A satellite of mass m is in a circular orbit of radius R 2around a spherical pla

Question

A satellite of mass m is in a circular orbit of radius R2around a spherical planet of radius R1 of mass M1. ( R2 is measured from the center of the planet, not its surface.) Use G for the universal gravitational constant.

A; Find the kinetic energy of this satellite, K.

Express the satellite's kinetic energy in terms of G, m, M1, R1, and R2.

B;Find U, the gravitational potential energy of the satellite. Take the gravitational potential energy to be zero for an object infinitely far away from the planet.

Express the satellite's gravitational potential energy in terms of G, m, M1, R1, and R2.

C;What is the ratio of the kinetic energy of this satellite to its potential energy?

Express K/U in terms of parameters given in the introduction.

Explanation / Answer

Circular orbits arise whenever the gravitational force on a satellite equals the centripetal force needed to move it with uniform circular motion.

Fc = Fg

mv2/ R2 = G M1 m/ R22

V2 = G M1/R2

Kinetic Energy = (1/2)mv2

                              = (1/2)mGM1/R2

Gravitational Potential Energy= - GM1m/R2

Kinetic Energy = -(1/2)Gravitational Potential Energy

Ratio : Kinetic energy/ Gravitational Potential Energy= -(1/2)

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