Relativistic Aberration & Doppler Beaming

Velocity

β = v / c 0.600

Display

Doppler colour shift Relativistic beaming (brightness) Rest-frame angle rings

Live Readouts

Lorentz factor γ

1.25

Rear/front compression

126.9°

Doppler factor, ahead

2.00×

Doppler factor, astern

0.50×

How it works

2,000 stars sit at fixed directions in the star field's own rest frame, spread evenly over the whole sky. You (the observer) fly through that field at speed v = βc along the forward axis. Special relativity says the direction you actually see each star from is not its rest-frame direction θ — it is aberrated:

cos θ' = (cos θ + β) / (1 + β cos θ)

where θ is the star's angle from your heading in the star field's frame and θ' is the angle you observe. As β → 1, this formula crushes almost the entire sky — including most of what was behind you — into a shrinking bright disc dead ahead. That is the same mechanism (stellar aberration, first measured classically by Bradley in 1727) taken to its relativistic extreme.

Each star's colour and brightness follow the relativistic Doppler factor for the angle you now see it at:

D(θ') = 1 / [ γ (1 − β cos θ') ]     γ = 1 / √(1 − β²)

Stars in the forward disc have D > 1 (blueshifted, and rendered brighter — flux scales roughly as D³, the same relativistic beaming that makes the jets of blazars flare when pointed near our line of sight). Stars behind you have D < 1: redshifted and dimmed. The "rear/front compression" readout is the rest-frame angle that lands exactly at your 90° sideways view — cos θ = −β — showing how much of the rear hemisphere has been folded into your forward field of view.

β slider / presets — sets your cruising speed as a fraction of c.
Doppler colour shift — toggles the blue-ahead / red-behind tinting; turn it off to see aberration in isolation.
Relativistic beaming — toggles the D³ brightness scaling that makes the forward disc flare and the rear fade.
Angle rings — five reference circles at 30°/60°/90°/120°/150° from your heading in the rest frame, redrawn each frame at their aberrated position so you can see the compression directly.
Drag inside the view to look around — the star field always stays centred on your direction of travel.

Drag to look around

Blueshifted (ahead) Neutral Redshifted (astern)

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