How to Calculate Orbital Period Using AU?

To calculate the orbital period of a planet or any celestial body using Astronomical Units (AU), you can use Kepler’s Third Law of Planetary Motion. This law relates the orbital period of a planet to its average distance from the Sun.

Kepler’s Third Law Formula:

The formula is given by:

P² = a³

Where:

• P is the orbital period in Earth years.
• a is the average distance from the Sun in Astronomical Units (AU).

Steps to Calculate Orbital Period:

1. Determine the average distance (a) of the planet from the Sun in AU. For example, if a planet is 2 AU from the Sun, then a = 2.
2. Cube the average distance (a³). For a = 2, a³ = 2³ = 8.
3. Take the square root of the result (√a³) to find the orbital period (P). For a³ = 8, P = √8 ≈ 2.83 Earth years.

Example Calculation:

Let’s calculate the orbital period of a planet that is 1.5 AU from the Sun.

1. a = 1.5 AU
2. a³ = 1.5³ = 3.375
3. P = √3.375 ≈ 1.84 Earth years

So, the orbital period of the planet is approximately 1.84 Earth years.

Important Notes:

• This formula assumes that the mass of the planet is negligible compared to the mass of the Sun.
• For objects orbiting other stars, the formula can be adjusted by incorporating the mass of the star.