![]() ![]() For this reason, observer A observes a frequency of arrival that is less than the frequency at which the disturbances are produced. On the other hand, each consecutive disturbance has a further distance to travel before reaching observer A. Thus, observer B observes that the frequency of arrival of the disturbances is higher than the frequency at which disturbances are produced. ![]() Subsequently, each consecutive disturbance has a shorter distance to travel before reaching observer B and thus takes less time to reach observer B. Since the bug is moving towards the right, each consecutive disturbance originates from a position that is closer to observer B and farther from observer A. Now suppose that our bug is moving to the right across the puddle of water and producing disturbances at the same frequency of 2 disturbances per second. If the bug produces disturbances at a frequency of 2 per second, then each observer would observe them approaching at a frequency of 2 per second. In fact, the frequency at which disturbances reach the edge of the puddle would be the same as the frequency at which the bug produces the disturbances. An observer at point A (the left edge of the puddle) would observe the disturbances to strike the puddle's edge at the same frequency that would be observed by an observer at point B (at the right edge of the puddle). These circles would reach the edges of the water puddle at the same frequency. The pattern produced by the bug's shaking would be a series of concentric circles as shown in the diagram at the right. Since each disturbance is traveling in the same medium, they would all travel in every direction at the same speed. If these disturbances originate at a point, then they would travel outward from that point in all directions. The bug is periodically shaking its legs in order to produce disturbances that travel through the water. The value for the surface of the sun is about 2 × 10 −6, corresponding to 0.64 km/s.Suppose that there is a happy bug in the center of a circular water puddle. For Earth's surface with respect to infinity, z is approximately 7 × 10 −10 (the equivalent of a 0.2 m/s radial Doppler shift) for the Moon it is approximately 3 × 10 −11 (about 1 cm/s). ![]() To first approximation, gravitational redshift is proportional to the difference in gravitational potential divided by the speed of light squared, z = Δ U / c 2. A gravitational redshift can also equivalently be interpreted as gravitational time dilation at the source of the radiation: if two oscillators (attached to transmitters producing electromagnetic radiation) are operating at different gravitational potentials, the oscillator at the higher gravitational potential (farther from the attracting body) will seem to ‘tick’ faster that is, when observed from the same location, it will have a higher measured frequency than the oscillator at the lower gravitational potential (closer to the attracting body). Gravitational redshift can be interpreted as a consequence of the equivalence principle (that gravity and acceleration are equivalent and the redshift is caused by the Doppler effect) or as a consequence of the mass-energy equivalence and conservation of energy ('falling' photons gain energy), though there are numerous subtleties that complicate a rigorous derivation. The effect was first described by Einstein in 1907, eight years before his publication of the full theory of relativity. The opposite effect, in which photons (seem to) gain energy when travelling into a gravitational well, is known as a gravitational blueshift (a type of blueshift). This loss of energy corresponds to a decrease in the wave frequency and increase in the wavelength, known more generally as a redshift. In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. The effect is greatly exaggerated in this diagram. The gravitational redshift of a light wave as it moves upwards against a gravitational field (produced by the yellow star below). ![]()
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