Geostationary satellites

I just completed one of the questions in the physics assignment I’m working on and was convinced I must have the wrong answer. The question involved finding the height at which a geostationary satellite orbits – ie one which orbits the earth in 24 hours thus effectively remaining stationary above a point on earth.

Now I’ve see heaps of diagrams of satellites in orbit where the earth covers most of the diagram and the satellite orbits are circles seemingly just above the earth’s surface, so I was expecting an answer which was small in comparison to earth’s radius. What I got was an answer that is some five and a half times the earth’s radius – so I drew a rough scale diagram and it looked nothing like what I expected.

After some research on the Internet I discovered that those diagrams I was used to seeing were of satellites in Low Earth Orbit (just above most of the earth’s atmosphere at between 300 to 1000 kms) and that a geostationary satellite really does orbit at nearly 40,000 kilometres above the earth’s surface.

Somehow it annoys me to realise I have reached my early forties without knowing this – almost as much as it did when I learnt a year or so ago that the earth’s magnetic field is produced by the rotation of its molten core, but that’s another story.