A constant potential energy of a satellite is given as PE =r( KE ) where, PE = potential energy and KE = kinetic energy. The value of r will be

Step-by-step solution

For a satellite orbiting a planet of mass M at a distance R with orbital speed v , the gravitational potential energy is given by PE = - GMm R . The kinetic energy of the satellite is given by KE = 1 2 mv^2 . Since the centripetal force is provided by the gravitational force, we have mv^2 R = GMm R^2 , which implies mv^2 = GMm R . Substituting this into the expression for kinetic energy, we get KE = 1 2 ( GMm R ) = GMm 2R . Comparing the expressions for potential energy and kinetic energy, we observe that PE = - GM