Define gravitational field at a point.
Fig. 3.1 depicts a lone point mass of mass $M$. Point P is located a distance $x$ from the mass. By using the force that the point mass exerts on a test mass of mass $m$ placed at P, derive an expression for the gravitational field strength $g$ at P in terms of $M$ and $x$. State any other symbols you use.
On Fig. 3.1, draw an arrow to show the direction of the gravitational field at P.
Point Q is located at distance $\frac{x}{2}$ from the point mass, on the opposite side of the mass from P, as illustrated in Fig. 3.2. Compare the gravitational field at Q with that at P.
Two identical isolated uniform spheres X and Y each have radius $R$. Their centres are separated by distance $L$, as shown in Fig. 3.3. Point P lies on the line joining the centres of X and Y and has variable displacement $x$ from the centre of sphere X. The gravitational field strength at the surface of each sphere is $g_0$. On Fig. 3.4, sketch how the gravitational field $g$ at point P varies with $x$ between $x = R$ and $x = L - R$.