Consider two point masses that are isolated in space and separated by a distance $x$. Give an expression that connects the gravitational force $F$ between them with the masses $M$ and $m$. State the name of any other symbol used.
A spacecraft is to be placed in a circular orbit around a spherical planet. The planet can be treated as isolated in space. The planet’s mass, taken to be concentrated at its centre, is $7.5 \times 10^{23}\ \text{kg}$. The radius of the planet is $3.4 \times 10^{6}\ \text{m}$.
The spacecraft is to travel in orbit at a height of $2.4 \times 10^{5}\ \text{m}$ above the planet’s surface. At this height, there is no atmosphere. Show that the orbital speed of the spacecraft is $3.7 \times 10^{3}\ \text{m s}^{-1}$.
For the spacecraft travelling from point B to point A, show that the change in gravitational potential energy of the spacecraft is $8.3 \times 10^9\,\text{J}$.
Using the changes in the spacecraft’s gravitational potential energy and kinetic energy, decide whether the spacecraft’s total energy rises or falls as it moves from point B to point A. A numerical answer is not needed.