Question

Calculate the angular distance of the Earth from the Sun in arcseconds as seen from Alpha Centauri . You can assume that the Earth's orbit is a circle that lies in the plane of the sky as seen from Alpha Centauri.

Answer 1

The angular distance of the Earth from the Sun as seen from Alpha Centauri is shown as in the above figure. R_es is the radius of the earth's orbit around the sun and L is the distance between the sun and Alpha Centauri. Since R_es is too small relative to L, the side R_es of the triangle formed by the three objects can be approximated as the arc of radius L subtended by R_es.

Alpha Centauri is 4.22 light-years away from the sun and the radius of the Earth's orbit around the Sun is 1 AU.

Using

Using

Note that ' denotes arcminutes and '' denotes arcseconds.