Problem 45553. SatCom #4: Satellite Orbit Altitude

Created by Mark Posen

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Satellite and Space Engineering - Problem #4This is part of a series of problems looking at topics in satellite and space communications and systems engineering.Determine the altitude (height above the surface of the Earth) for a satellite in a circular Earth orbit with a known orbit period.You are given the satellite orbit period (in s). Calculate the orbit altitude (in km).You should take the radius of the Earth to be 6371km, the mass of the Earth to be 5.9722e24 kg and Newton's Universal Gravitational Constant to be 6.6743015e-11 m3/kg/s.Hints: 1) Newton's Law of Universal Gravitation will tell you the force between the satellite and the Earth (see: <a href = "https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation">https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation</a>); 2) The centripetal force maintaining the orbit (see: <a href = "https://en.wikipedia.org/wiki/Centripetal_force#Formula">https://en.wikipedia.org/wiki/Centripetal_force#Formula</a>) should be equal to the gravitational force; 3) Hmmm... but what about the mass of the satellite?Example: The altitude of a geostationary satellite, with orbit period 86164.0905 s is around 35,793 km.Some future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!

*Satellite and Space Engineering - Problem #4*

_This is part of a series of problems looking at topics in satellite and space communications and systems engineering._

Determine the altitude (height above the surface of the Earth) for a satellite in a circular Earth orbit with a known orbit period.

You are given the satellite orbit period (in s). Calculate the orbit altitude (in km).

You should take the radius of the Earth to be 6371km, the mass of the Earth to be 5.9722e24 kg and Newton's Universal Gravitational Constant to be 6.6743015e-11 m3/kg/s.

Hints: 1) Newton's Law of Universal Gravitation will tell you the force between the satellite and the Earth (see: <https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation>); 2) The centripetal force maintaining the orbit (see: <https://en.wikipedia.org/wiki/Centripetal_force#Formula>) should be equal to the gravitational force; 3) Hmmm... but what about the mass of the satellite?

Example: The altitude of a geostationary satellite, with orbit period 86164.0905 s is around 35,793 km.

_Some future problems in this series will build on work done in previous problems, so if you get a working solution I suggest you hang onto the code!_

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Problem 45553. SatCom #4: Satellite Orbit Altitude

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