5. HUBBLE'S LAW:

In 1912, Vesto Slipher was observing the spectra of galaxies at the Lowell Observatory in Flagstaff, Arizona. He made the remarkable discovery that the spectral lines of most galaxies are shifted to the red, indicating that the galaxies are moving away from the Milky Way. (One notable exception is the nearby giant spiral galaxy M31 in Andromeda, which is actually moving toward the Milky Way.) Then, in 1929, Edwin Hubble, working with the new 2.4 meter telescope on Mt. Wilson, near Los Angeles, made an even more remarkable discovery. He plotted the recession velocities of galaxies (V, inferred from their redshifts) versus their estimated distances (D), in what we now call a Hubble diagram (see below).

When Hubble did this, he found that the recession velocity of the galaxies tended to increase with their distance. Fitting a straight line to the data, he wrote down a formula that we now call Hubble's Law:

V = H₀D.

This simple equation is one of the most important formulas in all astronomy (indeed, in all science). The number H₀ is called Hubble's constant. H₀ is usually expressed in units km/sec/Mpc, so that the formula gives the recession velocity V of the galaxy in km/s if the distance D is expressed in units of Mpc (1 Mpc = 1 million parsecs = 3 million light years).

When Hubble discovered this relationship, he had no reliable way of measuring the distances of galaxies. He only guessed their distances from their sizes and brightness -- and he was way off! He underestimated their actual distances by almost a factor of 10. From such estimates, he inferred a value H₀ = 500 km/s/Mpc. To find the Hubble constant, astronomers must measure both the recession velocities and distances of many distant galaxies. It's easy to measure the recession velocities to a precision better than 1% from the redshifts of their spectral lines. The hard part is to measure the distances of galaxies, as we have discussed in the previous section. A few years ago, the distances of galaxies were uncertain to a factor of about two; but today, we believe that we can measure distances to an accuracy of +/- 15%. As a result of such measurements, we now believe that H₀ lies in the range 65 - 75 km/s/Mpc.

Hubble's Law tells us something profound: the entire universe is expanding, as if it began in a huge explosion! Moreover, the value of the Hubble constant tells us the age of the universe since this explosion. We'll have a lot more to say about the implications of Hubble's Law in Lesson 12. But for now, we'll merely take it as an empirical fact and consider how it can be used to determine the distances of any galaxy. All we need to do is to take a spectrum of the galaxy and measure the wavelengths, l(apparent), of its spectral lines. Then we can infer its recession velocity V from the Doppler formula:

[l(apparent) - l(true)]/l(true) = V/c

and calculate its distance from V and Hubble's Law.

If we trust that Hubble's Law is a universal law of nature, we can use it to measure the distances of galaxies even if we can find no standard candles (such as Type Ia supernovae or Cepheid Variable stars) in them. Thus, Hubble's Law becomes a powerful tool for mapping the distribution of galaxies in the universe.