The calculation of 1 Parsec

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I don’t understand it enough to explain it, actually I don’t really understand it myself at all

In: Physics

One parsec is the distance from which a scientist measuring the distance from the Sun to the Earth would measure an angle of one second of arc (1/3600^th of a degree).

This works out to about 3.26 light years (3.086 × 10^13 kilometers). The distance from the Earth to the Sun is pretty large, and one second of arc is a very, very small angle.

A parsec is ~3.26 lightyears, which is the distance light can travel in the vacuum of space (~6 trillion miles).

Why is a parsec such an odd number? I assume this is what you’re struggling with. Draw a large dot on a piece of paper. That’s the sun. Draw a line straight up from the sun. Now draw a smaller dot next to the sun. This is the earth. Assuming the distance between the sun and the earth is at average, this is your starting point. Now draw a short line from the earth thats parallel with the line from the sun. This is degree 0. Now draw a line from the same starting point, but at 1/3600 of a degree (an arc second) leaning toward the sun. (You can draw any angle. This isn’t to scale). Where the angled earth line and the straight sun lines meet is one parsec from the sun.

The reason this is so complicated is because from where we are on earth, the easiest way to measure the distance between earth and another celestial body is parallax. We know how far earth is from the sun. We know when the earth is at any specific point in its orbit around the sun. Using the diameter of the earth’s orbit, and the distance a celestial body appears to move in our sky between these two points can be used to calculate how far away it is.

A parsec is a geometry thing. So easiest to see [using a diagram](https://en.wikipedia.org/wiki/File:Stellarparallax_parsec1.svg) or [two](https://en.wikipedia.org/wiki/File:Parsec_(1).svg).

If you take a right-angled triangle where one side is 1 AU (the average distance from the Earth to the Sun), and the opposite angle is 1 arcsecond (1/3600 of a degree or 1/1,296,000 of a whole circle), then the other side of the triangle will be 1 parsec long.

You can calculate the length using a bit of trigonometry if you’re comfortable with that.

Its use comes from the fact that as the Earth goes around the Sun distant stars appear to move in the sky, and by comparing their position when the Earth is on opposite sides of the Sun we can figure out how far away they are.

I’ll simplify what they are all saying.
– Pretend there is a straight line that connects your eyes.
– Pretend a straight line is shooting directly out of your right eye forward.
– Pretend theres a straight line at an angle that meets the end of the line from your right eye.

It makes a triangle. Your right eye is the sun. Left eye is the earth. The distance between your eyes is the average distance between them.

The point where the two lines meet is a parsec.