MandysNotes

Astronomy

AstroCat1

 

 

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

AstroDistanceChart800


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.

Parallax1d-600

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).

[To learn more about parsecs and stellar parallax, please click here.]

[To learn more about cosmic distance scales, please click here.]

Because stars are so far away their apparent angular diameters--that is, the number of degrees they cover in an arc across the celestial sphere as seen from Earth--are tiny. And so they are essentially point sources of light.

When a stream of photons from a star is scattered by the molecules in the atmosphere the photons that are scattered do not reach our eyes, and so the star appears to twinkle.

From space, above the atmosphere; or on the surface of the Moon, which has no atmosphere, stars do not appear to twinkle.

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).

Planets have angular diameters that are much larger than those of stars, and so even if some of the photons they reflect towards Earth are scattered by our atmosphere, there are plenty of other photons that still get through the atmosphere, and so planets do not appear to twinkle.

Twinklealt

NOTRad