Moon orbital speed calculator

Enter the primary body's mass in kilograms and the mean center-to-center orbital distance in metres. The result is the mean orbital speed in metres per second, calculated with the standard circular-orbit relationship. It is useful for astronomy exercises, early mission studies, simulation checks, and quick comparisons between moon systems without setting up a spreadsheet or writing a script.

Choose the primary mass and distance correctly

Start with the mass of the body that the moon orbits, not the mass of the moon itself. For Earth's Moon, the primary is Earth; for Europa, the primary is Jupiter. Supply that mass in kilograms. The orbital distance must be the distance from the center of the primary to the center of the moon, expressed in metres. Do not use altitude above the primary's surface unless you first add the primary body's radius. For an orbit that is not perfectly circular, use the semimajor axis as the representative distance when you want a simple mean circular-orbit estimate. Consistent SI units matter because the built-in gravitational constant is expressed in cubic metres per kilogram per second squared. A positive distance is mandatory: zero or a negative value has no physical meaning in this formula and produces an input error. Check scientific notation carefully, especially when copying values listed in kilometres or in powers of ten. Converting kilometres to metres requires multiplying by one thousand.

Understand the circular-orbit calculation

The calculator evaluates v = sqrt(GM/r), where v is speed, G is the gravitational constant, M is the primary mass, and r is orbital distance. This relationship comes from equating the gravitational acceleration supplied by the primary with the centripetal acceleration needed for circular motion. The calculation uses G = 6.67430 × 10^-11 in SI units and returns metres per second. It is deterministic: identical numeric inputs always produce the same result, with no network lookup or hidden choice of astronomical data. The moon's own mass is omitted under the common small-satellite approximation. That approximation is excellent when the primary is much more massive than its moon. In a binary system with comparable masses, a two-body treatment using the sum of both masses and an appropriately defined separation is more suitable. The returned number is not rounded to a prescribed display precision, so consumers may round it according to their measurement uncertainty rather than implying more accuracy than the input data supports.

Interpret the estimate and its limits

Treat the output as the constant speed of an ideal circular orbit at the supplied distance. Real moons often follow elliptical paths, so their instantaneous speed changes: they move faster near periapsis and slower near apoapsis. Perturbations from other moons, the star, an uneven gravitational field, tides, and relativistic effects are also outside this compact model. Even so, the circular estimate is a strong first check for classroom work, order-of-magnitude analysis, and validating a simulation's initial conditions. You can compare scenarios by changing one input at a time. At a fixed distance, a more massive primary gives a higher speed; around the same primary, a more distant moon gives a lower speed. If you need kilometres per second, divide the returned metres-per-second value by one thousand. If you need an orbital period, do not mistake speed for period: use the orbit's circumference together with the speed, or use a dedicated period equation. Always retain the original inputs alongside the result so later readers can reproduce the estimate and understand the assumptions behind it.