system
Given the following post, respond as if you're commenting on Reddit:
human
How long would it take to fall from geosynchronous orbit?

I'm assuming the object is correct distance from the earth to be in geosynchronous orbit but it's angular velocity is zero.
gpt
You can find this from conservation of energy. Let r*_g_* be the radius of a geosynchronous orbit and R be the radius of the Earth. Conservation of energy says:

-GM/r*_g_* = -GM/r + v^(2)/2,

where v is the speed of the object when it is at radius r. Rearranging:

dr/dt = sqrt[2GM(1/r - 1/r*_g_*)]

dt = [2GM(1/r - 1/r*_g_*)]^(-1/2) dr.

Now we just have to integrate this equation, from 0 to T on the left side, and from r*_g_* to R on the right side.

I integrated it numerically using WolframAlpha and got about 4 hours.