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# Kepler’s Third Law – Planetary Motion Calculator

Table of Contents:

Formula

**Satellite Orbit Period :**

T = √(4∏^{2}r^{3}/GM)

**Satellite Mean Orbital Radius :**

r = 3*√(T^{2}GM/4∏^{2})

**Planet Mass :**

M = 4 ∏^{2} r^{3}/GT

**Where,**

G = Universal Gravitational Constant = 6.6726 x 10-^{11}N-m^{2}/kg^{2}

r = Satellite Mean Orbital Radius

M = Planet Mass

Kepler’s Third Law states that the ratio of the squares of the orbital period for two planets is equal to the ratio of the cubes of their mean orbit radius. As per Kepler’s Third Law the orbit of every planet is an ellipse with the Sun at one of the two foci. The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. The Satellite Orbit Period is denoted by the symbol ‘T’.

Kepler’s third law is the velocity of a circular Earth orbit at any other distance r is similarly calculated. The square of the orbital period is directly proportional to the cube of the orbit's semi major axis. The advanced online Kepler’s Third Law Calculator is used to calculate and find the planetary motion when Satellite Mean Orbital Radius(r) and Planet Mass (M) are known.

**Example:**

Calculate planetary motion, Satellite Orbit Period for the given details.

Satellite Mean Orbital Radius(r) = 25 m

Planet Mass (M) = 15 kg

**Solution:**

**Apply Formula:**

T = √(4∏^{2}r^{3}/GM)

T = √(4*3.14^{2}*25^{3}/6.6726 x 10-^{11}N-m^{2}/kg*15

T = 24813343.69 s

**Satellite Orbit Period (T) = 24813343.69 s**