as one astronomical unit, The Gaussian gravitational constant k = , therefore, under the same conditions as above, for any particular planet and again taking the semi-major axis as one astronomical unit, Mean motion and mean anomaly Mean motion also represents the rate of change of mean anomaly, and hence can also be calculated, where M1 and M0 are the mean anomalies at particular points in time, and Δt (≡ t1-t0) is the time elapsed between the two. M0 is referred to as the mean anomaly at epoch t0, and Δt is the time since epoch. Formulae For Earth satellite orbital parameters, the mean motion is typically measured in revolutions per day. In that case, where d is the quantity of time in a day, G is the gravitational constant, M and m are the masses of the orbiting bodies, a is the length of the semi-major axis. To convert from radians per unit time to revolutions per day, consider the following: From above, mean motion in radians per unit time is: therefore the mean motion in revolutions per day is where P is the orbital period, as above. See also Gaussian gravitational constant Kepler orbit Mean anomaly Mean longitude Mean motion resonance Orbital elements Notes References External links Glossary entry mean motion at the US Naval Observatory's Astronomical Almanac Online Orbits Equations of astronomy