26.5 The Expanding Universe
By the end of this section, you will be able to:
- Describe the discovery that galaxies getting farther apart as the universe evolves
- Explain how to use Hubble’s law to determine distances to remote galaxies
- Describe models for the nature of an expanding universe
- Explain the variation in Hubble’s constant
We now come to one of the most important discoveries ever made in astronomy—the fact that the universe is expanding. Before we describe how the discovery was made, we should point out that the first steps in the study of galaxies came at a time when the techniques of spectroscopy were also making great strides. Astronomers using large telescopes could record the spectrum of a faint star or galaxy on photographic plates, guiding their telescopes so they remained pointed to the same object for many hours and collected more light. The resulting spectra of galaxies contained a wealth of information about the composition of the galaxy and the velocities of these great star systems.
Slipher’s Pioneering Observations
Curiously, the discovery of the expansion of the universe began with the search for Martians and other solar systems. In 1894, the controversial (and wealthy) astronomer Percival Lowell established an observatory in Flagstaff, Arizona, to study the planets and search for life in the universe. Lowell thought that the spiral nebulae might be solar systems in the process of formation. He therefore asked one of the observatory’s young astronomers, Vesto M. Slipher (Figure 1), to photograph the spectra of some of the spiral nebulae to see if their spectral lines might show chemical compositions like those expected for newly forming planets.
Figure 1. Slipher spent his entire career at the Lowell Observatory, where he discovered the large radial velocities of galaxies. (credit: Lowell Observatory)
The Lowell Observatory’s major instrument was a 24-inch refracting telescope, which was not at all well suited to observations of faint spiral nebulae. With the technology available in those days, photographic plates had to be exposed for 20 to 40 hours to produce a good spectrum (in which the positions of the lines could reveal a galaxy’s motion). This often meant continuing to expose the same photograph over several nights. Beginning in 1912, and making heroic efforts over a period of about 20 years, Slipher managed to photograph the spectra of more than 40 of the spiral nebulae (which would all turn out to be galaxies).
To his surprise, the spectral lines of most galaxies showed an astounding redshift. By “redshift” we mean that the lines in the spectra are displaced toward longer wavelengths (toward the red end of the visible spectrum). Recall from the chapter on Radiation and Spectra that a redshift is seen when the source of the waves is moving away from us. Slipher’s observations showed that most spirals are racing away at huge speeds; the highest velocity he measured was 1800 kilometers per second.
Only a few spirals—such as the Andromeda and Triangulum Galaxies and M81—all of which are now known to be our close neighbors, turned out to be approaching us. All the other galaxies were moving away. Slipher first announced this discovery in 1914, years before Hubble showed that these objects were other galaxies and before anyone knew how far away they were. No one at the time quite knew what to make of this discovery.
The profound implications of Slipher’s work became apparent only during the 1920s. Georges Lemaître was a Belgian priest and a trained astronomer. In 1927, he published a paper in French in an obscure Belgian journal in which he suggested that we live in an expanding universe. The title of the paper (translated into English) is “A Homogenous Universe of Constant Mass and Growing Radius Accounting for the Radial Velocity of Extragalactic Nebulae.” Lemaître had discovered that Einstein’s equations of relativity were consistent with an expanding universe (as had the Russian scientist Alexander Friedmann independently in 1922). Lemaître then went on to use Slipher’s data to support the hypothesis that the universe actually is expanding and to estimate the rate of expansion. Initially, scientists paid little attention to this paper, perhaps because the Belgian journal was not widely available.
In the meantime, Hubble was making observations of galaxies with the 2.5-meter telescope on Mt. Wilson, which was then the world’s largest. Hubble carried out the key observations in collaboration with a remarkable man, Milton Humason, who dropped out of school in the eighth grade and began his astronomical career by driving a mule train up the trail on Mount Wilson to the observatory (Figure 2). In those early days, supplies had to be brought up that way; even astronomers hiked up to the mountaintop for their turns at the telescope. Humason became interested in the work of the astronomers and, after marrying the daughter of the observatory’s electrician, took a job as janitor there. After a time, he became a night assistant, helping the astronomers run the telescope and record data. Eventually, he made such a mark that he became a full astronomer at the observatory.
