Why Geostationary Orbit Is Used by Satellites
The Importance of a Fixed Satellite Location to Dishes and Receivers
Jul 8, 2009
Many satellites orbiting the Earth need to stay above the same place on the planet. They are usually directly above the Equator. These types of device are said to be in geostationary orbit, and they are all at about the same height, or geostationary altitude. The height needed to stay in geostationary orbit may be calculated as around 40,000 kilometers, or 24,000 miles.
What Is Geostationary Orbit?
Geostationary orbit means that an object resides at a fixed height above the Earth, and does not move relative to the ground below it. It does not fall to Earth, nor does it move farther away. The height needed to attain geostationary orbit is derived later. Not all satellites need to be in this type of orbit, but for some it is essential for them to function.
Which Satellites Use Geostationary Orbits?
GPS satellites and other types of communications satellite such as those used in phone networks, satellite TV etc. need to stay in place. The ground receivers either point towards them, without moving, or rely on them sending timed signals so that the GPS device on the ground may calculate its position.
This article describes how fixed position satellites maintain their position. Some other satellites must move around the Earth to do their job; the pictures taken for Google Earth could not be taken from a stationary satellite.
The reader will note that satellite phones send signals directly to a satellite, and may be used in remote areas, unlike cell-phones that need to be near a local cell mast.
How Is Geostationary Orbit Radius Calculated?
Figure 1 shows a satellite revolving around the Earth. It has an altitude r, that needs to be calculated. Earth has a mass of M kilogrammes, and the satellite has a mass of m kilogrammes. Earth rotates at an angular velocity of ω and this is the desired angular velocity of the satellite, if it is to remain at the same point above the Earth.
The forces acting on the satellite are gravity (towards Earth), and centripital force. When these are equated, the formula may be derived.
Derivation of Geostationary Orbit Formula
SI units will be used here:
Centripital Force = Gravitational Force, so
m.ω².r = G.M.m ÷ r²
Where G = Gravitational Constant (which is dimensionless, and can be used in any measurement units). It is equal to 6.67 × 10^(-11)
The equation rearranges to:-
r³ = G.M ÷ ω²
r = (G.M / ω²)^(1/3)
The values are:
M = 6 × 10^(24) kg
ω = 2 × PI per day (86,164 seconds)
Substituting ω = 2 × PI per 86,164 seconds
r = (G.M / (2 × PI / 86,164)²)^(1/3)
r = (G.M × 86,164² / (2 × PI) ²)^(1/3)
Substituting in the values shown gives a geostationary radius of 42,200 kilometers.
Summary of Geostationary Orbits
Some satellites need to stay above the same spot on Earth. For example, so that a satellite dish does not have to move, or so that ground based GPS devices can take timed signals from them to calculate distances.
To attain a fixed position relative to the Earth, they must be sent into a radius that balances the force of gravity to the centripital force around the Earth. This distance is just over 42,000 kilometers.
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