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A scale factor is usually a decimal which scales, or multiplies, some quantity. In the equation y = Cx, C is the scale factor for x. C is also the coefficient of x, and may be called the constant of proportionality of y to x. For example, doubling distances corresponds to a scale factor of two for distance, while cutting a cake in half results ...
The scale factors for the elliptic coordinates (,) are equal to = = + = . Using the double argument identities for hyperbolic functions and trigonometric functions, the scale factors can be equivalently expressed as
The scale factor is dimensionless, with counted from the birth of the universe and set to the present age of the universe: [4] giving the current value of as () or . The evolution of the scale factor is a dynamical question, determined by the equations of general relativity , which are presented in the case of a locally isotropic, locally ...
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Contains the three translations along the coordinate axes; μ – scale factor, which is unitless; if it is given in ppm, it must be divided by 1,000,000 and added to 1. R – rotation matrix. Consists of three axes (small [clarification needed] rotations around each of the three coordinate axes) r x, r y, r z. The rotation matrix is an ...
Rewriting the metric in spherical coordinates reduces four coordinates to three coordinates. The radial coordinate is written as a product of a comoving coordinate, r, and a time dependent scale factor R(t). The resulting metric can be written in several forms.
Comoving coordinates separate the exactly proportional expansion in a Friedmannian universe in spatial comoving coordinates from the scale factor () . This example is for the ΛCDM model. The comoving time coordinate is the elapsed time since the Big Bang according to a clock of a comoving observer and is a measure of cosmological time .
In each zone the scale factor of the central meridian reduces the diameter of the transverse cylinder to produce a secant projection with two standard lines, or lines of true scale, about 180 km on each side of, and about parallel to, the central meridian (Arc cos 0.9996 = 1.62° at the Equator). The scale is less than 1 inside the standard ...