gravitationsparameter

Gravitationsparameter, often denoted μ (mu) and commonly written as GM, is the product of Newton's gravitational constant G and the mass M of a gravitating body. It represents the strength of the body's gravitational field and has units of cubic meters per square second (m^3 s^-2). The parameter is central to the description of orbital motion in Newtonian gravity.

In orbital mechanics the gravitational parameter appears directly in the equations of motion for a body under gravity. For a two-body problem with a central body of mass M, the acceleration of the orbiting body is proportional to −μ r̂ / r^2, or more compactly d^2 r/dt^2 = − μ r / r^3. For bound orbits Kepler's third law relates μ to the orbital period P and the semi-major axis a via P^2 = 4π^2 a^3 / μ.

A key advantage of μ is that it consolidates G and M into a single parameter that is often known more accurately than either G or M separately. This makes μ particularly useful for spacecraft navigation, trajectory design, and gravity-field modeling, where precise knowledge of the central body's gravitational influence is essential.

Typical values illustrate its use: Earth μ_E ≈ 3.986004418×10^14 m^3 s^-2; the Sun μ_S ≈ 1.32712440018×10^20 m^3 s^-2; the Moon μ_M ≈ 4.9048695×10^12 m^3 s^-2; Mars μ_Mars ≈ 4.282837×10^13 m^3 s^-2.