The square root of the gravitational constant G, as computed from Kepler's third law

(1)

where T is the sidereal year expressed in days ( days ), a is the semimajor axis of the Earth 's orbit expressed in astronomical units (a = 1 AU), and M is the mass of the Sun expressed in solar masses (). Solving for gives

(2)

so

(3)

Gravitational Constant, Kepler's Third Law, Mean Motion