[paulat (OP)]

I know that there are various "types" of satellite such as geostationary (geosynchronous), spy satellites, communications satellites, weather satellites etc. But how far out in space are they? Are some orbiting closer than others, and do their orbits eventually decay such that they will all fall back to Earth, or will they eventually wander off into space?

P

[ukmicky]

The altitude of a satelite is mainly dependent on what its required to do, ,how long you require it to last and whether frequent repair or resupply missions are required (ISS).

Most satelites are in low earth orbit which is a satelite orbiting below 2000 km between the radiation belt and the earths atmosphere. The ISS is the most well known example and orbits between 320 to 350 kms which is the best compromise for the station as any higher and it would require the shuttle to carry and burn to much fuel to reach it reducing its max payload,any lower and its orbital velocity would need to be increased and the earth gravitational influence would interfere with the experiments being carried out on board.
Due to the ISS's low orbit it requires frequent re-boosts to regain altitude because its low earth orbit causes it to drag against the earths atmosphere, the amount of altitude which it losses is dependent on how active the sun is. At times of high activity the earth is hit by lots of high energy solar flares which cause the earth atmosphere to swell increasing atmospheric density within the ISS's orbit.

Satelite's in high Geostationary orbits 23,000 miles about 37,000km  are beyond the van Allen radiation belt and need good radiation shielding and tend to be of the communication or weather type satelites as they need to remain permanently over one point of the earth.

[syhprum]

Not many are placed in higher orbits one exception being the SOHO solar obeservation satellite that orbits at the langrain L1 point about 1.5 million Km from the Earth at a stable point where the Earths and Suns gravity balance

[daveshorts]

The other reason that the ISS isn't any lower, is that where it is the atmosphere exerts a significant drag on it causing it to loose altitude, and to require frequent pushes from the shuttle and it's own rockets to stop it falling to earth. The lower it is the more atmosphere there is, the quicker it comes down.

[paulat (OP)]

Thank you for these excellent answers.

So how does one calculate how high / fast to put a satellite if you want it to be geostationary?

P

[ukmicky]

Hi paulat this may help
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Circular Geosynchronous Orbit
 If we wanted to know how high (the altitude) above the earth a Geosynchronous Satellite should be, we can use the formula below by inserting all the information we already know. Since we know that the earth turns every 24 hours (one day) and the period of an orbit is the time it takes to circle the earth once, the period for the satellite is approximately 24 hours. This makes the only unknown (a) in the equation below which is the orbit's semi-major axis. And, for a circular orbit the semi-major axis is just the radius.
Solving for (a) we get about 42,164 kilometers. By subtracting the radius of the earth we get the altitude. The earths radius is roughly 6378 kilometers. Therefore, the altitude is approximately 35,786 kilometers.

where
P: the orbital period
 (pronounced 'Pie'): mathematical constant, 3.141593
a: the semi-major axis of the orbit (same as the radius of the circle for a circular orbit!)
 (pronounced 'Mew'): gravitational parameter (a constant ~398601 km3 / Sec2 for Earth)