What is Kepler’s Third Law?

Kepler’s Third Law, also known as the Law of Periods, is a fundamental principle in astronomy that describes the relationship between the orbital period of a planet and its average distance from the sun. Formulated by Johannes Kepler in the early 17th century, this law states that the square of a planet’s orbital period is directly proportional to the cube of the semi-major axis of its orbit.

Mathematically, Kepler’s Third Law is expressed as:

T² = (4π² / GM) * a³

Where:

• T is the orbital period
• G is the gravitational constant
• M is the mass of the central body (e.g., the sun)
• a is the semi-major axis of the orbit

This law applies not only to planets orbiting the sun but also to any satellite orbiting a central body, including moons around planets or artificial satellites around Earth.

How to Use the Kepler’s Third Law Calculator

Step 1: Determine what you want to calculate

Decide whether you want to find the orbital period or the semi-major axis of an orbit. You’ll need to know one of these values to calculate the other.

Step 2: Enter the known value

If you know the semi-major axis, enter it in the “Semi-Major Axis (in AU)” field. If you know the orbital period, enter it in the “Orbital Period (in Earth years)” field. Remember, AU stands for Astronomical Unit, which is approximately the average distance between the Earth and the Sun.

Step 3: Input the star’s mass

Enter the mass of the central star in solar masses in the “Star Mass” field. If you’re calculating for planets in our solar system, you can leave this at the default value of 1 (representing the Sun’s mass).

Step 4: Click “Calculate”

Press the “Calculate” button to perform the calculation. The calculator will automatically determine which value you’re trying to find based on the information you provided.

Step 5: Interpret the results

The calculator will display the result in the “Results” section. You’ll see either the calculated orbital period in Earth years or the semi-major axis in AU, depending on what you were solving for. Additionally, a brief explanation of how the result was calculated will be provided.

By following these steps, you can easily use the Kepler’s Third Law Calculator to explore orbital mechanics and planetary motion. This tool is valuable for students, astronomy enthusiasts, and anyone interested in understanding the fundamental principles governing the movement of celestial bodies.