Figure 2. Humason was Hubble’s collaborator on the great task of observing, measuring, and classifying the characteristics of many galaxies. (credit: Caltech Archives)
By the late 1920s, Humason was collaborating with Hubble by photographing the spectra of faint galaxies with the 2.5-meter telescope. (By then, there was no question that the spiral nebulae were in fact galaxies.) Hubble had found ways to improve the accuracy of the estimates of distances to spiral galaxies, and he was able to measure much fainter and more distant galaxies than Slipher could observe with his much-smaller telescope. When Hubble laid his own distance estimates next to measurements of the recession velocities (the speed with which the galaxies were moving away), he found something stunning: there was a relationship between distance and velocity for galaxies. The more distant the galaxy, the faster it was receding from us.
In 1931, Hubble and Humason jointly published the seminal paper where they compared distances and velocities of remote galaxies moving away from us at speeds as high as 20,000 kilometers per second and were able to show that the recession velocities of galaxies are directly proportional to their distances from us (Figure 3), just as Lemaître had suggested.
We now know that this relationship holds for every galaxy except a few of the nearest ones. Nearly all of the galaxies that are approaching us turn out to be part of the Milky Way’s own group of galaxies, which have their own individual motions, just as birds flying in a group may fly in slightly different directions at slightly different speeds even though the entire flock travels through space together.
Written as a formula, the relationship between velocity and distance is
where v is the recession speed, d is the distance, and H is a number called the Hubble constant. This equation is now known as Hubble’s law.
Mathematical relationships such as Hubble’s law are pretty common in life. To take a simple example, suppose your college or university hires you to call rich alumni and ask for donations. You are paid $2.50 for each call; the more calls you can squeeze in between studying astronomy and other courses, the more money you take home. We can set up a formula that connects p, your pay, and n, the number of calls
where A is the alumni constant, with a value of $2.50. If you make 20 calls, you will earn $2.50 times 20, or $50.
Suppose your boss forgets to tell you what you will get paid for each call. You can calculate the alumni constant that governs your pay by keeping track of how many calls you make and noting your gross pay each week. If you make 100 calls the first week and are paid $250, you can deduce that the constant is $2.50 (in units of dollars per call). Hubble, of course, had no “boss” to tell him what his constant would be—he had to calculate its value from the measurements of distance and velocity.
Astronomers express the value of Hubble’s constant in units that relate to how they measure speed and velocity for galaxies. In this book, we will use kilometers per second per million light-years as that unit. For many years, estimates of the value of the Hubble constant have been in the range of 15 to 30 kilometers per second per million light-years The most recent work appears to be converging on a value near 22 kilometers per second per million light-years If H is 22 kilometers per second per million light-years, a galaxy moves away from us at a speed of 22 kilometers per second for every million light-years of its distance. As an example, a galaxy 100 million light-years away is moving away from us at a speed of 2200 kilometers per second.
Hubble’s law tells us something fundamental about the universe. Since all but the nearest galaxies appear to be in motion away from us, with the most distant ones moving the fastest, we must be living in an expanding universe. We will explore the implications of this idea shortly, as well as in the final chapters of this text. For now, we will just say that Hubble’s observation underlies all our theories about the origin and evolution of the universe.
Hubble’s Law and Distances
The regularity expressed in Hubble’s law has a built-in bonus: it gives us a new way to determine the distances to remote galaxies. First, we must reliably establish Hubble’s constant by measuring both the distance and the velocity of many galaxies in many directions to be sure Hubble’s law is truly a universal property of galaxies. But once we have calculated the value of this constant and are satisfied that it applies everywhere, much more of the universe opens up for distance determination. Basically, if we can obtain a spectrum of a galaxy, we can immediately tell how far away it is.
The procedure works like this. We use the spectrum to measure the speed with which the galaxy is moving away from us. If we then put this speed and the Hubble constant into Hubble’s law equation, we can solve for the distance.
Hubble’s law (v = H × d) allows us to calculate the distance to any galaxy. Here is how we use it in practice.
We have measured Hubble’s constant to be 22 km/s per million light-years. This means that if a galaxy is 1 million light-years farther away, it will move away 22 km/s faster. So, if we find a galaxy that is moving away at 18,000 km/s, what does Hubble’s law tells us about the distance to the galaxy?
Note how we handled the units here: the km/s in the numerator and denominator cancel, and the factor of million light-years in the denominator of the constant must be divided correctly before we get our distance of 818 million light-years.
