How can you find the parallax angle of a star?

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Answer 1 · 2017-01-09T16:16:43

See the explanation.

With respect to a star, the Earth E turns around its star Sun along

half of its nearly-circular orbit, of radius 1 AU, in one half year..

The diameter ( of length 2 AU ) of the Earth's orbit joining these

two positions P and Q subtends the so-called

parallax $∠ P S Q = α$ $angle PSQ = alpha$ , at the star S.

Easily, the distance of the star ES, in AU unit, is given by

$1 A U = E P = E S tan (\frac{α}{2})$ $1 AU = EP = ES tan (alpha/2)$ .

As $(\frac{α}{2})$ $(alpha/2)$ radian is quite small for a distant star S,

$1 A U = E S (\frac{α}{2})$ $1 AU = ES (alpha/2)$ , nearly.

In the case of the Sun, $α$ $alpha$ is not small., and so, tan(alpha/2)

should be retained as such, and the distance reasd

ES = cot(alpha.2) AU = 1 AU.

So, $\frac{α}{2} = \frac{π}{4}$ $alpha/2=pi/4$ , giving $α = \frac{π}{2}$ $alpha = pi/2$ , ignoring small eccentricity

of the Earth's orbit.

Note that all these results are for half-year spacing PQ = 2AU,.