Suppose s1 be some nearby star whose distance d from the earth is to be found. Let us take some very distant star whose position and direction is fixed as the rotates round the sun. The parallax angle θ1 between distant star and nearby star s1 is determined at any time, when the earth is at the position P(say). After six months, the earth will at position Q. The angle of parallax θ2 is again determined between Q and s1. Total parallax angle subtended by the near by star s1 on the earth'* orbital diameter PQ is (θ1 + θ2).
But θ1 = θ2 = θ, hence sinθ = OQ/QS
Because θ is very small, therefore Sinθ ≅ θ.
and θ = OQ/QS1 or QS1 = OQ/θ
or, d =r/θ
Thus measuring r and θ, distance of the nearby star from earth can be determined.
