3)What is the ratio of the kinetic energy of this satellite to itspotential ener

Question

3)What is the ratio of the kinetic energy of this satellite to itspotential energy?
any help would be appreciated A satellite of mass m is in a circular orbit ofradius R2around a spherical planet ofradius R1 made of a material withdensity rho. ( R2 is measured from the center of theplanet, not its surface.) Use G for the universal gravitational constant. 1)Find the kineticenergy of this satellite, K. Express the satellite's kinetic energy in terms of G, m, pi, R1, R2, and rho. 2)Find U, the gravitational potential energy of thesatellite. Take the gravitational potential energy to be zero foran object infinitely far away from the planet. Express the satellite's gravitational potential energy in termsof G, m, pi, R1, R2, and rho. 3)What is the ratio of the kinetic energy of this satellite to itspotential energy? Express frac{K}{U} in terms ofparameters given in the introduction. any help would be appreciated

Explanation / Answer

(a)   We know that : .          K.E = (1/2) m vo2 .                 = (1/2) m (g R2) .                  = (1/2) m ( G M / R2 )   --------------(1) . Here Mass of Spherical planet is :   m = Density * volume = * (4/3) R13 . Hence equation (1) becomes ; .       K.E   =   0.5 * m [ ( G * 4 R13 ) / 3 R2 ] . (b)   Potential energy is : .        U     =  G m M /R22 .                =  [ G m * 4 R13   / 3*R22   ] . (c)    K.E / U is : .         K.E / U = 0.5 * m [ ( G * 4 R13 ) / 3 R2 ]/   [ G m * 4 R13   / 3*R22   ] .                      = ---------- . Solve it . Hope this helps u!

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