Find out the total energy of earth in its circular orbit around the sun in terms of gravitational constant
Let R be the total distance between the earth and the sun. If and are the mass of earth and sun respectively, the gravitational force of motion of earth and sun is given by
where G is the gravitational constant. Since the centripetal force balances the gravitational force of attraction, we have
v being the velocity with which earth is moving. Hence we have
Therefore kinetic energy of earth in motion is
As we know that , force in terms of potential energy is
Now total energy of the earth in the orbit around the sun is
This is the required expression.