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Orbital Speed Formula

The orbital speed of the body which is usually a planet or a natural satellite is the speed at which it orbits around the barycenter of a system which is usually around a massive body. The orbital speed of the earth around the sun is 108,000 km/h. It relates the mass of a given planet to the gravitational constant and radius through the equation.
The orbital speed formula is provided by,

Where,
G = gravitational constant,
M = mass of planet
r = radius.

Example 1
The mass of the Moon is given as 8.35×1022 Kg and the radius is given as 2.7×106m. Determine the orbital speed.

Solution:

Given:
Mass of the Moon, M = 8.35×1022kg
Radius, R = 2.7×106m
G = 6.673×10-11m3/kgs2
Orbital speed equation is given by,
vorbit = √GM / R

vorbit = √6.673×10−11 ×8.35×1022 / 2.7×106
= 20.636 x 106 m/s.

Example 2
The mass of the Jupiter is given by 2.89×1027 Kg and the radius is given as 71400 km, determine the orbital speed.
Solution:

Given,
Mass of the Jupiter, M = 2.898×1027 kg
Radius, R = 71400 km
G = 6.673×10-11m3/ kgs2
Orbital speed equation is given by
vorbit = √GMR

= 6.673 x 10-11 x 2.898 x 1027 / 71400
= 2.708 x 1012 km/s