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. Treat the Earth as an isolated uniform sphere whose mass $M$ is concentrated at its centre.
(a(i))[3]

Show that the kinetic energy $E_K$ of the satellite is given by the expression $E_K = \frac{GMm_s}{2x}$, where $G$ is the gravitational constant. Include your working.

(a(ii))[1]

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

(a(iii))[2]

Using answers from (i) and (ii), derive an expression for the total energy $E_T$ of the satellite.

(b(i))[1]

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

(b(ii))[1]

Use your answers in (a) to state, for the satellite, whether the radius of orbit increases, decreases or remains constant.

(b(iii))[1]

Use your answers in (a) to state, for the satellite, whether the potential energy increases, decreases or remains constant.

(b(iv))[1]

Use your answers in (a) to state, for the satellite, whether the kinetic energy increases, decreases or remains constant.

Worked solution & mark scheme

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

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