Potential Energy Between Two Point Masses and System of Point Masses
Gravitational Potential Energy between two point masses
Definition: Gravitational potential energy is energy an object possesses because of its position in a gravitational field. The most common use of gravitational potential energy is for an object near the surface of the Earth where the gravitational acceleration can be assumed to be constant at about 9.8m/s2. Since the zero of gravitational potential energy can be chosen at any point (like the choice of the zero of a coordinate system), the potential energy at a height h above that point is equal to the work which would be required to lift the object to that height with no net change in kinetic energy.
Two masses m1 and m2 separated at a distance r has potential energy: U=rGm1m2
Gravitational Energy of a System
Example: A planet of mass m1 revloves round the sun of mass m2. The distance between the sun and the planet is r. Considering the motion of the sun find the total energy of the system assuming the orbits to be circular.
Solution: Velocity of planet is v=rGm2 And the total energy is P.E+K.E ⇒R−Gm1m2+21mv2=2R−Gm1m2