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In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is uniformly isotropic and homogeneous when viewed on a large enough scale, since the forces are expected to act equally throughout the universe on a large scale, and should, therefore, produce no observable inequalities in the large-scale structuring over the course ...
For example, in the vicinity of a typical star the ratio of radiation-to-gravity force on a hydrogen atom or ion, = =,, hence radiation force is negligible in general, except perhaps around a luminous O-type star of mass , or around a black hole accreting gas at the Eddington limit so that its luminosity-to-mass ratio / is defined by =.
The definition of "unimodal" was extended to functions of real numbers as well. A common definition is as follows: a function f(x) is a unimodal function if for some value m, it is monotonically increasing for x ≤ m and monotonically decreasing for x ≥ m. In that case, the maximum value of f(x) is f(m) and there are no other local maxima.
The equation of hydrostatic equilibrium may need to be modified by adding a radial acceleration term if the radius of the star is changing very quickly, for example if the star is radially pulsating. [9] Also, if the nuclear burning is not stable, or the star's core is rapidly collapsing, an entropy term must be added to the energy equation. [10]
Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. [1] [2] As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the nature of the heavenly bodies, rather than their positions or motions in space—what they are, rather than where they are", [3] which is studied ...
Atomic physics plays a key role in astrophysics as astronomers' only information about a particular object comes through the light that it emits, and this light arises through atomic transitions. Molecular astrophysics , developed into a rigorous field of investigation by theoretical astrochemist Alexander Dalgarno beginning in 1967, concerns ...
Typical examples are the halo stars passing through the disk of the Milky Way at steep angles. One of the nearest 45 stars, called Kapteyn's Star, is an example of the high-velocity stars that lie near the Sun: Its observed radial velocity is −245 km/s, and the components of its space velocity are u = +19 km/s, v = −288 km/s, and w = −52 ...
Evolution of central pressure against compactness (radius over mass) for a uniform density 'star'. This central pressure diverges at the Buchdahl bound. In general relativity , Buchdahl's theorem , named after Hans Adolf Buchdahl , [ 1 ] makes more precise the notion that there is a maximal sustainable density for ordinary gravitating matter.