Physics 9702 · AS & A Level · Gravitational field

Gravitational field — practice question

You may treat the Earth as an isolated uniform sphere, with its mass of $6.0 \times 10^{24}\,\text{kg}$ 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 gravitational field strength at a point.

(b)[3]

Calculate the radius of the satellite’s orbit.

(c(i))[2]

The satellite’s rockets are fired so that it moves into a different circular orbit with a period of $150\,\text{minutes}$. The change in the satellite’s mass may be assumed to be negligible. Show that the radius of the new orbit is $9.4 \times 10^{6}\,\text{m}$.

(c(ii))[1]

State, with a reason, whether the gravitational potential energy of the satellite increases or decreases.

(c(iii))[3]

Determine the size of the change in the gravitational potential energy of the satellite.

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