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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.
= (+) is the standard gravitational parameter of the bodies; h {\displaystyle h\,\!} is the specific relative angular momentum of the same body referenced [ 2 ] to the center of mass. In other context h is used in the sense of a total for two bodies expressed as relative angular momentum of the system divided by the reduced mass, giving the ...
In astrodynamics, the vis-viva equation is one of the equations that model the motion of orbiting bodies.It is the direct result of the principle of conservation of mechanical energy which applies when the only force acting on an object is its own weight which is the gravitational force determined by the product of the mass of the object and the strength of the surrounding gravitational field.
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).
where μ is the standard gravitational parameter, a constant for any particular gravitational system. If the mean motion is given in units of radians per unit of time, we can combine it into the above definition of the Kepler's 3rd law, = (),
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.