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).

- Skill level:
- Moderately Easy

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### Things you need

- Scientific calculator

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## 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-sec ²) * (5.974*10^24kg ) * (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) = 42,158,000m, or 42,158km

This distance is the radius of a geostationary orbit measured from the centre of the Earth.

- 4
Subtract the Earth's radius (6,371km) to calculate the height of a geostationary orbit above mean sea level:

42,158 -- 6,371 = 35,787km

#### Tips and warnings

- You can use this equation to calculate the geostationary orbit of any celestial body, as long as you know the period and the values of G and M for the body.