Gravitational Potential Energy : Gravitational potential energy is the energy acquired by an object due to a shift in its position when it is present in a gravitational field. In simple terms, it can be stated that gravitational potential energy is an energy that is linked to gravity or gravitational force.The gravitational potential energy equation is: GPE = m × g × h, m = mass in kilograms, g = acceleration (9.8 ms-2 on Earth) h = height. Gravitational Potential Energy Derivation Equation -: Let us consider an object, of mass M, which is placed along the x-axis, and there is a test mass m at infinity. Work done at bringing it without acceleration through a minimal distance (dx) is given by: dw = Fdx Here, F is an attractive force and towards the negative x-axis direction is the displacement. Therefore, F and dx are in a similar direction. dw=(GMm/x²)dx Now , we are Intergrating both the side of above equ, w=∫∞r(GMm/x2)dx w=−[GMm/x] w=−[GMmr]−(−GMm/∞) w=−[GMm/r] As the potential energy is stored as U, the gravitational potential energy at ‘r’ distance from the object having mass ‘M’ is: U = - GMm/r Now if another mass inside the gravitational field moves from one point inside the field to another point of the field of mass M, the other mass experiences a change in potential energy given by: ΔU = GMm (1/ri–1/rf) ( ri= initial position and rf= final position )If ri > rf then ΔU is negative. For calculating the potential energy of earth moon system by the help of given fomula method: U=-(G*M1*M2)/R Where: - U is the gravitational potential energy - G is the gravitational constant (6.67 x 10^-11 N·m^2/kg^2) - M1 is the mass of the Earth (5.97 x 10^24 kg) - M2 is the mass of the Moon (7.34 x 10^22 kg) - r is the distance between the Earth and Moon centers (3.84 x 10^8 m) Plugging in these values gives the total gravitational potential energy of approximately 4.6 x 10^29 Joules for the Earth-Moon system.

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