# MandysNotes

## Astronomy

### Table of Distances

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Below is a table of various distances in various units that are important in astronomy and astrophysics.

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### Stellar Parallax

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Consider two stars that appear close together in the night sky. Suppose that one star is relatively close to our solar system (what this means exactly we will come to shortly) while the second star is extremely distant.

As the Earth revolves around the sun, the apparent positions of the two stars will shift. The far distant star will not suffer any noticeable change in position, but the nearer star will be seen to move around the distant star in an ellipse.

Let $$\alpha$$ be the maximum angular separation between the two stars expressed in radians.

If $$d_{o}$$ is one A. U., i.e. the distance from the Earth to the Sun, and $$d_{\star},$$ is the distance from the Sun to the star, then $$d_{\star} \alpha \approx d_{0}.$$

Because in practice the distances to stars are so great, and the angles so small, this approximation is an excellent one and we can write:

$d_{\star} = \frac{ d_{0}}{\alpha} = \frac{1 (A.U.)}{\alpha}$

In this way, if we can measure the angle of parallax, $$\alpha$$ we can find the distance to a star.

### Why do Stars Twinkle but Planets Don't?

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When we view stars from the surface of the Earth, we a looking up through a ''sea'' of air, the atmosphere, about three hundred miles thick.

Stars are suns, like our own sun, and we see them because they emit particles of light called photons.

The closest star to our solar system, Proxima Centauri, is more than a parsec from our Sun

(1 parsec $$\approx 10 \times 10^{13}$$ miles $$\approx 3 \times 10^{18}$$ cm),

and most stars are much farther away (hundreds or thousands of parsecs--the Milky Way Galaxy has a radius of about eight thousand parsecs).

Planets are part of our solar system and so are much closer than the closest star. The Kuiper belt, of which Pluto is a member, is about $$2 \times 10^{-4}$$ parsecs away from the sun (that is, about 2 thousandths of a parsec).