###### By Emily Levesque, University of Washington

## Six years after Edwin Hubble’s discovery that the Andromeda Nebula was actually another galaxy, he made another astounding pronouncement that led to an equation known as Hubble’s law. He had measured the distances to other nearby galaxies, along with how fast those galaxies were moving away from us, and discovered that the farther a galaxy was, the faster it was moving away from us.

### Hubble’s Law Summarized in a Single Equation

The discovery could be summarized in a single, but astonishing, equation—*v* equals *H*-naught times *D*. The velocity, *v*, of a galaxy—how fast it’s moving away from us—is equal to the distance to that galaxy, *D*, multiplied by a single, devilish number: a constant, *H*-naught, that’s come to be known as the Hubble constant.

This equation, called Hubble’s law at the time, quantified the first observational evidence for the expansion of our universe, and revealed one of its most fundamental properties.

### Understanding the Equation

To begin, what do we mean when we say the universe is expanding? How do we know that galaxies are moving away from us? And why is an expanding universe so important? To understand the importance of these questions, we first need to take a close look at each part of Hubble’s equation, and consider where it came from.

The *D* on the right side of the equation is straightforward: it stands for an object’s distance. Hubble began by measuring how rapidly a Cepheid’s brightness appeared to vary, and then used the Leavitt law to compute that Cepheid’s luminosity. Finally, comparing the Cepheid’s actual luminosity to its apparent brightness, Hubble calculated the distance to the star thanks to the inverse square law, and thereby computed the distance to the galaxy!

The *v* in the equation seems a bit more complicated at first. It stands for radial velocity, or how quickly a galaxy is moving directly away from us. But how, exactly, do we measure something like this?

### Redshift

The answer to the question above comes from a phenomenon known as redshift. A galaxy streaking away from Earth at many millions of miles an hour is moving away from us so fast that the very light it emits is being stretched; with a longer wavelength, the spectrum of light would shift and appear redder to us. Conversely, if a galaxy was moving rapidly toward Earth, the light it emitted would be compressed; with a shorter wavelength, the spectrum of light would shift and appear bluer to us.

Astronomers can diagnose the effects of blueshift or redshift by using spectroscopy. We know that the most abundant elements in the galaxy—hydrogen, helium, oxygen, and so on—will absorb or emit light at very specific wavelengths, creating characteristic patterns of bright lines in a galaxy’s spectrum.

If we expect to see these sets of lines at one wavelength, but instead observe them at another, we can use the difference between them to calculate the galaxy’s radial velocity, or exactly how fast it’s moving directly toward or away from us. That radial velocity measurement becomes the *v* in this equation.

This article comes directly from content in the video seriesGreat Heroes and Discoveries of Astronomy. Watch it now, on Wondrium.

### Constructing a Diagram

Once measured, the relationship between the distances and velocities of distant objects can be easily illustrated. If we measure the distances and radial velocities for a large sample of galaxies, we can, in principle, place them on a diagram plotting distance on the horizontal axis and velocity on the vertical axis.

This trick doesn’t work well for very nearby galaxies, mainly because these galaxies are gravitationally bound to one another and thereby move according to local effects. However, if we move to slightly more distant galaxies that are in what we call the Hubble flow—galaxies whose motion is primarily dictated by the expansion of the universe—we expect that those galaxies’ distances and velocities should fall neatly along a single line in this diagram.

### Dealing with Large Measurements

To make our lives easier, we’ll also want to use a measure of distance on the horizontal axis and a measure of speed on the vertical axis that makes the enormous numbers we’re dealing with manageable. Astronomers tend to use kilometers per second rather than miles per hour when we talk about speed because things are moving so quickly. Something moving at one kilometer per second works out to a speed of more than 2,000 miles per hour!

Similarly, a good measure of distance when we’re talking about the universe is a megaparsec. A light-year may sound enormous—about six trillion miles—but even that’s just a short hop in cosmic terms. To deal with these incredible distances, one megaparsec is equal to 3.3 million light-years. Putting our data in terms of these immense speeds and distances helps us to avoid constantly running into gigantic numbers when we work with Hubble’s equation.

### Determining Hubble’s Constant

If we compare this diagram to our original equation, we can see where we should find *H*-naught, the Hubble constant: it should simply be the slope of that line! All we need to do is measure the line’s slope—how many kilometers per second do we go up for every megaparsec we move to the right—and we’ll have determined Hubble’s constant!

That constant, in units of velocity per unit distance, will then reveal the rate of expansion of our universe, with profound implications for the universe’s history and ultimate fate.

### Common Questions about the Discovery of Hubble’s Law

**Q: What is the equational summary of Hubble’s law?**Hubble’s law can be shown in an equation: *v *equals *H*-naught times *D*. Here, *D *stands for the distance to the galaxy, how far away it is. *H*-naught stands for the Hubble constant, and *v* means velocity, namely how fast the galaxy in question is moving away from us.

**Q: What is redshift?**Because distant galaxies are moving away from us, the wavelengths of the light they send our way is stretched by the time it reaches us. This means that it appears redder to us which is called redshifting.

**Q: What measurements do scientists use when calculating the distance and velocity of galaxies?**Scientists use megaparsec; every megaparsec is equal to 3.3 million light-years. For velocity, kilometers per second is used.