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.
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Orbital Distance Formula
The calculator uses the simplified form of Kepler’s third law for an object orbiting a central body with about 1 solar mass, such as the Sun. In this form, the orbital period is measured in years and orbital distance is measured in astronomical units, or AU.
Use this formula when you know the period of orbit and want to find the orbital distance.
Use this formula when you know the orbital distance and want to find the period of orbit.
- a = orbital distance, or semi-major axis, in AU
- P = period of orbit in years
- AU = astronomical unit, approximately the average distance from Earth to the Sun
The calculator first converts your entered value into the base units used by the formula: years for period and AU for distance. It then applies the correct version of Kepler’s third law and converts the answer back into the unit you selected.
If you enter a period, the calculator solves for orbital distance using a = P^(2/3). If you enter an orbital distance, it solves for period using P = a^(3/2). You should enter exactly one value and leave the other field blank.
Common Solar System Orbital Distances and Periods
These approximate values can help you compare a calculated result with familiar objects orbiting the Sun.
| Object | Average Orbital Distance | Orbital Period |
|---|---|---|
| Mercury | 0.387 AU | 0.241 years, about 88 days |
| Venus | 0.723 AU | 0.615 years, about 225 days |
| Earth | 1.000 AU | 1.000 year |
| Mars | 1.524 AU | 1.881 years |
| Jupiter | 5.203 AU | 11.86 years |
Unit Conversions Used for Orbital Distance
| Unit | Equivalent |
|---|---|
| 1 AU | 149,597,870.7 kilometers |
| 1 AU | 92,955,807.3 miles |
| 1 year | 365.25 days |
| 1 day | 24 hours |
Example Calculations
Example 1: Find orbital distance from period
Suppose an object has an orbital period of 8 years around a Sun-like star.
The orbital distance is 4 AU.
Example 2: Find period from orbital distance
Suppose an object has an orbital distance of 9 AU around a Sun-like star.
The orbital period is 27 years.
FAQ
What does orbital distance mean in this calculator?
Orbital distance means the semi-major axis of the orbit. For a nearly circular orbit, this is close to the average distance from the central body. For an elliptical orbit, it is half the longest width of the ellipse, not the closest or farthest distance.
Why does the calculator assume a 1-solar-mass central body?
The simplified formulas a = P^(2/3) and P = a^(3/2) work directly when the central body has about the same mass as the Sun and the units are AU and years. If the central body has a very different mass, such as a small star, giant star, planet, or black hole, you need the more general form of Kepler’s third law.
Can this calculator be used for planets orbiting Earth?
No, not accurately. This calculator is set up for orbits around an approximately 1-solar-mass body. Satellites orbiting Earth need a formula that uses Earth’s gravitational parameter and distances measured from Earth’s center.
