Circular orbit height and speed calculator

Main body name	Height above surface of main body km ft
If "Other", edit: Main body mass: kg
If "Other", edit: Main body diameter= km

Orbit height km	km
Orbit height ft	ft
Circular orbit speed or velocity m/s	m/s
Circular orbit speed or velocity ft/sec	ft/sec
Period of circular orbit minutes	minutes
Period of circular orbit hours	hours
Period of circular orbit days	days
Period of circular orbit years	years

Gravitational constant G	6.6743 x 10^-11 Nm²s^-2
Mass of the main body M	kg
Standard gravitational parameter for main body μ = GM km³s^-2	km³s^-2
Diameter of main body	km
Radius of orbit (= height + diameter of main body / 2 )	km

This page is about orbital height, speed and period. It works for circular orbits.

The calculator uses information about the mass and diameter of the main 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.

9 Aug 2022:
Added an option (select Main body called "Other"), so you may input your own values for Main body diameter and mass.
Added a height input in feet to suit low orbits like 60,000 ft above lunar surface.

The formulas used in the above are as follows:

To work out the velocity or speed. Velocity = square root of (Gravitational constant times Mass of main body / radius).

To work out orbit period or time to go around the orbit: Orbit period = 2 * PI * square root of ( (half-diameter ^ 3) / μ ) / 60 minutes;

Note:

Velocity in metres/sec (or alternatively in ft/sec as shown in output table above).
Gravitational Constant G is 6.6743 x 10^-11 m³ kg^-1 s^-2Mass of main body M in kg
Radius of circular orbit in km (equals half the diameter of the main body plus height)
Standard gravitational parameter μ = GM (This is different, according to your choice of the main body)
The Standard gravitational parameter μ may be expressed in units of m³ s^-2 or km³ s^-2. km³ s^-2 is frequently used in the scientific literature and in spacecraft navigation.

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 (Mars radius: 3396.2km. Phobos semi major axis: 9376km)

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 16 June 2020, updated 17 Nov 2024.