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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 IAU abandoned the defined value of k in 2012 in favour of a defined value of the astronomical unit of 1.495 978 707 00 × 10 11 m exactly, while the strength of the gravitational force is now to be expressed in the separate standard gravitational parameter G M ☉, measured in SI units of m 3 ⋅s −2.
The astronomical seeing conditions at an observatory can be conveniently described by the parameters r 0 and t 0. For telescopes with diameters smaller than r 0 , the resolution of long-exposure images is determined primarily by diffraction and the size of the Airy pattern and thus is inversely proportional to the telescope diameter.
Calculations in celestial mechanics can also be carried out using the units of solar masses, mean solar days and astronomical units rather than standard SI units. For this purpose, the Gaussian gravitational constant was historically in widespread use, k = 0.017 202 098 95 radians per day , expressing the mean angular velocity of the Sun ...
For astronomical bodies other than Earth, and for short distances of fall at other than "ground" level, g in the above equations may be replaced by (+) where G is the gravitational constant, M is the mass of the astronomical body, m is the mass of the falling body, and r is the radius from the falling object to the center of the astronomical body.
In most fields of astronomy, the ellipticity is defined as , where = is the axis ratio of the ellipse. In weak gravitational lensing , two different definitions are commonly used, and both are complex quantities which specify both the axis ratio and the position angle ϕ {\displaystyle \phi ~} :
Astrometry is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It provides the kinematics and physical origin of the Solar System and this galaxy , the Milky Way .
An N-body simulation of the cosmological formation of a cluster of galaxies in an expanding universe. In physics and astronomy, an N-body simulation is a simulation of a dynamical system of particles, usually under the influence of physical forces, such as gravity (see n-body problem for other applications).