How to Calculate Geostationary Orbit

Written by kelvin o'donahue
  • Share
  • Tweet
  • Share
  • Pin
  • Email
How to Calculate Geostationary Orbit
A satellite in a geostationary orbit is always above the same point on the Earth's surface. (satellite image by photlook from Fotolia.com)

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

Other People Are Reading

Things you need

  • Scientific calculator

Show MoreHide

Instructions

  1. 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. 2

    Calculate the denominator of the fraction (4 * pi^2):

    4 * (3.14159)^2 = 39.4784

  3. 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. 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.

Don't Miss

Filter:
  • All types
  • Articles
  • Slideshows
  • Videos
Sort:
  • Most relevant
  • Most popular
  • Most recent

No articles available

No slideshows available

No videos available

By using the eHow.co.uk site, you consent to the use of cookies. For more information, please see our Cookie policy.