Given that the mass of Earth is 5.98x1024 kg, what is the orbital radius of a satellite that has an orbital period of exactly one day (assume that a day is exactly 24 hours in length)?

The orbital radius is approximately 42,259 kilometers.

Explanation:

From Newton's Law of Gravitation we find that acceleration experimented by the satellite (), measured in meters per square second, is defined by:

(1)

Where:

- Gravitational constant, measured in cubic meters per kilogram-square second.

- Mass of Earth, measured in kilograms.

- Orbital radius, measured in meters.

By supposing the satellite rotates at constant speed and in a circular path, we find that acceleration is entirely centripetal and can be defined in terms of period, that is:

Where is period, measured in seconds.

If we know that , and , then orbital radius of the satellite is:

The orbital radius is approximately 42,259 kilometers.

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