In relativistic physics, a velocity-addition formula is an equation that specifies how to combine the velocities of objects in a way that is consistent with the requirement that no object's speed can
The special theory of relativity, formulated in 1905 by Albert Einstein, implies that addition of velocities does not behave in accordance with simple vector addition.
Hippolyte Fizeau (1819–1896), a French physicist, was in 1851 the first to measure the speed of light in flowing water.
James Bradley (1693–1762) FRS provided an explanation of aberration of light correct at the classical level, at odds with the later theories prevailing in the nineteenth century based on the existence of aether.
Christian Doppler (1803–1853) was an Austrian mathematician and physicist who discovered that the observed frequency of a wave depends on the relative speed of the source and the observer.
In astronomy, aberration is a phenomenon where celestial objects exhibit an apparent motion about their true positions based on the velocity of the observer: It causes objects to appear to be displace
Velocity-addition formula
…rotation of the coordinate system and a boost. Standard applications of velocity-addition formulas include the Doppler shift, Doppler navigation, the aberration of light, and the dragging of light in moving water observed in the 1851 Fizeau experiment. The notation employs u as velocity of a body within a Lorentz frame…
Bradley's observations of Eltanin (γ Draconis) and 35 Camelopardalis as reduced by Busch to the year 1730
Hypothetical observation of Eltanin if its movement was caused by parallax
Hypothetical observation of γ Draconis and 35 Camelopardalis if their movements were caused by nutation
Figure 2: As light propagates down the telescope, the telescope moves requiring a tilt to the telescope that depends on the speed of light. The apparent angle of the star φ differs from its true angle θ.