Run through rain falling straight down and it strikes you from the front. You have to tilt your umbrella forward.
The velocity of the drops seen by the runner is the drops' velocity minus the runner's own, which points in from ahead at a slant. The rain falls just as before; what changed is the speed of the one watching.
The same happens with light, and it is called aberration. For light, though, velocities combine by the addition rule, so the tilt does not come out of the same calculation as for rain.
From Bradley measured the position of Draconis, a star passing almost overhead. Over a year its apparent position traces a small ellipse with a semi-major axis of about arcseconds.
He was looking for annual parallax, a change in a star's direction with the Earth's position. But the motion he found followed the direction of the Earth's velocity rather than its position, three months out of step with parallax.
In Bradley explained the motion by combining the finite speed of light with the Earth's orbital speed. It was the first observation to show directly that the Earth moves around the Sun.
Light that arrives, in the rest frame, from a direction at angle to the direction of motion arrives, in a frame moving at speed , from the angle given by
The figure uses : light from , , , and degrees arrives from , , , and degrees.
For small the shift is about , largest for light from the side. For the Earth's orbit , and since one radian is arcseconds, the shift is about arcseconds, which matches what Bradley measured.
As grows, the shift is no longer a small angle. Stars scattered across the sky crowd toward the direction of travel.
A star seen directly to the side ( degrees) in the rest frame moves to the direction with . At that is degrees from straight ahead.
The stars in the figure rearrange for , , and in turn. Their number does not change; only their arrangement closes up toward the front.
Not only directions but brightness crowds forward too. A source that shines equally in all directions in its own frame, seen moving from the rest frame, sends its light into a narrow cone ahead.
Light sent into the forward half in the source's frame falls, in the rest frame, within the angle with . For large this angle is about radians, about degrees at . This is called the headlight effect.
The source in the figure speeds up through , and , with equal to , and , and the curve showing the brightness stretches forward.
Fast electrons curving in an accelerator emit a narrow beam of light (synchrotron radiation), and a jet from a distant galaxy looks bright on one side only: both come from this effect.