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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: = (+).
The square of this quotient is proportional to the parameter (that is, the latus rectum) of the orbit and the sum of the mass of the Sun and the body. This is a modified form of Kepler's third law. He next defines: 2p as the parameter (i.e., the latus rectum) of a body's orbit, μ as the mass of the body, where the mass of the Sun = 1,
In astrodynamics, canonical units are defined in terms of some important object’s orbit that serves as a reference. In this system, a reference mass, for example the Sun’s, is designated as 1 “canonical mass unit” and the mean distance from the orbiting object to the reference object is considered the “canonical distance unit”.
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 ...
This will rise to 10 −6 M ☉ /year on the asymptotic giant branch, before peaking at a rate of 10 −5 to 10 −4 M ☉ /year as the Sun generates a planetary nebula. By the time the Sun becomes a degenerate white dwarf, it will have lost 46% of its starting mass. [15] The mass of the Sun has been decreasing since the time it formed.
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An equivalent formulation of the old definition of the astronomical unit is the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with a mean motion of 0.017 202 098 95 radians per day. [5] The speed of light in IAU is the defined value c 0 = 299 792 458 m/s of the SI units.