The Cosmic Distance Ladder, I: Parallax

This article will be the first of a series on the Cosmic Distance Ladder, which calibrates the distance to everything outside our solar system.

Astronomers face a simple problem. How do you figure out how far away something is when you can't put a ruler between here and there? Fortunately in the solar system, we can do nearly as well by bouncing radar signals off planets to determine their distances from Earth. With these measurements we can calibrate angular measurements of the motions of the sun and planets to determine their distances, as well as the mass of the sun (via Newtonian gravity).

Having measured accurately the distance between the sun and Earth (the Astronomical Unit, 1 A.U. = 1.49 x 10¹³cm), we can use a method called parallax to determine the distance to nearby stars. To explain the method, I will use a simple analogy. First hold out your thumb at arm's distance and close one eye. Focus on a distant object behind your thumb, such as an outside building. Then close that eye and open the other. Your thumb seems to jump. As you blink back and forth, you thumb jumps back and forth. When you open both eyes, you can see two images of your thumb, or focus on your thumb, so that it just looks closer than a distant object, because your brain has been programmed to recognize parallax as an indicator of distance.

The same effect occurs for nearby stars on opposite sides of Earth's orbit. If one observes a star in June, then again in December, the star will have moved slightly against the background sky, just as your thumb moved against the background, because the Earth is 2 A.U. away in December from where it was in June. Now this effect is tiny, because stars are very far away. The nearest star is so far that the parallax effect amounts to less than an arcsecond on the sky. An arcsecond is 1/3600th of a degree, or the angle subtended by a period in a newspaper 100 meters away. An arcsecond is the separation which is just at the level that telescopes on the Earth can reliably detect.

Because an arcsecond is the fundamental unit for this work, a unit of distance, the parsec is used to reflect the physical distance at which an object produces as parallax of one arcsecond. This distance is:

1 A.U. x (1 radian/1 arcsecond) = 1.50 x 10¹³ cm x 206000 = 3.08 x 10¹⁸ cm = 3.26 light-years

While earth-based telescopes can separate objects relibably at the arcsecond level, they can reliably center objects relative to each other at the few

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