, which in the limit may be approximated by . Relativistic explanation The reasoning in the relativistic case is the same except that the relativistic velocity addition formulas must be used, which can be derived from Lorentz transformations between different frames of reference. These formulas are where , giving the components of the light beam in the Earth's frame in terms of the components in the Sun's frame. The angle of the beam in the Earth's frame is thus In the case of , this result reduces to , and in the limit this may be approximated by . This relativistic derivation keeps the speed of light constant in all frames of reference, unlike the classical derivation above. Relationship to light-time correction and relativistic beaming Aberration is related to two other phenomena, light-time correction, which is due to the motion of an observed object during the time taken by its light to reach an observer, and relativistic beaming, which is an angling of the light emitted by a moving light source. It can be considered equivalent to them but in a different inertial frame of reference. In aberration, the observer is considered to be moving relative to a (for the sake of simplicity) stationary light source, while in light-time correction and relativistic beaming the light source is considered to be moving relative to a stationary observer. Consider the case of an observer and a light source moving relative to each other at constant velocity, with a light beam moving from the source to the observer. At the moment of emission, the beam in the observer's rest frame is tilted compared to the one in the source's rest frame, as understood through relativistic beaming. During the time it takes the light beam to reach the observer the light source moves in the observer's frame, and the 'true position' of the light source is displaced relative to the apparent position the observer sees, as explained by light-time correction. Finally, the beam in the observer's frame at the moment of observation is tilted compared to the beam in source's frame, which can be understood as an aberrational effect. Thus, a person in the light source's frame would describe the apparent tilting of the beam in terms of aberration, while a person in the observer's frame would describe it as a light-time effect. The relationship between these phenomena is only valid if the observer