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Examples include: sunrise, weather, fog, ... Over many intervals of time, natural phenomena have been observed by a series of countless events as a feature created by ...
A tautochrone curve or isochrone curve (from Ancient Greek ταὐτό 'same' ἴσος 'equal' and χρόνος 'time') is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point on the curve.
This is described by: = + /, where v(t) is the velocity at a time t, a is the acceleration of the spaceship and t is the coordinate time as measured by people on Earth. [ p 20 ] Therefore, after one year of accelerating at 9.81 m/s 2 , the spaceship will be travelling at v = 0.712 c and 0.946 c after three years, relative to Earth.
For a more complex example involving observers in relative motion, consider Alfred, who is standing on the side of a road watching a car drive past him from left to right. In his frame of reference, Alfred defines the spot where he is standing as the origin, the road as the x -axis, and the direction in front of him as the positive y -axis.
The failure of any experiment to detect motion through the aether led Hendrik Lorentz, starting in 1892, to develop a theory of electrodynamics based on an immobile luminiferous aether (about whose material constitution Lorentz did not speculate), physical length contraction, and a "local time" in which Maxwell's equations retain their form in ...
The apparent motion of the heavenly bodies with respect to time is cyclical in nature. Apollonius of Perga (3rd century BC) realized that this cyclical variation could be represented visually by small circular orbits, or epicycles, revolving on larger circular orbits, or deferents. Hipparchus (2nd century BC) calculated the required orbits ...
A more intuitive characteristic of exponential decay for many people is the time required for the decaying quantity to fall to one half of its initial value. (If N(t) is discrete, then this is the median life-time rather than the mean life-time.) This time is called the half-life, and often denoted by the symbol t 1/2. The half-life can be ...
This formulation of the geodesic equation of motion can be useful for computer calculations and to compare General Relativity with Newtonian Gravity. [1] It is straightforward to derive this form of the geodesic equation of motion from the form which uses proper time as a parameter using the chain rule. Notice that both sides of this last ...