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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 ...
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.
The standard gravitational parameter of a celestial body is the product of the gravitational constant and the mass of the body, μ = G M . {\displaystyle \mu =GM.} Why is it called "standard" as if there were many other gravitational parameters for the body in question?
is the standard gravitational parameter. Conclusions: For a given semi-major axis the specific orbital energy is independent of the eccentricity. Using the virial theorem to find: the time-average of the specific potential energy is equal to −2ε the time-average of r −1 is a −1
μ = G(M + m), a gravitational parameter, [note 2] where G is Newton's gravitational constant, M is the mass of the primary body (i.e., the Sun), m is the mass of the secondary body (i.e., a planet), and; p is the semi-parameter (the semi-latus rectum) of the body's orbit. Note that every variable in the above equations is a constant for two ...
The gravitational potential energy is the potential energy an object has because it is within a gravitational field. The magnitude & direction of gravitational force experienced by a point mass m {\displaystyle m} , due to the presence of another point mass M {\displaystyle M} at a distance r {\displaystyle r} , is given by Newton's law of ...
μ is the standard gravitational parameter t = 0 {\displaystyle t=0\!\,} corresponds to the extrapolated time of the fictitious starting or ending at the center of the central body. At any time the average speed from t = 0 {\displaystyle t=0\!\,} is 1.5 times the current speed, i.e. 1.5 times the local escape velocity.