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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.}
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 = 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 value of G times the mass of an object, called the standard gravitational parameter, is known for the Sun and several planets to a much higher accuracy than G alone. [13] As a result, the solar mass is used as the standard mass in the astronomical system of units.
Gravitational parameter: m 3/ s 2: 1.327×10 20: Density: g/cm 3: 1.409 Equatorial gravity: m/s 2 g: 274.0 27.94 Escape velocity: km/s: 617.7 Rotation period days: 25.38 Orbital period about Galactic Center [4] million years 225–250 Mean orbital speed [4] km/s: ≈ 220 Axial tilt to the ecliptic: deg. 7.25 Axial tilt to the galactic plane ...
is the standard gravitational parameter, (+), often expressed as when one body is much larger than the other. r {\displaystyle r\,} is the distance between the orbiting body and center of mass. a {\displaystyle a\,\!} is the length of the semi-major axis .
An orbit will be Sun-synchronous when the precession rate ρ = dΩ / dt equals the mean motion of the Earth about the Sun n E, which is 360° per sidereal year (1.990 968 71 × 10 −7 rad/s), so we must set n E = ΔΩ E / T E = ρ = ΔΩ / T , where T E is the Earth orbital period, while T is the period of the spacecraft ...
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 ...