Parallax Equation

[joeWyncoll]

How was/is the equation used in computing parallax formed?

[JulianO]

It's basic trigonometry. You have two right angle triangles, you know the base, and you know angle viewed from either end of the base.

Therefore sin x = opposite / hypotenuse

we know x, we know the opposite distance, so we can work out the hypotenuse (distance to object).

For stars, the angle is so small the sin(x) is often replaced by x as it is almost the same, and the opposite distance is 1AU as we measure it across the earths orbit.

See http://en.wikipedia.org/wiki/Parallax for some diagrams.

[joeWyncoll]

What would the angle to the star be measured in?

[JulianO]

Well if you use the small angle approximation it needs to be radians. Otherwise degrees and have your calculator set on degree for the sin function to work.

The angle for stars is usually measured in arc seconds, so in 3600's of a degree. A parsec is the distance a star will show 1 arc second of parallax.

[Mr Q]

And don't forget that we take those base line views of a star when the Earth is in its opposite position around the Sun for a more accurate and usable base line each time the star's position is compared to the other stars in the field.