of Titan is determined by fitting the theory to the data. (3) Preparation of visual observations. We develop the procedures required to prepare micrometric observations of Saturn's satellites for comparison with a dynamical model. For each observation we require the topocentric position of Saturn at the instant of the observation (corrected for light-time), the precession -nutation matrix to enable us to convert coordinates from the integration reference frame to that of the True Equator and Equinox of date and the Besselian Day Numbers C and D to calculate the effect of aberration upon the observed positions. (4) Numerical integration of the motion of the outer satellites. We compare the observations prepared in (3) with a numerical integration of the motion of Titan, Hyperion and Iapetus over the period 1874 to 1947. An iterative least-squares method is used to calculate corrections to the parameters of the integration. 'Best-fit' values of these parameters are obtained, including values of J _2 and the mass of Titan.
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