explain how the parsec is derived?

Answer 1

zee_prime's got a good answer there. Very precise and correct. I'm gonna take another approach to it, though, and try to make it intelligible for those who don't have a lot of math or physics behind them. My answer'll be correct, too, it'll just use smaller words--and more of them! (-;

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PARSEC:
A parsec is a standard unit of astronomical distance equal to 3.26 light years. It is also the distance a star has to be from earth so that its parallax is one arcsecond.

Ouch! What the heck does all that mean?

First off, we need to know about "parallax". Parallax is easy. It's just the change in the apparent position of an object when your position changes.

A great example is easy to show: hold a thumb up in front of your face, about 20 centimeters away. Close your left eye, and move your thumb so that while looking through your right eye it is lined up with some distant object like a tree. Now close your right eye and look at your thumb through your left eye. See how it no longer lines up with the tree? That's because the angle formed by your eye, your thumb and the tree has changed. That angle is called the parallax angle.

Parallax angle depends on two things: (1) how far apart your eyes are (the baseline), and (2) how far away your thumb is. If your eyes are really far apart, the angle gets bigger. If the thumb is held farther away, the angle gets smaller.

When you are in a car and you look at trees nearby, they appear to race past you. Far away trees appear to move slowly. This is because for the nearby trees the parallax angle is large and so it changes rapidly if the car moves a little bit. Trees farther away appear to change less as the car moves along. Their parallax angle is small.

This parallax method has been used for over a hundred years to find the distances to nearby stars. The Earth has an orbit about 300 million kilometers across. That's a long baseline! Even nearby stars will appear to change position due to parallax when you have such a long baseline.

Astronomers needed some sort of unit to measure this change in position. What they decided was to make a standard unit for the distance. A star at that distance would change position by 1 arcsecond due to parallax. The distance is 3.26 light years, and is abbreviated parsec for PARallax SECond. (Ummm, one arcsecond is 1/3600 of a degree--which comes from 360 degrees of a full circle.)

Stars farther away than one parsec would shift by less than 1 arcsecond, and closer stars by more. The nearest star to the Sun is Proxima Centauri, which is about 4.3 light years away, or 1.3 parsecs away. That means that even the closest star has a parallax less than an arcsecond. Stars out to a distance of about 100 parsecs have had their distance measured this way.

To imagine how small a shift that really is, imagine someone standing 125 miles (about 200 kilometers) away from you and then moving to the left by one centimeter. That is the same shift!

Got it?

Answer 2

Parsec is short for parallax second. It's the distance at which the radius of the Earth's orbit, 150 million km., would appear 1 second of arc across. It's equal to 3.26 light years. That's about 3.3x10^13 km. The reason for this choice of unit is, the distance to the closest stars is worked out by comparing their apparent directions at different times of the year, when the Earth is at different points in its orbit around the Sun.