Enter either the orbital period or the orbital distance into the Orbital Distance Calculator (enter exactly one value and leave the other blank). This calculator uses the simplified form of Kepler’s Third Law for orbits around an approximately 1-solar-mass central body (e.g., the Sun) and returns the orbital semi-major axis as “orbital distance.” 

Orbital Distance Calculator

Enter exactly one value to calculate the other

Assumes an orbit around an approximately 1-solar-mass central body (e.g., the Sun). “Orbital Distance” refers to the semi-major axis.

Orbital Distance Formula

The following formula is used to calculate the Orbital Distance. 

D = (P^2)^{1/3}
  • Where D is the orbital distance (semi-major axis) (AU)
  • P is the period of orbit (years) 

To calculate the orbital distance, square the orbital period, then raise the result to the one-third power (take the cube root). Note: this simplified form assumes the orbit is around an approximately 1-solar-mass central body (e.g., the Sun) and uses years and AU. In general, Kepler’s Third Law is P2 = (4π2 / (G(M + m)))a3.

How to Calculate Orbital Distance?

The following example problems outline how to calculate Orbital Distance.

Example Problem #1:

  1. First, determine the period of orbit (years).
    • The period of orbit (years) is given as: 50.
  2. Finally, calculate the Orbital Distance using the equation above: 

D = (P^2)^(1/3)

The values given above are inserted into the equation below and the solution is calculated:

D = (50^2)^(1/3) ≈ 13.572 (AU)

FAQ

What is an AU in the context of Orbital Distance?

AU stands for Astronomical Unit, which is a standard unit of measurement in astronomy. It is approximately equal to the average distance from the Earth to the Sun: about 149.6 million kilometers (≈ 92.96 million miles).

How does the period of orbit affect the Orbital Distance?

The period of orbit directly influences the Orbital Distance (semi-major axis). In the simplified Sun-like-mass case used on this page, D (in AU) is proportional to P2/3 (with P in years), and equivalently P is proportional to D3/2.

Can the Orbital Distance formula be used for any celestial body?

The general form of Kepler’s Third Law can be used for any two-body orbit, but it must include the total mass of the system: P2 = (4π2 / (G(M + m)))a3. The simplified formula on this page (and in the calculator) assumes the orbit is around an approximately 1-solar-mass central body and uses years and AU; it will not be accurate for systems with significantly different masses (for example, moons orbiting planets, or planets orbiting lower- or higher-mass stars) unless the mass term is included.