**3. Gravitational potential**

The intensity of gravitational field depends only on position, the analysis of such fields can often be simplified by using the concept of potential.

The potential at a point in a gravitational field is defined as the work required for arbitrary reference point to the point in question.

The acceleration at a distance (r) from (p) is

$$=\mathbf{Gm}/\mathbf{r}^2\tag{4}$$

The work necessary to move the unit mass a distance (ds) having a component (dr) in the direction of (p) is

$$= \left(\mathbf{Gm}\_1/\mathbf{r}^2\right)\mathbf{dr} \tag{5}$$

The work (U) done in moving the mass from infinity to a point (O), (**Figure 1**) in the gravitational field of (m1) is

$$\mathbf{U} = \mathbf{G} \mathbf{m}\_1 \mathbf{J}^{\mathbb{R}} \text{ d}\mathbf{r}/\mathbf{r}^2 \tag{6}$$

$$U = Gm\_1 \frac{1}{r}|\_a^R = \frac{-Gm\_1}{R} \tag{7}$$

$$\mathbf{U} = \mathbf{Gm}/\mathbf{R} \tag{8}$$

The quantity (Gm1/R) is the gravitational potential. It is depend only on the distance (R) from the point source (m1). By differentiating both sides of the above equation it can be seen that the gravitational acceleration is the derivative of the potential with respect to (r).

Any surface along with the potential is constant, so it is referred as an equipotential surface.

Sea level, for example, is an equipotential surface, even though the actual force of gravity varies along the sea surface by more than (0.5%) between the equator and either of the poles.
