Kepler's Third Law Calculator

Kepler's 3rd Law Calculator displays the detailed work to find the basic parameters of the planet's motion around the Sun, like the semi-major axis, planet period easily. It uses Kepler's third law formula to find the unknown parameters. Just enter star mass, semi-major axis and hit the submit button to check the orbital period.

Choose Option
Semi-major axis
Planet Period

Kepler's 3rd Law Calculator: Want to calculate the planet period and don't know how to do calculations? Then, use this handy Kepler's third law calculator as it does all the difficult math work and provides the exact answer. It is based on the fact that the ratio of radius to the period is constant for all planets in the planetary system. Read more to know Kepler's 3rd law definition, equation and solved example questions.

Step by Step Process to Find Planet Period

Go through the simple steps to calculate the planet period using the Kepler's 3rd law formula.

  • Find the star mass, semi-major axis details.
  • Get the cube of the radius.
  • Add star mass, planet mass and multiply it with the gravitational constant.
  • Multiply the product from above two steps.
  • Divide it by the 4π².
  • The square root of the result is the planet period.

Kepler's Third Law Equation

According to the Kepler's third law, the square of the orbital period of the planet is directly proportional to the cube of its radius.

T2 ∝ a3

It shows the relationship between the distance from sun of eah planet in the system to its orbital period.

Kepler's third law equation is nothing but the constant.

a³/T² = 4 * π²/[G * (M + m)] = constant


a is the semi-major axis

T is the planet period

G is the gravitational constant and it is 6.67408 x 10⁻¹¹ m³/(kgs)

M is the mass of the central star

m is the mass of the planet


Question: Phobos orbits Mars with an average distance of about 9500 km from the center of the planet around a rotational period of about 8 hr. Estimate the mass of Mars.


Given that

semi-major axis a = 9500 km = 9.5 x 106 m

Planet periord T = 8 hrs = 28800 sec

Kepler's equation is a³/T² = 4 * π²/[G * (M + m)]

(9.5 x 106)³/(28800)² = 4 * π²/[6.67408 x 10⁻¹¹ * (M + m)]

0.01 x 1016 = 39.43/[6.67408 x 10⁻¹¹ * (M + m)]

M + m = 39.43/6674.08

M + m = 5.9

The mass of mars is 5.9 km

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FAQ's on Kepler's Third Law Calculator

1. What is Kepler's 3rd law in simple terms?

Kepler's third law of period's states that the square of the time period of the revolution of the planet around the sun is proportional to the cube of its semi-major axis.

2. What is Kepler's third law equation?

This law can be proved using Newton's law of gravitation. The Kepler's third law formula is T² = (4π² x a3)/[G(m + M)].

3. How to compute Kepler's third law?

Using Kepler's 3rd law, you can calculate the basic parameters of a planet's motion such as the orbital period and radius. Substitute the values in the formula and solve to get the orbital period or velocity.

4. What is Kepler's constant equal to?

The constant in Kepler's 3rd law is the ratio of the cube of the semi-major axis to the square of the planet period. The value is constant = a³/T² = 4 * π²/[G * (M + m)].

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