The space in the surrounding of any body in which its gravitational pull can be experienced by other bodies is called gravitational field.

Intensity of Gravitational Field

The gravitational force acting per unit mass at Earth any point in gravitational field is called

intensity of gravitational field at that point.

It is denoted by E_g or I.E_g or I = F / m

Intensity of gravitational field at a distance r from a body of mass M is given by

E_g or I = GM / r²

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 M_g is defined by Newton’s law of gravitation.

M_g = F_g / g = W / g = Weight of body / Acceleration due to gravity

∴ (M₁)g / (M₂)g = F _g1g2 / F _g2g1

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 V_g.

Gravitational potential, V_g = W / m = – GM / r

Its SI unit is J / kg and it is a scalar quantity. Its dimensional formula is [L³ 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

The negative sign shows that the gravitational potential energy decreases with increase in distance.

Gravitational potential energy at height h from surface of earth

Uh = – GMm / R + h = mgR / 1 + h/R