Question

How is the distance between two stars measured?

Answer 1

`S_1S_2=sqrt(d_1^2+d_2^2-2 xx d_1 xx d_2 xx cos angle S_1ES_2)`, where `d_1 and d_2` are distances of stars `S_1 and S_2`, from Earth E and `angle S_1 ES_2` is the angular spacing.

Explanation:

The distance SE of a star S from the Earth E is obtained in AU units

from parallax angle `alpha` radian as

`ES = 1/alpha` AU, nearly.

In light years (ly), this is

ES = 1/(63242 alpha) ly, nearly.

Observed from E,

If the angular spacing between the two stars `S_1 and S_2` is

`angle S_1ES_2`, then the distance between the two stars at

distances `d_1=ES_1 and d_2=ES_2` is

`S_1S_2`

`=sqrt(d_1^2+d_2^2-2 xx d_1 xx d_2 xx cos angle S_1ES_2)`