The Geostationary Orbit

I’m was mucking out this blog’s blocked comments folder and unsurprisingly found a few from Mr Hine, a regular if sadly deranged correspondent.

One of his blocked comments begins

In the forlorn hope that Mr Hine might some day learn something scientifically correct I thought I’d repost this problem, which is very easy if you have a high school education in physics or applied mathematics but no doubt very difficult if you’re Mr Hine.

Verify that the radius of a circular geostationary orbit around the Earth is about 42,000 km, i.e. find the radius of a circular orbit around the Earth which has a period of 24 hours so that its orbital period matches the Earth’s rotation period, thus ensuring that an object travelling in such an orbit in the same direction as the Earth’s rotation is always above the same point on the Earth’s surface.

(You will need to look up the mass of the Earth.)

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A Problem with a Geostationary Orbit

I’ve been sorting through some old problem sets for my course on Astrophysics and Cosmology, and thought I would post this one in the Cute Problems folder for your amusement. The first part is easy, the second part not so much…

1. Verify that the radius of a circular geostationary orbit around the Earth is about 42,000 km, i.e. find the radius of a circular  orbit around the Earth which has a period of 24 hours so it is always above the same point on the Earth’s surface . (You will need to look up the mass of the Earth.)
2. Use the answer to (1)  to estimate what fraction of the Earth’s surface is visible at any  time from a satellite in such an orbit. (You will need to look up the radius of the Earth.)

Answers to (2) through the comments box please – and don’t forget to explain your working!

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