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The standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of that body. For two bodies, the parameter may be expressed as G ( m 1 + m 2 ) , or as GM when one body is much larger than the other: μ = G ( M + m ) ≈ G M . {\displaystyle \mu =G(M+m)\approx GM.}
Every object in a 2-body ballistic trajectory has a constant specific orbital energy equal to the sum of its specific kinetic and specific potential energy: = = =, where = is the standard gravitational parameter of the massive body with mass , and is the radial distance from its center. As an object in an escape trajectory moves outward, its ...
Since 2012, the AU is defined as 1.495 978 707 × 10 11 m exactly, and the equation can no longer be taken as holding precisely. The quantity GM —the product of the gravitational constant and the mass of a given astronomical body such as the Sun or Earth—is known as the standard gravitational parameter (also denoted μ).
The standard acceleration of gravity or standard acceleration of free fall, often called simply standard gravity and denoted by ɡ 0 or ɡ n, is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is a constant defined by standard as 9.806 65 m/s 2 (about 32.174 05 ft/s 2).
A common misconception occurs between centre of mass and centre of gravity.They are defined in similar ways but are not exactly the same quantity. Centre of mass is the mathematical description of placing all the mass in the region considered to one position, centre of gravity is a real physical quantity, the point of a body where the gravitational force acts.
Standard gravitational parameter (μ) — quantity equal to the mass of the central body times the gravitational constant G. This quantity is often used instead of mass, as it can be easier to measure with precision than either mass or G , and will need to be calculated in any case in order to find the acceleration due to gravity.
For an elliptic orbit, the specific orbital energy equation, when combined with conservation of specific angular momentum at one of the orbit's apsides, simplifies to: [2] = where = (+) is the standard gravitational parameter;
The first paragraph currently defines the "standard gravitational parameter" as based on the sum of the two objects' masses and states the mass of one object times the gravitational constant (GxM) is an approximation of the "standard gravitational parameter". If this is the "true" meaning of the phrase, a source should be cited.