# Kepler's Third Law Tutorial

## Kepler's Third Law Tutorial

Kepler's Third Law states that the squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of the orbits.

#### Planetary Motion Formula:

###### Satellite Orbit Period:  ###### Planet Mass: ###### where,

G = Universal Gravitational Constant = 6.6726 x 10-11N-m2/kg2 r = Satellite Mean Orbital Radius M = Planet Mass

#### Kepler's Third Law Examples:

##### Case 1:

The period of the Moon is approximately 27.2 days (2.35x106 s). Determine the radius of the Moon's orbit. Mass of the earth = 5.98x1024 kg, T = 2.35x106 s, G = 6.6726 x 10-11N-m2/kg2.

###### Step 1:

Substitute the values in the below Satellite Mean Orbital Radius equation: This example will guide you to calculate the Satellite Mean Orbital Radius manually.

##### Case 2:

Determine the mass of Uranus which has the orbital period of 1,166,400 s and distance 582,600,000 m from the moon r = 582,600,000 m, T = 1,166,400, G = 6.67x 10-11 M = (4π2r3) / (GT2) By applying all given values, M = [4π2 (582,600,0003)] / [(6.67x 10-11) * (1,166,4002)] M = 8.6 x 1025

This example will guide you to calculate the Mass of the object manually.

#### Related Topic:

This tutorial will help you dynamically to find the Planetary Motion of Kepler's Third Law problems.