Other
Scientific paper
Nov 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976icar...29..427g&link_type=abstract
Icarus, vol. 29, Nov. 1976, p. 427-433.
Other
11
Gravitational Effects, Laplace Equation, Natural Satellites, Orbit Perturbation, Uranus (Planet), Uranus Satellites, Albedo, Ariel, Density, Eccentric Orbits, Mass, Miranda, Satellite Orbits, Umbriel
Scientific paper
It is noted that the mean motions of Uranus' satellites Miranda, Ariel, and Umbriel exhibit nearly the same commensurability as that observed among the three inner Galilean satellites of Jupiter, which is referred to as the Laplace relation. The theory of the Laplace relation among the Uranian satellites is completed by generating terms due to the first-order portions of the disturbing functions, using a generalization of Souillart's approach for the Galilean satellites. The theory is compared with past observations of Miranda's mean motion to obtain an upper limit on the product of the masses of Ariel and Umbriel. This mass limit is examined in terms of implied density and albedo constraints for comparison with the bulk properties of other solar-system bodies. The results suggest that if Ariel and Umbriel both have the same geometric albedo and density, then Ariel's radius would have to be less than about 1200 km and Umbriel's, less than about 800 km.
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