page_title: Velocity-addition formula
section_title: Aberration of light
hierarchical_section_title: Velocity-addition formula / Applications / Aberration of light
context_page_description: In relativistic physics, a velocity-addition formula is a three-dimensional equation that relates the velocities of objects in different reference frames. Such formulas apply to successive Lorentz transformations, so they also relate different frames. Accompanying velocity addition is a kinematic effect known as Thomas precession, whereby successive non-collinear Lorentz boosts become equivalent to the composition of a 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 S, and v as velocity of a second frame S′, as measured in S, and u′ as the transformed velocity of the body within the second frame.
context_section_description: Another basic application is to consider the deviation of light, i.e. change of its direction, when transforming to a new reference frame with parallel axes, called aberration of light. In this case, v′ = v = c, and insertion in the formula for tan θ yields
  For this case one may also compute sin θ and cos θ from the standard formulae,
  Trigonometry
  the trigonometric manipulations essentially being identical in the cos case to the manipulations in the sin case. Consider the difference,
  correct to order ​ᵛ⁄c. Employ in order to make small angle approximations a trigonometric formula,
  where cos(θ + θ′) ≈ cos θ′, sin(θ − θ′) ≈ (θ − θ′) were used.
  Thus the quantity
  the classical aberration angle, is obtained in the limit ​ⱽ⁄c → 0.
caption: James Bradley (1693–1762) FRS, provided an explanation of aberration of light correct at the classical level,[17] at odds with the later theories prevailing in the nineteenth century based on the existence of aether.
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