Relativistic Aberration of Light Calculator

How it is calculated

cos θ′ = (cos θ − β) / (1 − β·cos θ), then θ′ = arccos(cos θ′) in degrees. Here θ is the angle in degrees between the direction the light travels and the direction of the observer's velocity, as measured in the original (rest) frame, β = v/c is the observer's speed as a fraction of the speed of light, and θ′ is the same direction as measured by the moving observer.

The angle must be from 0 to 180 degrees and β from 0 up to but not including 1; other values give no result. With β = 0 nothing changes, and light travelling exactly along or against the motion (0° or 180°) keeps its angle. For all angles in between, the observed angle comes out larger than the original, and the effect grows as β approaches 1. The tool gives one angle only, not the Doppler shift or the intensity change.

Common mistakes

• Entering β as a speed in km/s or m/s: β is the ratio v/c, so 0.6 means 60% of the speed of light; a value of 1 or more gives no result.
• Using radians: the angle field is in degrees, from 0 to 180.
• Measuring the angle from the wrong axis, for example from the sideways direction: it is measured from the direction of the observer's motion.
• Reading θ′ as the apparent position of the source: it is the travel direction of the light, so the apparent source direction is 180° − θ′ from the line of motion.