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How to Calculate Geostationary Orbit

Geostationary orbit describes a body in orbit around the Earth, whose position with respect to the surface of the Earth does not change. Communications satellites travel in a geostationary orbit so that their signals always provide the same geographic coverage. A satellite can only be placed in a geostationary orbit in the plane of Earth's equator.

The formula for calculating the radius of a geostationary orbit is R = ((G * M * period^2)/4 * pi^2))^(1/3).

Things You'll Need

Scientific calculator

Instructions

- 1
  Calculate the numerator of the fraction (G * M * period^2), where G = Newton's constant of gravity; M = the mass of the Earth; and the period (length of Earth's day) is 86,160 seconds:
  
  (6.67x10^(-11) m³/kg-sec²) * (5.974*10^24 kg ) * (86,160 sec * 86,160 sec) = 2.958 * 10^24 m³
  
  Note that the kilogram and second units cancel.
- 2
  Calculate the denominator of the fraction (4 * pi^2):
  
  4 * (3.14159)^2 = 39.4784
- 3
  Divide the numerator by the denominator, and calculate the cube root (1/3 power):
  
  ((2.958 * 10^24 m³) / (39.4784)) ^ (1/3) = 42,158,000 m, or 42,158 km
  
  This distance is the radius of a geostationary orbit measured from the center of the Earth.
- 4
  Subtract the Earth's radius (6,371 km) to calculate the height of a geostationary orbit above mean sea level:
  
  42,158 -- 6,371 = 35,787 km

Astronomy