Calculate orbital distance or period from Kepler’s third law for a one-solar-mass body, with results in AU, km, miles, meters, and time units.

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.