How to use (3 steps)
- Choose whether to solve for orbital period T or semi-major axis a.
- Pick the central mass μ (in solar masses) with a preset or type it, then enter the known value (a or T).
- Press Compute to get the other quantity, see steps, and compare with the Solar System. Copy URL shares the same setup.
Inputs
Quick: defaults auto-calc Earth’s orbit so results show immediately. Calculations stay in your browser.
Typical ranges: μ ≈ 0.1–10 for many stars, a ≈ 0.01–100 AU for planetary orbits, and T from hours up to thousands of years. Extreme values may be less realistic.
Results
| Quantity | Value |
|---|
Solar System comparison (a–T log plot)
Dots show log10(a) vs log10(T) in years; Kepler’s law makes them fall close to a straight line. Your orbit is highlighted.
Top-down orbit scale
Orbits are shown as circles from above. Radii use log scaling so inner and outer planets fit in one view.
| Orbit | a (AU) | T (year) |
|---|
Calculation steps
FAQ
What is Kepler's third law?
Kepler's third law states that for objects orbiting the same central body, the square of the period T² is proportional to the cube of the semi-major axis a³. Using the gravitational constant G and central mass M, it can be written as T² = 4π² a³ / (G M).
Why can we write T² = a³/μ?
By taking Earth’s orbit (a = 1 AU, T = 1 year) as a reference and defining the mass ratio μ = M/M☉, the constants combine so that T² = a³/μ. This calculator uses that ratio form for quick scaling.
Are the orbits really circles here?
Real planetary orbits are elliptical, but many have modest eccentricity. For learning the scaling between a and T, a circular approximation using the semi-major axis is sufficient, and this tool draws the orbits as circles.
How accurate is this model?
This tool uses an idealised Keplerian model: it assumes a single massive central body, point-mass planets, and T² = a³/μ with no relativistic effects, resonances, or strong perturbations. For Solar System–like orbits it gives good approximate periods and scales, but it is not a precise orbit integrator.
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