Astronomy 162: Professor Barbara Ryden

``How far would I travel

To be where you are?

How far is the journey

From here to a star?''

- Irving Berlin

- Distances in the universe are important to know, but difficult to measure.
- The distance to a nearby star can be found from its PARALLAX.
- On average, a nearby star will have a larger PROPER MOTION than a distant star.

- The luminosity of an object (a 25-watt bulb 50 meters away appears just as bright as a 100-watt bulb 100 meters away).
- The size of an object (a large distant object [e.g. the Sun] can be the same angular size as a small nearby object [e.g. the Moon])
- The mass of an object (this can be computed from Kepler's Third Law if the object is part of an orbiting system).

- Ptolemy [2nd century AD]: thought that all stars were at the same (relatively short) distance, attached to a crystalline sphere
- Copernicus [16th century AD]: knew that stars were at a large (but unknown) distance
- Friedrich Bessel [1838]: first person to measure the distance to a star other than the Sun - used the method of stellar parallax

Simple example: Hold thumb at arm's length. Look first through one eye, then through other. Thumb's position changes relative to background. The closer your thumb to your eyes, the larger the jump in position.

More sophisticated example: Look at a star - first in June,
then in December, six months later.
Your location changes by 2 AU between these times. Therefore, the star's
position changes relative to more distant background
stars. The angle p (see the
diagram below) is the star's **parallax**.

After measuring p, and knowing the size of the Earth's orbit, we can compute the distance to the star using trigonometry. Note that the distance to even the nearest stars (other than the Sun) is much larger than 1 AU; therefore, the angle p is small.

- 360 degrees = full circle
- 60 arcminutes = 1 degree
- 60 arcseconds = 1 arcminute

1 arcsecond = angular size of dime 2 kilometers away

p = parallax, measured in arcseconds

The **parsec** is defined as the distance at
which a star has a parallax of 1 arcsecond. In other units,

1 parsec = 3.26 light years = 206,000 AU.

Parsecs are the units most often used by professional
astronomers in measuring interstellar distances.

d = 1/0.77 = 1.30 parsec = 4.23 light years

Because stellar parallaxes are so small, they can only be measured accurately for relatively nearby stars.

- From the ground, the smallest measurable parallax is p = 0.01 arcsec
(corresponding to a distance d = 100 parsecs = 326 light years).
- From a satellite, the smallest measurable parallax is p = 0.002 arcsec (corresponding to a distance d = 500 parsecs = 1600 light years).

On average, close stars have faster proper motions than distant stars. (This is only an average statement: a star which happens to be moving directly toward or away from the Sun, for instance, will have no proper motion.)

Examples:

- Proxima Centauri: proper motion = 3.85 arcseconds/year, distance = 1.3 parsecs
- Betelgeuse: proper motion = 0.03 arcseconds/year, distance = 150 parsecs

Prof. Barbara Ryden (ryden@astronomy.ohio-state.edu)

Updated: 2003 Jan 13

Copyright © 2003, Barbara Ryden