Abstract
THE motion of Hyperion, the seventh satellite of Saturn, is of special interest from the commensurability of its period with that of Titan, the two being in the ratio of 4 to 3. The late Prof. Newcomb wrote an important paper, “On the Motion of Hyperion: a New Case in Celestial Mechanics.” The present work carries the investigation some steps further. The differential equations are broken up into partial systems, giving the inequalities proportional to the successive powers of e′ the eccentricity of Titan's orbit. Newcomb had regarded this development as impracticable, but the present work demonstrates the contrary. The development is at present carried only to the first power of e′, which suffices to give a close approximation to the observed inequalities. For example, the ratio of masses of Saturn and Titan is deduced as 3986, which is close to the values 4172, 4125 found by Eichelberger and Santer respectively. Incidentally, we may note that the mass of Titan is about twice that of the moon, and two-thirds that of Mercury. Also the coefficient of the large inequality that depends on Titan's eccentricity is found as 12.96°, not differing much from the value 14.0° found by H. Struve from observation.
Investigations in the Theory of Hyperion.
By Dr. J. Woltjer jun. Pp. iii + 71. (Leyden: E. J. Brill, 1918.)
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CROMMELIN, A. Investigations in the Theory of Hyperion . Nature 105, 675 (1920). https://doi.org/10.1038/105675a0
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DOI: https://doi.org/10.1038/105675a0
