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Calculating the Radius of a Geostationary Orbit

To calculate the radius of a geostationary orbit, the centripetal force must equal the gravitational force on the satellite or mass.

Through the use of re-arranging the above equation, we can come to the equation:

r³ = G (m2) T² / 4π²

We  know that (m2) is the mass of the earth at 5.98×10^24 kg, T is the time period and G the universal gravitation constant at 6.67 x10^-11 kg^-2 .

Radius Of A Geostationary Orbit

We know every bit of information in the above equation to work out the radius of a geostationary orbit. The time period will be 24 hours which is 86400 seconds. Therefore, for a geostationary orbit,

r = 4.23×10^7 metres.

However this is the radius to from the center of the Earth. Therefore, we will need to deduct the radius of the Earth from this number: the height of the satellite from Earth = r – r(E) where r is the distance of the satellite from the center of the Earth and r(E) is the radius of the Earth.

From this, the radius of a geostationary orbit for the earth is 3.6×10^7 meters.

Summary

  • A geostationary orbit is an orbit which is fixed in respect to a position on the Earth. Therefore, the time period will always be 24 hours.
  • From combining the centripetal force, gravitational force and basic velocity force equations, we can deduce that the radius required for a geostationary orbit is 3.6×10^7 meters.
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