Check Your Learning
Using 22 km/s/million light-years for Hubble’s constant, what recessional velocity do we expect to find if we observe a galaxy at 500 million light-years?
Variation of Hubble’s Constant
The use of redshift is potentially a very important technique for determining distances because as we have seen, most of our methods for determining galaxy distances are limited to approximately the nearest few hundred million light-years (and they have large uncertainties at these distances). The use of Hubble’s law as a distance indicator requires only a spectrum of a galaxy and a measurement of the Doppler shift, and with large telescopes and modern spectrographs, spectra can be taken of extremely faint galaxies.
But, as is often the case in science, things are not so simple. This technique works if, and only if, the Hubble constant has been truly constant throughout the entire life of the universe. When we observe galaxies billions of light-years away, we are seeing them as they were billions of years ago. What if the Hubble “constant” was different billions of years ago? Before 1998, astronomers thought that, although the universe is expanding, the expansion should be slowing down, or decelerating, because the overall gravitational pull of all matter in the universe would have a dominant, measureable effect. If the expansion is decelerating, then the Hubble constant should be decreasing over time.
The discovery that type Ia supernovae are standard bulbs gave astronomers the tool they needed to observe extremely distant galaxies and measure the rate of expansion billions of years ago. The results were completely unexpected. It turns out that the expansion of the universe is accelerating over time! What makes this result so astounding is that there is no way that existing physical theories can account for this observation. While a decelerating universe could easily be explained by gravity, there was no force or property in the universe known to astronomers that could account for the acceleration. In The Big Bang chapter, we will look in more detail at the observations that led to this totally unexpected result and explore its implications for the ultimate fate of the universe.
In any case, if the Hubble constant is not really a constant when we look over large spans of space and time, then the calculation of galaxy distances using the Hubble constant won’t be accurate. As we shall see in the chapter on The Big Bang, the accurate calculation of distances requires a model for how the Hubble constant has changed over time. The farther away a galaxy is (and the longer ago we are seeing it), the more important it is to include the effects of the change in the Hubble constant. For galaxies within a few billion light-years, however, the assumption that the Hubble constant is indeed constant gives good estimates of distance.
Models for an Expanding Universe
At first, thinking about Hubble’s law and being a fan of the work of Copernicus and Harlow Shapley, you might be shocked. Are all the galaxies really moving away from us? Is there, after all, something special about our position in the universe? Worry not; the fact that galaxies are receding from us and that more distant galaxies are moving away more rapidly than nearby ones shows only that the universe is expanding uniformly.
A uniformly expanding universe is one that is expanding at the same rate everywhere. In such a universe, we and all other observers, no matter where they are located, must observe a proportionality between the velocities and distances of equivalently remote galaxies. (Here, we are ignoring the fact that the Hubble constant is not constant over all time, but if at any given time in the evolution of the universe the Hubble constant has the same value everywhere, this argument still works.)
To see why, first imagine a ruler made of stretchable rubber, with the usual lines marked off at each centimeter. Now suppose someone with strong arms grabs each end of the ruler and slowly stretches it so that, say, it doubles in length in 1 minute (Figure 4). Consider an intelligent ant sitting on the mark at 2 centimeters—a point that is not at either end nor in the middle of the ruler. He measures how fast other ants, sitting at the 4-, 7-, and 12-centimeter marks, move away from him as the ruler stretches.
The ant at 4 centimeters, originally 2 centimeters away from our ant, has doubled its distance in 1 minute; it therefore moved away at a speed of 2 centimeters per minute. The ant at the 7-centimeters mark, which was originally 5 centimeters away from our ant, is now 10 centimeters away; it thus had to move at 5 centimeters per minute. The one that started at the 12-centimeters mark, which was 10 centimeters away from the ant doing the counting, is now 20 centimeters away, meaning it must have raced away at a speed of 10 centimeters per minute. Ants at different distances move away at different speeds, and their speeds are proportional to their distances (just as Hubble’s law indicates for galaxies). Yet, notice in our example that all the ruler was doing was stretching uniformly. Also, notice that none of the ants were actually moving of their own accord, it was the stretching of the ruler that moved them apart.
Now let’s repeat the analysis, but put the intelligent ant on some other mark—say, on 7 or 12 centimeters. We discover that, as long as the ruler stretches uniformly, this ant also finds every other ant moving away at a speed proportional to its distance. In other words, the kind of relationship expressed by Hubble’s law can be explained by a uniform stretching of the “world” of the ants. And all the ants in our simple diagram will see the other ants moving away from them as the ruler stretches.
