Square the year, cube the distance

For anything going round the Sun, the year squared equals the distance cubed —

Why it works

Gravity falls off as the square of distance, and that single fact fixes the speed a

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

Open Solar System →

More in Physics

• Hohmann is the cheapest transfer — until the ratio passes about 12Two burns on opposite sides of an ellipse is the minimum-energy route between circular orbits, a…
• A narrower gap spreads light more, not lessDiffraction angle goes as wavelength over aperture, so halving the opening doubles the spread — …
• Geostationary runs on the sidereal day, not the 24-hour oneThe altitude falls straight out of the period: match Earth\’s rotation and the orbit radius is f…
• ζ = 1 is critical dampingWhen the damping ratio hits 1, the system returns to rest as fast as possible without overshoot …

How long is a year on another planet?

For anything going round the Sun, the year squared equals the distance cubed — Gravity falls off as the square of distance, and that single fact fixes the speed a .

Browse all 163 rules of thumb →