# How can you find the parallax angle of a star?

Jan 9, 2017

See the explanation.

#### 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 $\angle P S Q = \alpha$, at the star S.

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

$1 A U = E P = E S \tan \left(\frac{\alpha}{2}\right)$.

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

$1 A U = E S \left(\frac{\alpha}{2}\right)$, nearly.

In the case of the Sun, $\alpha$ 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, $\frac{\alpha}{2} = \frac{\pi}{4}$, giving $\alpha = \frac{\pi}{2}$, ignoring small eccentricity

of the Earth's orbit.

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