State Newton’s law of gravitation in words.
A satellite travels in a circular orbit around a planet. Its orbit has radius $R$ and period $T$. The planet is a uniform sphere. Use Newton’s law of gravitation to show that $R$ and $T$ satisfy $4\pi^2 R^3 = GMT^2$, where $M$ represents the mass of the planet and $G$ is the gravitational constant.
Treat the Earth as a uniform sphere with mass $5.98 \times 10^{24}\,\text{kg}$ and radius $6.37 \times 10^6\,\text{m}$. A geostationary satellite orbits the Earth. Use the expression from part (b) to find the satellite’s height above the Earth’s surface.
A second satellite follows a circular orbit around the Earth with the same orbital radius and period as the satellite in (c). Calculate the angular speed of this satellite. Include a unit in your answer.
Although its orbital period is the same, this satellite’s orbit is not geostationary. Suggest two ways in which this satellite’s orbit could differ from the orbit of the satellite in (c).