Astronomy
Orbital Period Calculator
Calculate orbital period in years, days, and seconds plus an approximate circular speed. The orbit visual scales the path around the central body and distinguishes orbital period from the circular-speed estimate.
Orbital period (years)-
Orbital period (days)-
Approximate circular orbital speed (km per s)-
Orbital period (seconds)-
Decision view
Keplerian orbit and period scale
Keplerian orbit and period scaleSemi-major axis and central mass define the idealized orbital period while circular speed remains a separate approximation.
Exact scenario comparisonSemi-major axis (AU) changes while all other entered assumptions remain constant.
| Semi-major axis (AU) | Orbital period (years) | Orbital period (days) | Approximate circular orbital speed (km per s) | Orbital period (seconds) |
|---|
How to use Orbital Period Calculator
- Use the orbit's semi-major axis rather than instantaneous radius.
- Express central mass in solar masses and axis in AU.
- Use a state-vector or ephemeris model when eccentricity, position, or mission timing matters.
Calculator guide
Understanding Orbital Period Calculator
In astronomical-unit and solar-mass units, Kepler's third law gives period squared equal to semi-major axis cubed divided by central mass for an idealized two-body orbit.
Calculation method
How the calculation works
Apply Kepler's third law in astronomical-unit and solar-mass form and provide an approximate circular orbital speed. Take the square root of semi-major axis cubed divided by central mass for years; convert to days and seconds, and scale Earth's circular speed by the square root of mass divided by axis.
Orbit intuition
Why farther orbits take disproportionately longer
A larger orbit adds distance while gravitational speed also falls.
Worked situations
Practical examples
- At 1 AU around 1 solar mass, period is about one year or 365.256 days.
- At 4 AU around the same mass, period is 8 years.
- The circular-speed estimate at 4 AU is about half Earth's, roughly 14.9 km/s.
Better inputs
Useful tips
- Use total system mass for comparable-mass binary bodies.
- Distinguish mean orbital period from rotation period.
- Treat the speed output as circular at the entered axis, not speed everywhere on an eccentric orbit.
Before relying on the result
Limitations and common mistakes
- The page uses an ideal two-body Keplerian relationship.
- Eccentric anomaly, current position, perturbations, non-spherical gravity, relativity, and mass loss are excluded.
- The speed output is a circular-orbit approximation.
Reference
Key terms
- Semi-major axis
- Half the longest diameter of an elliptical orbit.
- Orbital period
- Time required for one modeled revolution.
- Central mass
- Entered gravitating mass in solar-mass units.
- Circular speed
- Speed for a circular orbit at the entered radius under the model.
Important note
Calculated from the entered values using the displayed astronomical model. Use current ephemerides and qualified references for observation or mission decisions.
Frequently asked questions
Why is Earth's result one year?
The chosen AU, solar-mass, and year units normalize the relationship to the Earth-Sun scale.
Does eccentricity change period?
For an ideal two-body orbit with the same semi-major axis, Kepler's third law gives the same period.
Is displayed speed valid for an ellipse?
No. It is the circular speed at the entered axis.
Can this model a moon?
Only after expressing axis in AU and central mass in solar masses; specialized units are usually more convenient.