Background

The International Astronomical Union voted in 2018 to rename Hubble’s Law the Hubble-Lemaître Law to recognize the contribution of Belgian astronomer Georges Lemaître, who published a paper on the expansion of the Universe two years before Hubble published his work. Lemaitre’s paper was published in a journal that had limited circulation, and therefore was not widely read until it was translated into English several years after Hubble’s publication.

The Hubble-Lemaître Law did not introduce the idea that the Universe was expanding. The idea of expansion preceded their work, and was supported both by theory and observations (from Einstein and Slipher). The entire progression of the work of the scientists referenced in the introduction to this investigation provides an outstanding example of science as a collaborative and progressive process. The Hubble-Lemaître Law provided evidence for the expansion of the Universe and launched the next set of inferences: the Universe had a beginning, the age of the Universe could be estimated from the slope of the Hubble plot (the Hubble Constant), the rate of expansion has changed over time, and expansion is accelerating.

At different times in the history of the Universe, different factors dominated the rate of expansion. Photons drove the rate of expansion before the matter in the Universe took over. Today, dark energy dominates, which is why the expansion of the Universe is now accelerating instead of expanding at a slowing rate. This accelerated expansion may be used to introduce a discussion of dark energy following this investigation. So the value of the Hubble “Constant” (the slope of the Hubble plot), isn’t constant but has been increasing over time.

OpenStax Astronomy textbook links:

The expansion of the Universe

Big Bang theory

Dark matter and dark energy

Teacher Notes

1. Our investigations are designed so that students cannot proceed to the next page without answering each question. If you would like to quickly preview the entire investigation, you can use “educator mode” on the Start page. Enter the passphrase: 3ducatorMod3 to activate it.
2. The data in this investigation differ from that in a typical Hubble plot. Velocity data are usually derived from the spectroscopic redshift of galaxies. Rubin Observatory uses a different technique that produces a photometric redshift. The advantage of using this different technique is that it can be applied to many more and much fainter galaxies. Cepheid variable stars are usually used to measure distances to galaxies out to about 165 Mly. This investigation substitutes a different type of standard candle, Type Ia supernovae, which are more precise than Cepheid variables and can be used at distances out to 3300 Mly.
3. The original Hubble plot, shown on p.1 of the investigation, shows three points that have a velocity less than zero (a negative velocity). Negative velocities can occur when nearby galaxies in the Local Group are approaching our galaxy. Hubble’s observations included many nearby galaxies, which accounts for the large scatter in the plot. Hubble determined most of the galaxy distances for this first plot by using the brightest stars in galaxies or by the luminosity of the galaxies themselves. Although Hubble had previously used a Cepheid variable star to estimate the distance to the Andromeda Galaxy, it was only later that he and other astronomers began to use Cepheids to measure distances to other galaxies.

4. Distant galaxies with supernovae will appear only as faint smudges or dots, and often the supernova will outshine the galaxy itself. The galaxy and the supernova can be distinguished from each other because the galaxy does not appear to change in brightness. Students may think that the galaxy itself is exploding, or that the supernova is outside of the galaxy. It is extremely rare that a star would be alone in space and not associated with a galaxy. You can assume that the supernova belongs to the galaxy.

5. The low image quality of the galaxy data used in this investigation are due to the images being very magnified after extraction from a larger (wide field) image. (Think about what would happen if you zoomed in on a small feature on a picture as much as possible.)
6. This investigation deals with the age of the Universe in a conceptual way rather than using the full model necessary to actually calculate the age of the Universe. The computation of a numerical age involves additional variables beyond the Hubble Constant. See this sample cosmology calculator for more information.
7. Students will struggle to infer that the Universe is expanding from the information in a Hubble plot. To help them understand, ask students to identify the direction of motion for the galaxies in the Hubble plot (all galaxies are moving away), then have them compare the speed of the galaxies that are far away to those that are much closer, and ask if the nearby galaxies will ever catch the distant galaxies. Then ask if these observations describe whether galaxies are getting closer together or farther apart from one another—and whether that means the Universe is getting bigger (expanding) or shrinking.
8. Students will have a difficult time understanding how the slope of the Hubble Plot is used to determine the expansion rate of the Universe. One way to help students understand this is to show them two Hubble plots with lines of different slopes, and ask students, "In which plot do the recessional velocities of galaxies increase more quickly with distance?” Follow this with “In which case does the Universe expand faster: a Hubble plot that has a steep slope or one that has a shallow slope?” This sequence of questions sets students up to then be shown a Hubble plot that has a curve, indicating a changing slope (and an accelerated expansion). Students can then be asked “Where on the graph is the slope steepest and most shallow?” and, “Is the expansion rate faster for the steeper slope or the more shallow slope?”
9. Students may struggle to reason how the slope of the Hubble plot and expansion rate are related to the age of the Universe. Show graphs with different slopes and ask, “In which graph is the expansion rate of the Universe fastest? Do you think a fast expanding Universe will get to its present size in less time or more time than a Universe that is expanding slowly? So will a fast expanding Universe result in a Universe with a younger or older age?”
10. Students may know that the Hubble plot can be used to estimate the age of the Universe, but not understand how this is determined. Remind students that the Hubble Constant (units of km/s/Mpc) represents the slope of the graph. It is the inverse of this number that is used to determine the age of the Universe.