Astronomy 162:
Introduction to Stellar, Galactic, & Extragalactic Astronomy

Lecture 5: Distances of the Stars

Key Ideas:

Why are Distances Important?

Distances are necessary for estimating:

The Problem of measuring distances

Question:
What do you do when an object is out of reach of your measuring instruments?

Examples:

Answer:

You resort to using GEOMETRY.

The Method of Trigonometric Parallaxes

Nearby stars appear to move with respect to more distant background stars due to the motion of the Earth around the Sun. This apparent motion (it is not "true" motion) is called Stellar Parallax.

parallax

In the picture above, the line of sight to the star in December is different than that in June, when the Earth is on the other side of its orbit. As seen from the Earth, the nearby star appears to sweep through the angle shown. Half of this angle, is the parallax, p.

Parallax decreases with Distance

As the distance to a star increases, the amount of parallax decreases. This is easy to see in the following two figures:


In the upper figure, the star is about 2.5 times nearer than the star in the lower figure, and has a parallax angle which is 2.5 times larger.

A movie demonstrating parallaxes is available (beware: it is big, don't try to download it over a slow modem link).

This gives us a means to measure distances by measuring the parallaxes of nearby stars. We call this powerful direct distance technique the method of Trigonometric Parallaxes

Stellar Parallaxes

Because the even the nearest stars are very far away, the largest measured parallaxes is very small; less than an arcsecond.

For example, the nearest star, alpha Centauri, has a parallax angle of 0.76-arcsec

This means that you cannot measure stellar parallaxes with naked eye.

First parallax observed 1837 (Friedrich Bessel) for the star 61 Cygni.

We use Photography or Digital Imaging today to measure parallaxes.

Parallax Formula:

We saw before that the smaller the parallax, the larger the distance. We can express this as a simple formula:

Where:

p = parallax angle in arcseconds

d = distance in "Parsecs" Writing our parallax formula in this way allows us to define a new "natural" unit for distances in astronomy: the Parallax-Second or Parsec.

Parallax Second= Parsec (pc)

Fundamental unit of distance in Astronomy

"A star with a parallax of 1 arcsecond has a distance of 1 Parsec."
1 parsec (pc) is equivalent to:
206,265 AU
3.26 Light Years
3.086x1013 km

Examples:

  1. alpha Centauri has a parallax of p=0.76-arcsec:

  2. A star is measured to have a parallax of p=0.02-arcsec:

Limitations

If the stars are too far away, the parallax can be too small to measure accurately.

In general, the greater the distance, the smaller the parallax, and the less precise the distance measurement is.

The smallest parallax measurable from the ground is about 0.01-arcsec. This means that from the ground, the method of Trigonometric Parallaxes has the following limitations.

Hipparcos

The Hipparcos satellite (launched by the European Space Agency in 1989) has measured precision parallaxes to an accuracy of about 0.001-arcsec.

Hipparcos represents a great leap in our knowledge of the distances (and motions) of nearby stars. The catalog was just released in late 1997, and is already having an impact on many areas of astronomy that rely in accurate distances.

Visit the Hipparcos Web Site at ESA Astrophysics.

Light Year (ly)

An alternative unit of astronomical distance is the Light Year.

"1 Light Year is the distance traveled by light in one year."
1 light year (ly) is equivalent to:
0.31 pc
63,270 AU
It is more popular these days among science popularizers and science fiction writers, and is rarely used in research astronomy. The reason is that the parsec is directly derived from the quantity that is measured (the stellar parallax angle), whereas the light-year must be derived from having previously measured the distance in parsecs. In this way, the parsec is a more "natural" unit to use than the light-year.