# Astronomical Parallax

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# Astronomical Parallax

## What is parallax

Parallax is the apparent displacement of a foreground object with respect to a background object caused by the movement of the observer. In plain words, nearby objects seem to shift more than distant objects when you move.

Consider the following image:

In the image, there are two sets of skyscrapers, and a tall mountain in the distance. An observer views the scene from 5 different positions. Suppose you were to draw the scene as seen by each observing position in the image.

Which building will appear to move the most?

What do you think would happen to the apparent position of the mountain in the distance?

We do the same thing in astronomy to find out how far the stars are from the Earth.

In astronomy, we can't move any closer to the stars, but we do move from side to side. Not only does the Earth turn on it's axis every day, but the Earth itself moves around the sun once a year.

In practice, astronomers take year round measurements of the sky as a whole. Most stars do not appear to move (like the mountain in the above example) but a few nearby ones seem to shift. If the exposures from each night are laid over each other, the nearby stars will show up as a streak across the sky. The closer the star, the larger the streak. The streak, or parallax, is measured as angle across the sky in arc seconds.

For a baseline given by the revolution of the Earth around the Sun, the distance of a star is inversely related to the parallax of the star relative to the background sky.

## Computing Distance

A special unit of distance, called the parsec, is used to make calculating distances very easy. A parsec is the distance away something would have to be to have a parallax of 1 arc second. This makes the equation to find distance

```            1
D (pc) = --------
P (as)
```

1 parsec is 3.3 light years, or about 30,000,000,000,000 km (3e13 km).