Using the definition of gravitational potential, explain why gravitational potential is a negative quantity.
Stars A and B have surfaces that are $1.4 \times 10^{12}\,\text{m}$ apart, as shown in Fig. 1.1. Point $P$ is located on the straight line joining the centres of the two stars. The distance $x$ of point $P$ from the surface of star A can be changed. Fig. 1.2 shows how the gravitational potential $\phi$ at point $P$ varies with distance $x$.
A rock of mass $180\,\text{kg}$ travels along the line joining the centres of the two stars, moving from star A towards star B. Use information from Fig. 1.2 to calculate the change in kinetic energy of the rock as it goes from the point where $x = 0.1 \times 10^{12}\,\text{m}$ to the point where $x = 1.2 \times 10^{12}\,\text{m}$. State whether the change is an increase or a decrease.
At the position where $x = 0.1 \times 10^{12}\,\text{m}$, the rock has speed $v$. Find the smallest value of $v$ for which the rock still reaches the point where $x = 1.2 \times 10^{12}\,\text{m}$.