3986004418×1014

3986004418×1014 is commonly used to denote the standard gravitational parameter of Earth, written as μ⊕ = G*M⊕. This quantity equals approximately 3.986004418×10^14 cubic meters per second squared (m^3 s^-2) and represents the product of the gravitational constant G with Earth's mass M⊕. In more convenient units for orbital calculations, μ⊕ is about 398,600.4418 cubic kilometers per second squared (km^3 s^-2).

The gravitational parameter is a fundamental constant in celestial mechanics because it combines the strength of gravity with the mass of the central body. It appears directly in the equations governing orbital motion, such as the vis-viva equation v^2 = μ⊕(2/r − 1/a), and in the two-body problem that describes satellite trajectories around Earth. It also determines orbital periods via Kepler’s third law, T = 2π√(a^3/μ⊕) for near-Earth orbits.

μ⊕ is defined by the product of G and M⊕, so its precise value depends on both the gravitational constant and the Earth’s mass as measured by geodesy and planetary science. The parameter is widely tabulated and used in mission planning, satellite tracking, and astrodynamics, where accurate gravity modeling is essential for predicting paths, designing maneuvers, and interpreting orbital data. While the Earth’s gravitational field is not perfectly central due to flattening and irregular mass distribution, μ⊕ remains a central reference value for many calculations.