Dynamical Theory of the Capture of Satellites And of the Division of Nebulae Und
Dynamical Theory of the Capture of Satellites And of the Division of Nebulae Und
T J J Thomas Jefferson Jackson See
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It should not, however, be concluded that retro- grade motion near these planets is wholly excluded; but merely that the chances of its surviving are very slight. VIII. Theoretical and observed distances of satellites in the solar system. In the theory of the closed surfaces about the planets it is shown that the superior limit of distance for a satellite which can just be retained by a planet is found by the condition that the neck of the hour-glass figure shall contract till the two separate ...surfaces meet in a point between the sun and planet, on the line SJ. This leads to a quintic equation, which, for small bodies such as those in our solar system, is shown to be capable of reduction to the simple form (» Periodic Orbits », p. 109): ? = 57+. P + V. (l5) where v is the mass of the Sun in terms of the planet's mass as unity, or the reciprocal of the planet's mass as ordinarily expressed. The following table gives the principal data for the planets and satellites of the solar system, and shows the comparative magnitude of the closed surfaces about the several bodies, and what parts of these spaces are known to be occupied.
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