29:50 Modern Astronomy
Fall 2002
Lecture 29 ...November 22, 2002
The Distances to Remote Objects

Look for new homework (assignment #7 ) on the web. It will help you endure boredom during Thanksgiving vacation!
New demonstration that there is a black hole at the galactic center.
Stars Orbiting the Black Hole at the Galactic Center
Recent research and proof that we orbit the center of the Milky Way.
Radio Image of the Galactic Center
demonstration and data.

Two Topics to Consider

In the next couple of lectures, I want to talk about two interesting issues.

1. How do we know the distances to remote galaxies? Cepheid variables work for very nearby galaxies but you can't see them very far out. Think about the galaxies in the ``Hubble Deep Field''.
   Picture of Hubble Deep Field
2. What are galaxies made of? That would seem to be obvious on the basis of what we have talked about all semester, but you are in for a big surprise.

Let's start with the discussion of measuring the distances to galaxies. It also permits me to inject some new physics that we will use a lot in the rest of the course. The new physics is the Doppler Effect.

The Doppler Effect has to do with moving sources of radiation, and the wavelength that is measured by an observer. Let's let a source emit radiation (sound waves, electromagnetic waves, the works). The source emits radiation at a wavelength . If the source is in motion with respect to us (either by us being stationary and it moving, it stationary and us moving, or a combination of the two), we measure a wavelength which is different from . The formula relating , , v, and the speed of the wave c is

This equation is defined such that a positive velocity means motion away from us, and a negative velocity means motion towards us.

Illustrations and Demonstrations of Doppler Effect.

Let's work out a couple of examples.
(1) The Earth moves around in its orbit at a speed of 30 km/sec = meters/sec. Let's say we observe a star (in the plane of the ecliptic) which has a spectral line ( ) of 650.000 nanometers. How much do we see it shift back and forth in wavelength?

When the Earth is moving towards the star, we see a ``blue shift'', or the wavelength is shorter than the rest wavelength. So . We have:

(2) Let's say we observe this same spectral line with a rest wavelength of 650.000 nm in another star. We observe it in a star at a wavelength nanometers. What is the motion of this star with respect to us?

First of all, the wavelength is longer than the rest wavelength so
Question for audience: is it moving towards us or away from us?
Let's grind out the numbers:

or 462 kilometers/sec.

Doppler Weather Radars use the Doppler Effect to measure the speed at which raindrops are falling.

What does this have to do with measuring the distances to galaxies?

After demonstrating that galaxies were independent systems outside the Milky Way, Edwin Hubble made an extremely important discovery. There were two parts to this discovery.

1. Outside of the local group, all galaxies are receding from us.
2. The further away a galaxy is, the faster it is receding.

The second of these is summed up in Hubble's Law,

where v is the speed of recession (in kilometers/sec), d is the distance (in Megaparsecs), and the constant is Hubble's Constant.

Use of Hubble's Law says that if we measure the speed of recession, we know the distance to an extragalactic object.
transparencies showing Hubble's Law.

Physically, Hubble's Law is an indication that the whole universe is expanding.

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