How does one calculate the parallax of stars?

Question

2622 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-27T03:42:35

See explanation

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

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

at $∠ β$ $angle beta$ ,

the parallax $∠ p = | β - α |$ $angle p =|beta-alpha|$ .

The distance of the star is now approximated as

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

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

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

$E S \times sin (\frac{p}{2}) = 1 A U$ $ES xx sin (p/2) = 1 AU$ , nearly, and .

as p is small,

$sin (\frac{p}{2}) = \frac{p}{2}$ $sin (p/2) = p/2$ , 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 $p = \frac{1}{4.246 \times 53242}$ $p = 1/(4.246 xx 53242)$

$= 0.0136$ $=0.0136$ radian

$= {0.077945}^{o}$ $=0.077945^o$

$= 4' 40.6''$ .