Q.The kinetic energy of the satellite orbiting around the earth is :

For an orbiting satellite, KE = GMm/(2r) and PE = -GMm/r, so the kinetic energy is smaller in magnitude than the potential energy.

For a satellite of mass m orbiting a planet of mass M at radius r, the gravitational force provides the centripetal force:

GMm/r^2 = mv^2/r which gives v^2 = GM/r

Kinetic energy:

KE = (1/2) m v^2 = GMm/(2r)

Gravitational potential energy:

PE = -GMm/r

Comparing magnitudes: the magnitude of PE = GMm/r = 2 x [GMm/(2r)] = 2 x KE

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For any satellite in a circular orbit, KE/|PE| = 1/2.

For a satellite of mass m orbiting a planet of mass M at radius r:

Gravitational potential energy: PE = -GMm/r

Orbital speed is found from the centripetal force condition: GMm/r^2 = mv^2/r, so v^2 = GM/r

Kinetic energy: KE = (1/2)mv^2 = (1/2)m(GM/r) = GMm/(2r)

Ratio of kinetic energy to potential energy (taking magnitudes, since PE is negative):

KE/|PE| = [GMm/(2r)] / [GMm/r] = 1/2 …