# Hubble’s Law – Using Historical Data 1

When teaching physics I think there is a lot of reliance upon writing down a law, Hubble’s Law for example, on the blackboard at the start of a lesson. Then without much or indeed any explanation as to how this result came about, students are left to to work out some example problems or do a couple of experiments using this result. They are expected to accept without question the “Law of Physics” we have given them. This doesn’t encourage critical thinking and this approach is one of the reasons so many students are turned off physics as a subject.

Chalk and talk teaching is unhelpful and frankly boring. A better way to teach is to supply information and allow the students to discover the results for themselves. Not only is this more interesting, but by doing the work themselves the students learn more effectively and this method mimics the actual scientific process of discovery and deduction. Now I appreciate we don’t have access to large telescopes and apparatus, I’m not suggesting we reproduce the entire experiment! We can make use of historical data to enable students to reproduce important results for themselves. I’m going to write a few posts which show how the data from various famous experiments can be used when teaching physics.

#### Teaching Hubble’s Law

Hubble’s Law is an example of a topic which can be taught this way. Usually it is taught by stating the relationship between distance and recessional velocity (Hubble’s Law V=Hr) and this equation is used to deduce the age of the universe etc. Some discussion is made of the interpretation of the recessional velocity – students are expected to understand that spacetime itself is expanding between the observer on Earth and the distant galaxy not that all galaxies are flying away from us.

So turn the lesson around and start with the data. Hubble’s original research paper is short and the data produces a nice line graph. Students can be given the data and be tasked with reproducing his graph of results. They can then construct their own interpretation of what the linear relationship implies. It is good practice to get students to label their graphs with a sentence or two describing the data for example: “a graph to show the relationship between recessional velocity of galaxies and the distance to those galaxies”. Teasing out precisely what relationship; linear, inversely proportional or whatever, can follow. Students can find a value for the Hubble constant from the gradient of their line of best fit. Comparing this to present day values shows the considerable advances in our measurements of redshifts and distances.

A little bit of algebraic manipulation draws out the units for the Hubble constant as being per unit of time. Time from what? is the key question to ask. What is the start time and what is the end time to find the difference in times that go with the difference in distance to give us a velocity? Change in distance/change in time = velocity. Every time I have taught this one student at least realises that 1/Ho is the time since the galaxies started to move apart and is therefor an estimate for the age of the Universe. You don’t have to tell them, they can work it out! This starts all sorts of discussion about how appropriate this estimate of the age of the Universe is. It is a great way to introduce the earlier, hotter, radiation dominated phase of the Universe where the rate of expansion was slightly different and then further back to Inflation and the Hot Big Bang Theory.

Active learning, the idea that students are working out the relationships not being passive recipients of them as Laws of Physics, has been shown time and time again to produce better learning outcomes. Students understand the topics better and recall more of the information correctly when assessed.

Here is a worksheet which allows more able GCSE 14-16 year olds or AS/A2 16-18 year olds to plot Hubble’s data. A scientific calculator is required and this activity wouldn’t be suitable for students who struggle with large numbers or data processing.

I have also attached Hubble’s paper “A Relation Between Distance and Radial Velocity Among Extra Galactic Nebulae” from 1929.

Equipment needed: graph paper, rulers, pencils and scientific calculators or log tables.

A RELATION BETWEEN DISTANCE AND RADIAL VELOCITY AMONG EXTRA-GALACTIC NEBULAE by Edwin Hubble