A The acceleration of free fall at the surface of a planet is

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

1. a The acceleration of free fall at the surface of a planet is gg, and the radius of the planet is RR. Deduce that the period of a satellite in a very low orbit is given by T=2πRgT = 2\pi\sqrt{\frac{R}{g}} . (a) The acceleration of free fall at the surface of a planet is gg, and the radius of the planet is RR. Deduce that the period of a satellite in a very low orbit is given by T=2πRgT = 2\pi\sqrt{\frac{R}{g}} . (b) Given that g=4.5 m s−2g = 4.5 \text{ m s}^{-2} and R=3.4×106 mR = 3.4 \times 10^6 \text{ m}, deduce that the orbital period of the low orbit is about 91 minutes. (c) A spacecraft in orbit around this planet has a period of 140 minutes. Deduce the height of the spacecraft from the surface of the planet.

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