The gravitational potential energy U r can be calculated by finding the sum of gravitational potential energy of each pair of particles. U Gm m Gm m Gm m Gm m Gm m Gm m Here r , r ... are distance between pair of particles U Gm m Gm m Gm m Gm m Gm m Gm m U G m m m m m m m m m m m m If all the masses are equal, then M U GM U GM . ACCELERATION DUE TO GRAVITY OF THE EARTH When objects fall on the Earth, the acceleration of the object is towards the Earth.
From Newton’s second law, an object is accelerated only under the action of a force. In the case of Earth, this force is the gravitational pull of Earth. This force produces a constant acceleration near the Earth’s surface in all bodies, irrespective of their masses. The gravitational force exerted by Earth on the mass m near the surface of the Earth is given by F GmM e e = − ˆ Now equating Gravitational force to Newton’s second law, - - - - Unit Gravitation Figure .
(a) Mass at a height h from the center of the Earth R e h O g GM h e e g GM h e e If h R e We can use Binomial expansion. Taking the terms upto first order g GM h e e g g h R e ( . ) We find that g g . This means that as altitude h increases the acceleration due to gravity g decreases.
ma GmM e e = − ˆ hence, acceleration is, a GM e e = − ˆ ( . ) The acceleration experienced by the object near