For a three-dimensional analogy, let’s look at the loaf of raisin bread in Figure 5. The chef has accidentally put too much yeast in the dough, and when she sets the bread out to rise, it doubles in size during the next hour, causing all the raisins to move farther apart. On the figure, we again pick a representative raisin (that is not at the edge or the center of the loaf) and show the distances from it to several others in the figure (before and after the loaf expands).
Measure the increases in distance and calculate the speeds for yourself on the raisin bread, just like we did for the ruler. You will see that, since each distance doubles during the hour, each raisin moves away from our selected raisin at a speed proportional to its distance. The same is true no matter which raisin you start with.
Our two analogies are useful for clarifying our thinking, but you must not take them literally. On both the ruler and the raisin bread, there are points that are at the end or edge. You can use these to pinpoint the middle of the ruler and the loaf. While our models of the universe have some resemblance to the properties of the ruler and the loaf, the universe has no boundaries, no edges, and no center (all mind-boggling ideas that we will discuss in a later chapter).
What is useful to notice about both the ants and the raisins is that they themselves did not “cause” their motion. It isn’t as if the raisins decided to take a trip away from each other and then hopped on a hoverboard to get away. No, in both our analogies, it was the stretching of the medium (the ruler or the bread) that moved the ants or the raisins farther apart. In the same way, we will see in The Big Bang chapter that the galaxies don’t have rocket motors propelling them away from each other. Instead, they are passive participants in the expansion of space. As space stretches, the galaxies are carried farther and farther apart much as the ants and the raisins were. (If this notion of the “stretching” of space surprises or bothers you, now would be a good time to review the information about spacetime in Black Holes and Curved Spacetime. We will discuss these ideas further as our discussion broadens from galaxies to the whole universe.)
The expansion of the universe, by the way, does not imply that the individual galaxies and clusters of galaxies themselves are expanding. Neither raisins nor the ants in our analogy grow in size as the loaf expands. Similarly, gravity holds galaxies and clusters of galaxies together, and they get farther away from each other—without themselves changing in size—as the universe expands.
Key Concepts and Summary
The universe is expanding. Observations show that the spectral lines of distant galaxies are redshifted, and that their recession velocities are proportional to their distances from us, a relationship known as Hubble’s law. The rate of recession, called the Hubble constant, is approximately 22 kilometers per second per million light-years. We are not at the center of this expansion: an observer in any other galaxy would see the same pattern of expansion that we do. The expansion described by Hubble’s law is best understood as a stretching of space.
For Further Exploration
Andrews, B. “What Are Galaxies Trying to Tell Us?” Astronomy (February 2011): 24. Introduction to our understanding of the shapes and evolution of different types of galaxies.
Bothun, G. “Beyond the Hubble Sequence.” Sky & Telescope (May 2000): 36. History and updating of Hubble’s classification scheme.
Christianson, G. “Mastering the Universe.” Astronomy (February 1999): 60. Brief introduction to Hubble’s life and work.
Dalcanton, J. “The Overlooked Galaxies.” Sky & Telescope (April 1998): 28. On low-brightness galaxies, which have been easy to miss.
Freedman, W. “The Expansion Rate and Size of the Universe.” Scientific American (November 1992): 76.
Hodge, P. “The Extragalactic Distance Scale: Agreement at Last?” Sky & Telescope (October 1993): 16.
Jones, B. “The Legacy of Edwin Hubble.” Astronomy (December 1989): 38.
Kaufmann, G. and van den Bosch, F. “The Life Cycle of Galaxies.” Scientific American (June 2002): 46. On galaxy evolution and how it leads to the different types of galaxies.
Martin, P. and Friedli, D. “At the Hearts of Barred Galaxies.” Sky & Telescope (March 1999): 32. On barred spirals.
Osterbrock, D. “Edwin Hubble and the Expanding Universe.” Scientific American (July 1993): 84.
Russell, D. “Island Universes from Wright to Hubble.” Sky & Telescope (January 1999) 56. A history of our discovery of galaxies.
Smith, R. “The Great Debate Revisited.” Sky & Telescope (January 1983): 28. On the Shapley-Curtis debate concerning the extent of the Milky Way and the existence of other galaxies.
