## Evidence for the Earth’s Rotation around the Sun

In 1729 James Bradley discovered the **aberration of starlight**. If the Earth is in motion at speed *v*, we must tilt a telescope in the direction of motion by an angle *θ* ≈ tan *θ* = *v/c*, so that the bottom of the telescope can meet a light ray which has entered the top of the telescope. Bradley observed this very small angle of tilt, *θ* ≈ 20.49″

⇒ *v* = *θc* ≈ (9.934 x 10^{-5} rad)(3 x 10^{5}kms^{-1}) ≈ 29.8 km/s

According to the heliocentric model of the solar system, nearby stars should exhibit parallax effects, against the farther ‘fixed stars’ of the celestial sphere. If the observed parallax angle of a star is π” then the star’s distance is,

d = (206,265/π”)AU

(206,265 is the number of arcseconds in one radian).

In 1838 Friedrich Wilhelm Bessel published the first observed **stellar parallax** of 0.294″ for the star 61-Cygni. F.G.W. Struve also found the parallax of Vega (α Lyrae) and T. Henderson found that of α Centauri. The nearest star (Proxima Centauri) has a parallax of 0.764″ and a distance of 270,000 AU (~ 4 light years).

If a star emits radiation at a wavelength λ_{0} and we observe this at a wavelength λ, then the **Doppler Effect** formula (*v *≪ *c*) is,

Δλ/λ_{0} = (λ – λ_{0})/λ_{0} = *v _{r}/c*

Where *v*_{r} is the relative line of sight speed, between the observer and the observed.

For stars at the ecliptic pole, no Doppler shift occurs because there is no radial component of the velocity. The maximum amplitude of this Doppler shift occurs for stars on the ecliptic. Measuring this gives the Earth’s speed of revolution as *v*_{⊕} ≈ 29.80km/s