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The standard gravitational parameter can be determined using a pendulum oscillating above the surface of a body as: [13] μ ≈ 4 π 2 r 2 L T 2 {\displaystyle \mu \approx {\frac {4\pi ^{2}r^{2}L}{T^{2}}}} where r is the radius of the gravitating body, L is the length of the pendulum, and T is the period of the pendulum (for the reason of the ...
The gravity of Earth, denoted by g, is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation).
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, = (),
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 gravitational parameter GM appears as above in Newton's law of universal gravitation, as well as in formulas for the deflection 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.
After reducing the problem to the relative motion of the bodies in the plane, he defines the constant of the motion c 3 by the equation ẋ 2 + ẏ 2 = 2k 2 M/r + c 3, where M is the total mass of the two bodies and k 2 is Moulton's notation for the gravitational constant. He defines c 1, c 2, and c 4 to be other constants of the
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 ...
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