CAIE A-Level Physics A2 13.2.3 Circular…al Force

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A planet may be assumed to be a uniform sphere. It has gravitational potential $\phi$ at distance r from the centre of the planet.

The variation with $\frac{1}{r}$ of $\phi$ is shown in Fig. 1.1.

Fig. 1.1

The period of rotation of the planet is 0.72 Earth days.

A satellite in orbit around the planet remains above the same point on the surface of the planet.

Use the mass of the planet in (b)(i) to determine the radius R of the orbit of the satellite.

either $G M m / r^{2}=m r \omega^{2} \quad$ and $\omega=2 \pi / T$

or $G M m / r^{2}=m v^{2} / r$ and $v=2 \pi r / T$

or $G M m / r^{2}=4 \pi^{2} m r / T^{2}$ $R^{3}=6.67 \times 10^{-11} \times 8.8 \times 10^{25} \times(0.72 \times 24 \times 60 \times 60)^{2} / 4 \pi^{2}$ $R=8.3 \times 10^{7} \mathrm{~m}$

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CAIE A-Level Physics A2 13.2.3 Circular Orbits in Gravitational Fields By Relating the Gravitational Force Topic Practice

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