ABC’s of Distance: http://www.astro.ucla.edu/~wright/distance.htm. A concise summary by astronomer Ned Wright of all the different methods we use to get distances in astronomy.
Cosmic Times 1929: http://cosmictimes.gsfc.nasa.gov/online_edition/1929Cosmic/index.html. NASA project explaining Hubble’s work and surrounding discoveries as if you were reading newspaper articles.
Edwin Hubble: The Man Behind the Name: https://www.spacetelescope.org/about/history/the_man_behind_the_name/. Concise biography from the people at the Hubble Space Telescope.
Edwin Hubble: http://apod.nasa.gov/diamond_jubilee/d_1996/sandage_hubble.html. An article on the life and work of Hubble by his student and successor, Allan Sandage. A bit technical in places, but giving a real picture of the man and the science.
NASA Science: Introduction to Galaxies: http://science.nasa.gov/astrophysics/focus-areas/what-are-galaxies/. A brief overview with links to other pages, and recent Hubble Space Telescope discoveries.
National Optical Astronomy Observatories Gallery of Galaxies: https://www.noao.edu/image_gallery/galaxies.html. A collection of images and information about galaxies and galaxy groups of different types. Another impressive archive can be found at the European Southern Observatory site: https://www.eso.org/public/images/archive/category/galaxies/.
Sloan Digital Sky Survey: Introduction to Galaxies: http://skyserver.sdss.org/dr1/en/astro/galaxies/galaxies.asp. Another brief overview.
Universe Expansion: http://hubblesite.org/newscenter/archive/releases/1999/19. The background material here provides a nice chronology of how we discovered and measured the expansion of the universe.
Edwin Hubble (Hubblecast Episode 89): http://www.spacetelescope.org/videos/hubblecast89a/. (5:59).
Galaxies: https://www.youtube.com/watch?v=I82ADyJC7wE. An introduction.
Hubble’s Views of the Deep Universe: https://www.youtube.com/watch?v=argR2U15w-M. A 2015 public talk by Brandon Lawton of the Space Telescope Science Institute about galaxies and beyond (1:26:20).
Collaborative Group Activities
- Throughout much of the last century, the 100-inch telescope on Mt. Wilson (completed in 1917) and the 200-inch telescope on Palomar Mountain (completed in 1948) were the only ones large enough to obtain spectra of faint galaxies. Only a handful of astronomers (all male—since, until the 1960s, women were not given time on these two telescopes) were allowed to use these facilities, and in general the observers did not compete with each other but worked on different problems. Now there are many other telescopes, and several different groups do often work on the same problem. For example, two different groups have independently developed the techniques for using supernovae to determine the distances to galaxies at high redshifts. Which approach do you think is better for the field of astronomy? Which is more cost effective? Why?
- A distant relative, whom you invite to dinner so you can share all the exciting things you have learned in your astronomy class, says he does not believe that other galaxies are made up of stars. You come back to your group and ask them to help you respond. What kinds of measurements would you make to show that other galaxies are composed of stars?
- Look at [link] with your group. What does the difference in color between the spiral arms and the bulge of Andromeda tell you about the difference in the types of stars that populate these two regions of the galaxy? Which side of the galaxy is closer to us? Why?
- What is your reaction to reading about the discovery of the expanding universe? Discuss how the members of the group feel about a universe “in motion.” Einstein was not comfortable with the notion of a universe that had some overall movement to it, instead of being at rest. He put a kind of “fudge factor” into his equations of general relativity for the universe as a whole to keep it from moving (although later, hearing about Hubble and Humason’s work, he called it “the greatest blunder” he ever made). Do you share Einstein’s original sense that this is not the kind of universe you feel comfortable with? What do you think could have caused space to be expanding?
- In science fiction, characters sometimes talk about visiting other galaxies. Discuss with your group how realistic this idea is. Even if we had fast spaceships (traveling close to the speed of light, the speed limit of the universe) how likely are we to be able to reach another galaxy? Why?
- Despite his son’s fascination with astronomy in college, Edwin Hubble’s father did not want him to go into astronomy as a profession. He really wanted his son to be a lawyer and pushed him hard to learn the law when he won a fellowship to study abroad. Hubble eventually defied his father and went into astronomy, becoming, as you learned in this chapter, one of the most important astronomers of all time. His dad didn’t live to see his son’s remarkable achievements. Do you think he would have reconciled himself to his son’s career choice if he had? Do you or does anyone in your group or among your friends have to face a choice between the passion in your heart and what others want you to do? Discuss how people in college today are dealing with such choices.
