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Elliptical Orbit height and speed calculator

Heavenly body name Low orbit height High orbit height
name

Perigee radius
Apogee radius
Semi-major axis
Velocity at perigee
Velocity at apogee
  
Standard gravitational parameter for main body GM = μ   km3s-2
Diameter of main body
Mass of the main body

This page is about elliptical orbital height, speed and period.  It works for circular orbits as well if you input the same heights for perigee and apogee. 

The calculator uses information about the mass and diameter of the body at the center of the orbit, typically the earth. There is a pull down menu with options for the Sun, the Moon and the Planets.  Ceres and Pluto are included. Ceres is one of many objects in the asteroid belt, but because it is particularly large for an asteroid, it was decided to call it a dwarf planet in 2006.  Pluto used to be called a Planet but Pluto's type  has recently been reviewed and it was decided to downgrade it to dwarf planet also.

The formulas used in the above are as follows:

To work out the velocity or speed, for an elliptical orbit the formula is  v = GM(2/r - 1/a)

where G = 6.67 x 10-11,
M is the mass of the planet (or object to be orbited),
r is the radial distance of the orbiting object from the center of the planet.
a is the semi-major axis of the elliptical orbit

Note:

Velocity in metres/sec.
Gravitational Constant G is 6.67408 x 10-11 m3 kg-1 s-2
Mass of main body M in kg
Perigee and Apogee Radii of orbit in km
Standard gravitational parameter μ  = GM (This is different, according to your choice of the main body)

Here is a NASA fact sheet with details of each planet, its orbital period and its distance from the sun.



Examples:

Earth orbiting the sun. The orbit is slightly elliptical, with height varying from 147.1 million km to 152.1 million km. Average 149.6 million km. Try this and the result is a little over 365.25 days.

Moon orbiting the earth:  Also somewhat elliptical, at perigee, bottom, 363,104 km at apogee, top. 405,696 km. Average 384,400 km.

Geostationary satellite: Height 35786km

Space station: Height 408 km

Starlink constellation: Height 540 - 570 km.  If above 600 km there is so little air drag that they might pollute the sky virtually for ever !

Rocket launch to an initial low earth orbit: Height 185 km

Photo satellite in orbit around Mars Global Surveyor: Height 378 km

Phobos is a moon in orbit around Mars: Height 5980 km

This calculator is only for educational purposes.  The results of may be in error and should not be used for orbital manoeuvres or the navigation of real spacecraft.

If anyone uses this page and is able to do the calculations independently themselves please tell me where I am wrong.


Any problems, suggestions for improvements or comments, please e-mail me Eric Johnston
This calculator is copyright (c) 2020 Satellite Signals Ltd.

Page started 27 Feb 2022, amended 27 Feb 2022, 18 June 2022.