Physics A2 · Gravitational fields. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Newton's law of gravitation says that two point masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. For a point outside a uniform sphere, the sphere behaves as if all its mass were at its centre, so r is always measured from centre to centre.
For a satellite in a circular orbit, the gravitational force is the centripetal force. Setting GMm/r2 equal to mv2/r shows that the mass of the satellite cancels: speed and period depend only on M and r.
A geostationary satellite stays above the same point on the Earth. Its period is 24 hours, it moves from west to east, and it is directly above the Equator.
Students use the height above the surface as r, or forget to square r. Always add the radius of the planet to the height, and change kilometres to metres first.
Answer: About 7.1 × 103 m s−1.
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