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Daily time dilation (gain or loss if negative) in microseconds as a function of (circular) orbit radius r = rs/re, where rs is satellite orbit radius and re is the equatorial Earth radius, calculated using the Schwarzschild metric. At r ≈ 1.497 [Note 1] there is no time dilation. Here the effects of motion and reduced gravity cancel.
Gravitational time dilation is closely related to gravitational redshift, [4] in which the closer a body emitting light of constant frequency is to a gravitating body, the more its time is slowed by gravitational time dilation, and the lower (more "redshifted") would seem to be the frequency of the emitted light, as measured by a fixed observer.
The motion of the lighter body (called the "particle" below) can then be determined from the Schwarzschild solution; the motion is a geodesic ("shortest path between two points") in the curved space-time.
An observer at rest observing an object travelling very close to the speed of light would observe the length of the object in the direction of motion as very near zero. Then, at a speed of 13 400 000 m/s (30 million mph, 0.0447 c) contracted length is 99.9% of the length at rest; at a speed of 42 300 000 m/s (95 million mph, 0.141 c), the ...
In order to find out the transformation of three-acceleration, one has to differentiate the spatial coordinates and ′ of the Lorentz transformation with respect to and ′, from which the transformation of three-velocity (also called velocity-addition formula) between and ′ follows, and eventually by another differentiation with respect to and ′ the transformation of three-acceleration ...
with dimensions of radians per unit time, degrees per unit time or revolutions per unit time. [2] [3] The value of mean motion depends on the circumstances of the particular gravitating system. In systems with more mass, bodies will orbit faster, in accordance with Newton's law of universal gravitation. Likewise, bodies closer together will ...
The relativistic mass is the sum total quantity of energy in a body or system (divided by c 2).Thus, the mass in the formula = is the relativistic mass. For a particle of non-zero rest mass m moving at a speed relative to the observer, one finds =.
In physics, angular velocity (symbol ω or , the lowercase Greek letter omega), also known as the angular frequency vector, [1] is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction.