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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 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.
As a consequence of the law of gravitation and Kepler's third law, k is directly proportional to the square root of the standard gravitational parameter of the Sun, and its value in radians per day follows by setting Earth's semi-major axis (the astronomical unit, au) to unity, k:(rad/d) = (G M ☉) 0.5 ·au −1.5.
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 ...
The Sun's orbital characteristics are listed in ... Gravitational parameter: m 3/ s 2: 1.327 ... The Moon is the only natural satellite with a standard abstract ...
It is approximately equal to the mean Earth–Sun distance. It was formerly defined as that length for which the Gaussian gravitational constant (k) takes the value 0.017 202 098 95 when the units of measurement are the astronomical units of length, mass and time. [1] The dimensions of k 2 are those of the constant of gravitation (G), i.e., L 3 ...
The Sun is moved by the gravitational pull of the planets. The center of the Sun moves around the Solar System barycenter, within a range from 0.1 to 2.2 solar radii. The Sun's motion around the barycenter approximately repeats every 179 years, rotated by about 30° due primarily to the synodic period of Jupiter and Saturn. [152]
The choice of solar mass, M ☉, as the basic unit for planetary mass comes directly from the calculations used to determine planetary mass.In the most precise case, that of the Earth itself, the mass is known in terms of solar masses to twelve significant figures: the same mass, in terms of kilograms or other Earth-based units, is only known to five significant figures, which is less than a ...