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The term "unit distance" is also used for the length A while, in general usage, it is usually referred to simply as the "astronomical unit", symbol au. 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 ...
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In the more general case where the bodies need not be a large one and a small one, e.g. a binary star system, we define: the vector r is the position of one body relative to the other; r, v, and in the case of an elliptic orbit, the semi-major axis a, are defined accordingly (hence r is the distance)
The astronomical unit of time is a time interval of one day (D) of 86400 seconds.The astronomical unit of mass is the mass of the Sun (S).The astronomical unit of length is that length (A) 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.
In astronomy, the binary mass function or simply mass function is a function that constrains the mass of the unseen component (typically a star or exoplanet) in a single-lined spectroscopic binary star or in a planetary system.
In orbital mechanics, Kepler's equation relates various geometric properties of the orbit of a body subject to a central force.. It was derived by Johannes Kepler in 1609 in Chapter 60 of his Astronomia nova, [1] [2] and in book V of his Epitome of Copernican Astronomy (1621) Kepler proposed an iterative solution to the equation.
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The equation of state for ordinary non-relativistic 'matter' (e.g. cold dust) is =, which means that its energy density decreases as =, where is a volume.In an expanding universe, the total energy of non-relativistic matter remains constant, with its density decreasing as the volume increases.