system
Given the following post, respond as if you're commenting on Reddit:
human
Why can geosynchronous satellites be only at a certain altitude?
gpt
A geosynchronous satellite is one that is always over the same place on the surface of the Earth.  This means that the period of the satellite's orbit must be equal to the period of the Earth's rotation (i.e., 1 day).  A few very simple calculations using Newton's Law of Gravity and the period of circular orbits tells us that orbital period is proportional to orbital radius to the 3/2 power, or

T α r^(3/2) 

Given a value for T (in this case, 1 day), there is only one value for r, which defines the altitude for geosynchronous orbit.  It works out to about 35,786 km above the surface.

Edit: 3/2, not 2/3.