Q.What is the gravitational potential due to the Earth at a point which is at a height of $2R_E$ above the surface of the Earth? Mass of the Earth is $6\times10^{24}$ kg, radius of the Earth = 6400 km and $G=6.67\times10^{-11}$ N m^2 kg^-2.

Gravitational potential is the work done per unit mass in bringing a test mass from infinity to a point in a gravitational field, given for a point mass M by V = -GM/r.

Every mass creates a gravitational field around it, and every point in that field can be assigned a gravitational potential energy per unit mass, called the gravitational potential.

Definition: The gravitational potential V at a point in a gravitational field is the amount of work done in bringing a unit mass (1 kg) from infinity to that point, without giving it any kinetic energy (i.e., moved slowly/quasi-statically against the field).

Mathematically, if W is the work done in bringing a mass m from infinity to a point, then

V = W/m

For a point mass M (or a spherically symmetric mass, treated as concentrated at its centre), the gravitational potential at a distance r from it is

V = -GM/r

…

Gravitational potential is defined the same way as electric potential, but for gravity: it is the work needed per unit mass to bring a test mass from far away (infinity) to the given point, and works out to V = -GM/r for a point mass (or spherical mass) M.

Definition: The gravitational potential (V) at a point in a gravitational field is the amount of work done in bringing a unit mass (1 kg) from infinity to that point, without giving it any acceleration (i.e., quasi-statically, against the gravitational pull).

For a point mass (or uniform sphere) of mass M, at a distance r from its centre:

V = -GM/r

where G is the universal gravitational constant.

Key points:

• V is a SCALAR quantity (unlike gravitational field, which is a vector).
• SI unit: J/kg (or equivalently, m²/s²). …