kepler's third law calculator

Kepler’s third law calculator uses the Kepler’s third law of planetary motion to calculate:

• Satellite Orbit Period T
• Planet Mass M
• Satellite mean orbital radius r

Let’s find out what is third law of Kepler, Kepler's third law formula, and how to find satellite orbit period without using Kepler’s law calculator.

Kepler’s 3^rd law equation

The satellite orbit period formula can be expressed as:
T = √ (4π²r³/GM)
Satellite Mean Orbital Radius
r = 3√ (T²GM/4π²)

Planet Mass
M = 4 π² r³/GT²

Where,

T refers to the satellite orbit period,
G represents universal gravitational constant (6.6726 x 10-¹¹N-m²/kg²),
r refers to the satellite mean orbital radius, and
M refers to the planet mass.

Kepler’s third law equation calculator uses above equations to perform planetary motion calculations.

What is Kepler’s third law?

Kepler's third law states that squares of the orbital periods of the planets are directly proportional to the cubes of the semi major axes of their orbits. Kepler's third law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit.

How to calculate satellite orbit period?

To calculate satellite orbit period with Kepler’s law, follow the steps below.

Example:

Find the satellite orbit speed if the mean orbital radius of satellite is 2000 m and mass of the planet is 25000 kg.

Solution:

Step 1: Identify and write down the values for calculation.

r = 2000 m

M = 25000 kg

G = 6.6726 x 10-¹¹N-m²/kg²

Step 2: Use the equation of Kepler’s third law and place the values.

T = √ (4π²r³/GM)

T = √ [(4×3.14159² × 2000³)/(6.6726 x 10-¹¹ × 25000)]

T = √ [(4×9.87×8×10⁹)/(1.67 × 10^-6 )]

T = √ (3.16×10¹¹/1.67×10^-6)

T = √ (1.89×10¹⁷)

T = 434906498.16 s

To verify the result, use Kepler’s constant calculator above.