## PARALLAX

Parallax is the shift in position of an object caused by your own motion. For example, if you look at some nearby object and move your head a little from side to side, the object looks like it is moving back and forth. Another way to observe parallax is to look at some object while you sit still but alternately cover your right and left eye. You will see the object "jump back and forth" as you do that.

Parallax is what allows us to estimate the distance to nearby objects. We use it all the time in such simple actions as picking up a pencil. Our right eye sees the pencil in a slightly different direction than our left eye sees it and our brain combines the two images to tell us instinctively how far to stretch. You can test the importance of this by trying to pick up a pencil while you keep one eye covered. It is much harder to do without the clues given by parallax.

A little experimentation will show you that parallax I smaller for objects farther away. Try looking a pencil close to you on the table, alternately covering your right and left eye and then try again with the pencil several feet farther from you. The amount by which its position shifts is much less if it is more distant.

This is the basis of the method astronomers use to measure the distance to nearby stars. For example, if we watch a star over a year as Earth orbits the Sun, the star's position will shift back and forth.

You can see this effect in the following short movie clip. Click here to see movie

Because stars are extremely far away, the angle by which they shift in position is very tiny - only fractions of a degree. The shift is so small, that astronomers use a smaller unit of angle equal to a sixtieth of a sixtieth of a degree called an arc-second. That is, an arc-second = 1/60x1/60 = 1/3600 degree. Such a tiny angle is imperceptible to the naked eye, but can be measured with special instruments.

The amount of the shift caused by our motion around the Sun depends on the star's distance from us. Just as a nearby object in the room shifts more than a more distant one if you move side to side, so a nearby star shifts more than more distant star. Thus, the amount of shift gives a clue to the star's distance.

You can see this effect in the following short movie clip that shows two nearby and relatively bright stars, one above the other. The movie illustrates how the star's positions would change if we watched over a year as the Earth orbited the Sun. Click here to see movie

Which star is closer, the top one or the bottom one?

Note that the top star moves less and is therefore farther away.

The relation between the shift ins position and a star's distance is given by the parallax formula. That formula states that a star's distance, D, is proportional to 1 divided by its parallax, p. That is, D ~ 1/p. If we use arc-seconds to measure p, then the distance turns out to be in units used by astronomers called the parsec. It turns out that a parsec is about 3.26 light years or about 3.18x1013 km.

Ex: Suppose a star's parallax is 0.1 arc-seconds. How far away is it?
Use the formula D=1/p
Plug in for p the value 0.1 arc-seconds
Thus, D=1/0.01 = 10 parsecs
The star is therefore 10 parsecs away from us.