Intensity of gravitational field at a distance r from a body of mass M is given by
Eg or I = GM / r 2
It is a vector quantity and its direction is towards the centre of gravity of the body .
Its S1 unit is N / m and its dimensional formula is [ LT -2 ]. Gravitational mass Mg is defined by Newton ’ s law of gravitation .
Mg = Fg / g = W / g = Weight of body / Acceleration due to gravity ∴ ( M1 ) g / ( M2 ) g = Fg1g2 / Fg2g1
Gravitational Potential
Gravitational potential at any point in gravitational field is equal the work done per unit mass in bringing a very light body from infinity to that point .
It is denoted by Vg . Gravitational potential , Vg = W / m = – GM / r
Its SI unit is J / kg and it is a scalar quantity . Its dimensional formula is [ L 3 r - 2 ].
Since work W is obtained , that is , it is negative , the gravitational potential is always negative .
Gravitational Potential Energy
Gravitational potential energy of any object at any point in gravitational field is equal to the work done in bringing it from infinity to that point . It is denoted by U .
Gravitational potential energy U = – GMm / r