# Orbital Speed Formula

## 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,

$v_{orbit}\,&space;=\,&space;\sqrt{\frac{GM}{R}}$

Where,
G = gravitational constant,
M = mass of planet

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
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
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

#### Practise This Question

A particle of charge 16×1018 coulomb moving with velocity 10 m/s along the x-axis enters a region where a magnetic field of induction B is along the y-axis, and an electric field of magnitude 104V/m is along the negative z-axis. If the charged particle continues moving along the x-axis, the magnitude of B is