standard gravitational parameter

The standard gravitational parameter (μ) of a body relates the acceleration of an object within its gravitational field to the object's distance from the body's center (according to Newtonian gravity):

a = μ/r²

• a - an object's acceleration (more specifically, the component of its acceleration specifically due to the body's gravity).
• μ - the body's standard gravitational parameter.
• r - the accelerating object's distance from the center of the body.

This assumes the object is external to the body and the body is spherically symmetric; as an approximation for less-than-symmetric objects, the relation improves with distance between the two, as well as with how close the body is to spherical symmetry. Standard gravitational parameters are generally cited in units of m³s^-2 or km³s^-2, the latter allowing representation by a number only 10^-9 as large. Example standard gravitational parameter determinations:

• Sun (aka heliocentric gravitational constant and solar mass parameter): 1.32712440018 × 10¹¹ km³s^-2
• Earth (aka geocentric gravitational constant): 3.986004418 × 10⁵ km³s^-2
• Moon: 4.9028695 × 10³ km³s^-2

A body's standard gravitational parameter depends entirely upon its mass, being its mass times the universal gravitational constant (G) and serves as short-hand sometimes used in formulae that incorporate G×M:

μ = GM

• G - universal gravitational constant, 6.674×10^-11 m³ kg^-1 s^-2, which in terms of force applied is N·m²kg^-2, i.e., newtons (N) times meters squared over kilograms squared.
• M - mass of the body in kg.

Note that the standard gravitational parameters of a number of solar system bodies are known far more precisely than the bodies' masses or the gravitational constant, likely one reason for using the standard gravitational parameter in calculations rather than the other two values. A body's standard gravitational parameter can be determined through careful monitoring of orbits, e.g., using orbital periods measured to the sub-second level over the course of years. Determinations of the gravitational constant are much less precise, and the most precise determinations of bodies' masses are from these two values.