The Earth can be treated as a uniform isolated sphere, with its mass of $6.0 \times 10^{24}\,\text{kg}$ taken to be concentrated at the centre. A satellite of mass $1200\,\text{kg}$ moves in a circular orbit around the Earth within the Earth’s gravitational field. The orbital period is $94\,\text{minutes}$.
(a)[1]
Define what is meant by gravitational field strength.
(b)[3]
Calculate the orbital radius of the satellite.
(c)
The rockets on the satellite are fired so that it moves into a different circular orbit with a period of $150\,\text{minutes}$. Any change in the satellite’s mass may be taken as negligible.
(c(i))[2]
Show that the new orbit has radius $9.4 \times 10^{6}\,\text{m}$.
(c(ii))[1]
State, with a reason, whether the satellite’s gravitational potential energy increases or decreases.
(c(iii))[3]
Calculate the magnitude of the change in the satellite’s gravitational potential energy.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Force exerted on each unit mass” …