Describe the main distinguishing features of spiral, elliptical, and irregular galaxies.
Why did it take so long for the existence of other galaxies to be established?
Explain what the mass-to-light ratio is and why it is smaller in spiral galaxies with regions of star formation than in elliptical galaxies.
If we now realize dwarf ellipticals are the most common type of galaxy, why did they escape our notice for so long?
What are the two best ways to measure the distance to a nearby spiral galaxy, and how would it be measured?
What are the two best ways to measure the distance to a distant, isolated spiral galaxy, and how would it be measured?
Why is Hubble’s law considered one of the most important discoveries in the history of astronomy?
What does it mean to say that the universe is expanding? What is expanding? For example, is your astronomy classroom expanding? Is the solar system? Why or why not?
Was Hubble’s original estimate of the distance to the Andromeda galaxy correct? Explain.
Does an elliptical galaxy rotate like a spiral galaxy? Explain.
Why does the disk of a spiral galaxy appear dark when viewed edge on?
What causes the largest mass-to-light ratio: gas and dust, dark matter, or stars that have burnt out?
What is the most useful standard bulb method for determining distances to galaxies?
When comparing two isolated spiral galaxies that have the same apparent brightness, but rotate at different rates, what can you say about their relative luminosity?
If all distant galaxies are expanding away from us, does this mean we’re at the center of the universe?
Is the Hubble constant actually constant?
Where might the gas and dust (if any) in an elliptical galaxy come from?
Why can we not determine distances to galaxies by the same method used to measure the parallaxes of stars?
Which is redder—a spiral galaxy or an elliptical galaxy?
Suppose the stars in an elliptical galaxy all formed within a few million years shortly after the universe began. Suppose these stars have a range of masses, just as the stars in our own galaxy do. How would the color of the elliptical change over the next several billion years? How would its luminosity change? Why?
Starting with the determination of the size of Earth, outline a sequence of steps necessary to obtain the distance to a remote cluster of galaxies. (Hint: Review the chapter on Celestial Distances.)
Suppose the Milky Way Galaxy were truly isolated and that no other galaxies existed within 100 million light-years. Suppose that galaxies were observed in larger numbers at distances greater than 100 million light-years. Why would it be more difficult to determine accurate distances to those galaxies than if there were also galaxies relatively close by?
Suppose you were Hubble and Humason, working on the distances and Doppler shifts of the galaxies. What sorts of things would you have to do to convince yourself (and others) that the relationship you were seeing between the two quantities was a real feature of the behavior of the universe? (For example, would data from two galaxies be enough to demonstrate Hubble’s law? Would data from just the nearest galaxies—in what astronomers call “the Local Group”—suffice?)
What does it mean if one elliptical galaxy has broader spectrum lines than another elliptical galaxy?
Based on your analysis of galaxies in [link], is there a correlation between the population of stars and the quantity of gas or dust? Explain why this might be.
Can a higher mass-to-light ratio mean that there is gas and dust present in the system that is being analyzed?
Figuring for Yourself
According to Hubble’s law, what is the recessional velocity of a galaxy that is 108 light-years away from us? (Assume a Hubble constant of 22 km/s per million light-years.)
A cluster of galaxies is observed to have a recessional velocity of 60,000 km/s. Find the distance to the cluster. (Assume a Hubble constant of 22 km/s per million light-years.)
Suppose we could measure the distance to a galaxy using one of the distance techniques listed in [link] and it turns out to be 200 million light-years. The galaxy’s redshift tells us its recessional velocity is 5000 km/s. What is the Hubble constant?
Calculate the mass-to-light ratio for a globular cluster with a luminosity of 106 LSun and 105 stars. (Assume that the average mass of a star in such a cluster is 1 MSun.)
Calculate the mass-to-light ratio for a luminous star of 100 MSun having the luminosity of 106 LSun.
- Hubble constant
- a constant of proportionality in the law relating the velocities of remote galaxies to their distances
- Hubble’s law
- a rule that the radial velocities of remove galaxies are proportional to their distances from us
- when lines in the spectra are displaced toward longer wavelengths (toward the red end of the visible spectrum)