Outline

1. Distances, Sizes, Masses, and Luminosities
2. The Hubble Law

Terms to Know

1. Distances, Sizes, Masses, and Luminosities

How can we measure those distances? Parallax from the Earth's orbit, the way we do with nearby stars? Nope -- galaxies are much too far away. Cepheid variable stars? YES!

Other methods of measuring distances are needed for galaxies further than the closest 100 or so galaxies, because Cepheids become too faint to detect at those distances. Most of those methods also rely on trying to identify some object or class of objects with which we are already familiar -- like using the apparent size of a tree to estimate the distance to a mountain. Some of those methods include:

• Identifying the brightest globular cluster
• Finding planetary nebulae, whose luminosities are well-known
• Searching for a particular kind of supernova that always has the same luminosity at its peak brightness
• Measuring the galaxy's rotation speed, which is closely tied to its luminosity (bright galaxies rotate faster). Comparing luminosity with apparent brightness yields distance.

The distance to the nearest major galaxy, the Andromeda Galaxy (M31), is about 2 million light years, or 700 kiloparsec (kpc) = 0.7 megaparsec (Mpc). M31 and the Milky Way are sister galaxies. Since their diameters are each about 25 kpc, they are separated by about 700/25 = 28 times their size -- like 2 basketballs 10 meters apart. Note how different this is than the case of nearby stars, which are like grapefruits separated by thousands of miles!

Once we know the distance to a galaxy, we can use that information together with its apparent size to measure its true, physical size. Typical sizes of galaxies can range from much smaller than the Milky Way -- around 1 kpc in diameter -- to much larger -- around 50 kpc. Some dwarf galaxies are barely larger than one of the Milky Way's globular clusters, while some giant ellipticals could swallow the Milky Way up whole.

Masses of galaxies can be difficult to measure accurately, but we can get pretty good estimates by using the same techniques used in the Milky Way: measure the orbital speed of stars and apply Kepler's Laws, just like "weighing" the Sun using planetary orbits. The Milky Way's mass is about 10¹²M_Sun, including dark matter. The smallest dwarf galaxies have masses of only 10⁸M_Sun or so, while the largest giant ellipticals can have up to 10¹⁴M_Sun.

Likewise, the luminosities of galaxies span a huge range, from 10⁷L_Sun to over 10¹²L_Sun. Generally, the most massive galaxies are the brightest and largest.

2. The Expanding Universe

Does this mean that we are at the center of the expansion? NO! Imagine painting dots on a balloon. Now blow up the balloon and measure the distances among 3 or 4 dots. Now blow up the balloon some more. What are the distances now? The greater the separation between two dots, the faster they grow more distant -- and every dot sees exactly the same thing , as if it were at the center of the expansion.

The relation between recession velocity and distance is called Hubble's Law :

• V_r = the recession velocity (speed away from us) in km/s of any galaxy
• d = the distance from us to that galaxy in Mpc, and
  
• H₀ = the famous "Hubble Constant", which tells how fast the Universe is expanding, in km/s per Mpc.

The value of H₀ is about 70 km/s per Mpc.

Example: say the value of H₀ is 70 km/s per Mpc (close to what the experts are now saying). How far away is a galaxy that is flying away from us at 1400 km/s?

Answer: Inverting Hubble's Law, we find d = V_r / H₀ = 1400 km/s / 70 km/s/Mpc = 20 Mpc, or about 60 million light years.

We will return to this expanding Universe soon!

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