A geosynchronous satellite is one that appears to remain over one spot on

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Earth......? Assume that a geosynchronous satellite has an orbital radius of 4.43 * 10^7 m.
Calculate its period
calculate its period in hours
 
well, without computing anything, if you want it to 'remain' over one spot is has to rotate around earth, matching the earth rotation

so its period is 24h (almost)

if you really want to compute,

T = 2pi*sqrt(a^3/ mu)

mu = gravitational constant = 398,600 .4418 km^3/s^2
a = orbital radius 4.43 * 10^4 km

T = 25.77 (in this case)

radius for true GEO orbit = 42164 km
 
If it is geosynchronous it doesn't matter what its altitude is its period is the same as a Sidereal day 23h 56m 04s
 
*** A geosynchronous satellite is one
*** that appears to remain over one spot on Earth

Incorrect. That's geostationary satellite.
A geosynchronous satellite is one that has orbital period equal to one siderial day. A geosynchronous satellite does not need to have circular orbit nor does it need to remain in equatorial plane.

Naturally it's better to have a satellite at the same point in the sky and at the same distance, but there are very few positions available for such satellites, only 120 positions separated by 3 degrees. So for many applications people have to settle for geosyncronous sattelites.
 
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