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Calculate the angular distance of the Earth from the Sun in arcseconds as seen from Alpha...

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.

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Answer #1

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

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.

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