Stellar Aberration of Light

What you are seeing: star positions as they appear to an observer moving at velocity $\beta c$ along the $+x$ axis, compared to their rest-frame positions. The Lorentz aberration formula $\cos\theta_\text{obs} = (\cos\theta_\text{rest} + \beta) / (1 + \beta \cos\theta_\text{rest})$ pulls every star toward the forward direction (relativistic beaming in geometry). For Earth's annual orbital aberration ( $\beta \approx 10^{-4}$ ), the maximum shift is the classical constant of aberration $\approx 20.5"$ .

Rest-frame stars are drawn at uniform angles around the observer (cyan dots); their observed positions cluster forward (orange dots). Connecting lines show the shift; the maximum-shift line is highlighted in accent. As $\beta \to 1$ the entire visible sphere concentrates into a forward cone.

Figure 1. Stellar aberration: rest vs observed positions on a polar plot. Method: closed-form Lorentz aberration.

log10 beta-4.00

WHAT TO TRY

Increase beta and the stars crowd forward: an observer in motion sees the whole sky swing toward the direction of travel, the relativistic aberration of starlight.
At Earth orbital speed the shift is only about 20 arcseconds, the stellar aberration Bradley found in 1727, the first direct proof the Earth moves.
Push beta toward 1 and the sky compresses into a bright forward spot: a relativistic traveller sees the stars pile up ahead, the relativistic headlight effect.