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Please help me with this problem: http://session.masteringphysics.com/problemAsset/1007466/22/5614.jpg http://session.masteringphysics.com/problemAsset/1007466/22/5614.jpg A satellite of mass "m" is in a circular orbit ofradius R_2 around a spherical planet of radius R_1 madeof a material with density "rho". ( R_2 is measured from thecenter of the planet, not its surface.) Use G for theuniversal gravitational constant. Part A: Find the kinetic energy of this satellite,K. Part B: Part C: What is the ratio of the kinetic energy ofthis satellite to its potential energy? Express K/U in terms ofparameters given in the introduction. What is the ratio of the kinetic energy ofthis satellite to its potential energy? Express K/U in terms ofparameters given in the introduction.

Explanation / Answer

(a) for any object in circularorbit        K = (1/2) G M m / r     so in your case .          M = (4/3) pi rho(R_1)3            and    r is R_2   so .    K =   2 G pi rho (R_1)3 m /  3(R_2) . (b) the potential energy is the same amount but doubledand negative: .    U = - 4 G pi rho (R_1)3 m /  3(R_2) . (c) for any circular orbit, the ratio of K/U is      -1/2

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