Physics 9702 · AS & A Level · Gravitational potential

Gravitational potential — practice question

A satellite with mass $m_s$ moves in a circular orbit of radius $x$ around the Earth. The Earth can be treated as an isolated uniform sphere whose mass $M$ is concentrated at its centre.
(a(i))[3]

Show that the satellite's kinetic energy $E_K$ can be expressed as $E_K = \dfrac{GMm_s}{2x}$, where $G$ is the gravitational constant. Explain your working.

(a(ii))[1]

State an expression, in terms of $G$, $M$, $m_s$ and $x$, for the satellite's potential energy $E_P$.

(a(iii))[2]

Using your answers to (i) and (ii), derive an expression for the satellite's total energy $E_T$.

(b(i))[1]

Use your answers in (a) to state, for the satellite, whether the total energy increases, decreases or stays constant when small resistive forces acting on the satellite make the radius of its circular orbit change.

(b(ii))[1]

Use your answers in (a) to state, for the satellite, whether the radius of orbit increases, decreases or stays constant when small resistive forces act on the satellite.

(b(iii))[1]

Use your answers in (a) to state, for the satellite, whether the potential energy increases, decreases or stays constant when small resistive forces act on the satellite.

(b(iv))[1]

Use your answers in (a) to state, for the satellite, whether the kinetic energy increases, decreases or stays constant when small resistive forces act on the satellite.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Gravitational force supplies the centripetal force

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