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Study D.1 Gravitational fields conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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A satellite powered by solar cells directed towards the Sun is in a polar orbit about the Earth.

The satellite is orbiting the Earth at a distance of 6600 km from the centre of the Earth.

Determine the orbital period for the satellite.

Mass of Earth $=6.0 \times 10^{24} \mathrm{~kg}$

$\begin{aligned} & \frac{m v^{2}}{r}=G \frac{M m}{r^{2}} & \text { leading to } T^{2}=\frac{4 \pi^{2} r^{3}}{G M} & T=5320 \text { «s» } \end{aligned}$

Alternative 2
$\begin{aligned} & \text { « } V=\sqrt{\frac{G m_{E}}{r}} \text { » }=\sqrt{\frac{6.67 \times 10^{-11} \times 6.0 \times 10^{24}}{6600 \times 10^{3}}} \text { OR } 7800 \text { « } \mathrm{ms}^{-1} \text { » } & \text { distance }=2 \pi r=2 \pi \times 6600 \times 10^{3} \text { « } \mathrm{m} \text { » or } 4.15 \times 10^{7} \text { « } \mathrm{m} \text { » } & \text { « } T=\frac{d}{v}=\frac{4.15 \times 10^{7}}{7800} \text { » }=5300 \text { « } \mathrm{S} \text { » } \end{aligned}$

Accept use of $\omega$ nistead of v

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Ion-thrust engines can power spacecraft. In this type of engine, ions are created in a chamber and expelled from the spacecraft. The spacecraft is in outer space when the propulsion system is turned on. The spacecraft starts from rest.

The mass of ions ejected each second is $6.6 \times 10^{-6} \mathrm{~kg}$ and the speed of each ion is $5.2 \times 10^{4} \mathrm{~m} \mathrm{~s}^{-1}$ . The initial total mass of the spacecraft and its fuel is 740 kg . Assume that the ions travel away from the spacecraft parallel to its direction of motion.

(a)

On arrival at the planet, the spacecraft goes into orbit as it comes into the gravitational field of the planet.

[ 3 ]

(i)

Outline what is meant by the gravitational field strength at a point.

[ 2 ]

(ii)

Newton's law of gravitation applies to point masses. Suggest why the law can be applied to a satellite orbiting a spherical planet of uniform density.

[ 1 ]

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IB Physics SL D 1 Gravitational Fields Topic Practice

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