Aberration of Starlight

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Parameters

Earth orbital speed v/c: 0.0001 Star elevation θ: 90° Star azimuth φ: 0° Animation speed: 1.0x

Aberration Data

—

α (arcsec)

20.5

κ constant

—

v_Earth (km/s)

—

Orbit phase

Theory

Classical: tan(α) = v·sinθ/c
α ≈ (v/c)·sinθ (small v/c)

Relativistic:
cos(θ') = (cosθ + β)/(1+β·cosθ)
β = v/c

κ = (v_E/c)·(1rad→arcsec)
= 29.8/3e5 × 206265 = 20.5"

Annual aberration: ellipse
Semimajor = κ·sin(90°−lat_star)