An orbiting satellite stays over a certain spot on the equator of (rotating) Earth. What is the altitude of the orbit (called a geosynchronous orbit?

Explanation

To find the altitude of a geosynchronous orbit, we can follow these steps:

### Step 1: Understand the Concept of Geosynchronous Orbit
A geosynchronous orbit is one where a satellite has an orbital period equal to the rotation period of the Earth, which is 24 hours (or 86400 seconds). This means the satellite remains over the same point on the equator.

### Step 2: Use Kepler's Third Law
Kepler's Third Law states that the square of the orbital period (T) of a satellite is directly proportional to the cube of the semi-major axis (r) of its orbit:
\[ T^2 = \frac{4\pi^2}{GM} r^3 \]
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