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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In the Dark 
May 16, 2020 at 5:30 pm
Pedantic quibble; the Earth’s rotation period relative to the “fixed stars” is 23h56m – the sidereal day. It is 24hours (a solar day) in a frame of reference which rotates once per year as the Earth orbits the Sun. That means the orbital period in GEO is 23h56m rather than 24h.
May 16, 2020 at 8:19 pm
Easy peasy pudding and Pie! (As my positional Astormony tutor used to say)
May 17, 2020 at 5:22 pm
I loved the idea of, once you have a convenient geostationary station, to build an elevator and do away with those silly rockets.
May 17, 2020 at 9:32 pm
Konstantin Tsiolkovsky (hope I have the name correct) proposed a tower to geostationary orbit. That was in 1895. Teska may have had the same idea. The idea to attach it to a geostationary satellite dates to 1957, from Yuri Artsutanov. Clarke published his novel 20 years later.
May 21, 2020 at 5:59 pm
… and another – GPS satellite are in non-equatorial 12hour orbits, not GEO!!
October 19, 2020 at 3:16 pm
Very interesting post. It would be nice to have the elevator.