# How does one calculate the parallax of stars?

Jan 27, 2017

See explanation

#### Explanation:

If S is a star observed from E, at an angle $\alpha$ to the

horizontal and the same star is observed again, after half a year,

at $\angle \beta$,

the parallax $\angle p = | \beta - \alpha |$.

The distance of the star is now approximated as

$\frac{1}{p} A U = \frac{1}{63242 p}$ light years, where p is in radian measure.

Note that the distance across, between the two positions of E, is

nearly the diameter of [the Earth](https://socratic.org/astronomy/our-

solar-system/the-earth)'s orbit = $2 A U = 2 \times 149387871$ km and

$E S \times \sin \left(\frac{p}{2}\right) = 1 A U$, nearly, and .

as p is small,

$\sin \left(\frac{p}{2}\right) = \frac{p}{2}$, nearly, and so,

ES = 1/p AU, nearly.

Vice versa, we can predict this p for the half year interval, if the

distance of the star is already known.

For example, the nearest S Proxima Centauri is at a distance ES =

4.246 ly, and this gives

Half year parallax $p = \frac{1}{4.246 \times 53242}$

$= 0.0136$ radian

$= {0.077945}^{o}$

$= 4 ' 40.6 ' '$ .