Show that the effect of a uniform distribution of dust of density p about the su

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Show that the effect of a uniform distribution of dust of density p about the sun is to add to the gravitational attraction of the sun on a planet of mass m an additional attractive central force F = -mkr, where k = 4 /3pG. If the mass of the sun is M. find the angular velocity of revolution of the planet in a circular orbit of radius r0, and find the angular frequency of small radial oscillations. Hence show that if F ' is much less than the attraction due to the sun. a nearly circular orbit will be approximately an ellipse whose major axis processes slowly with angular velocity p = -2 p Gr30/M

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