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 describes the expansion of spacetime

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.


Hubble’s Law worksheet

Phases of the Moon for Young Children

Recently I went in to my daughter’s primary school and spent the afternoon running an activity for the 60 children aged 6-7 in her year group. They had been studying the Solar System and I’m happy to offer my services as an expert of all things astrophysics. I ended up delivering a lesson which introduced the key science skills of observation, spotting patterns and making a prediction as part of the topic of the phases of the moon.

Misconceptions and Remedies

There are many common misconceptions regarding the Moon which children arrive with at secondary school. It never ceases to surprise me how many 11 year olds don’t think the Moon is ever visible by day, despite the fact that they have all seen it! This is easily fixed with a few reminders of times they have seen the Moon outside, often it is actually in the sky during the lesson, or photos can be shown with the moon in daylight.

They have no grasp of the relative sizes, distances or position of the Moon with respect to the Earth. I have often spent a lesson with tennis balls and plasticine blobs getting the students to make scale models with the Moon 30 times the Earth’s diameter away. I always discuss how the photos we commonly see of the Earth-Moon as a pair are doctored to bring the Moon much closer – this really does need explaining to students.

Typical Earth-Moon image:

Actual Earth Moon separation:

Students without fail believe the Moon orbits the Earth’s equator. In fact the Earth is tilted by 23 degrees to the ecliptic and the Moon is a further 5 degrees above that. Reminding students of the Earth’s own tilt is often enough to get them to realise the Moon must alternate its position above and below the equator. They also benefit from discussion about the locations where solar eclipses occur to further realise the Moon can’t stay over the midline of the Earth. This nicely introduces the idea of the ecliptic plane of the Solar System and the various orbital tilts that planets have. The idea of planetary alignment and paranormal events is quite common in science fiction and fantasy shows on TV, conjunctions are never perfectly aligned however and you can explain why.

So there are some significant gaps in the children’s understanding of our Earthly relationship to our nearest neighbour in space. In an attempt to get the children thinking about what they could see of our Moon with their own eyes, I planned a Phases of the Moon lesson.

Lesson Plan – Outline

AIM: to introduce the names for the phases of the Moon and to recognise the shapes associated with the names. To observe the shape of Moon over the course of a week and predict what it would look like the following week. More able students will be able to offer an explanation in terms of the shadow face/illuminated face of the moon and our position with respect to those two hemispheres.

TIMING: 45 minutes

5 minutes: Elicitation and questions

20 minutes: Copy and name the moon phases, practise naming the phases

10 minutes: Observe the “moon” in pairs

10 minutes: Discuss conclusions and explain observation task

LOCATION: A room large enough for 30 children to sit and with space to walk around the illuminated ball (see below). Curtains or blinds will be needed to darken the room.

APPARATUS: One large inflatable gym ball, roughly 60cm in diameter, with a stool to sit it on; a bright torch positioned to shine straight onto the ball from the side; some A4 pictures of the Moon printed from NASA’s website and therefor publicly useable (all NASA pictures are usable for educational purposes). A worksheet and pencil each.

ORGANISATION/BEHAVIOUR MANAGEMENT: The children need to sit and write on their sheets for part of the lesson. They sat on the floor or a bench in 3 rows. Ideally I would give them clip boards to use next time. When pairs of children are observing the ball the remainder of the class needs to be kept busy. During this time one teacher practised the shapes and names with them again which worked well.

Lesson Plan – Activity Details


  1. Elicitation and questions: Firstly students are seated facing the front and asked what they know about the Moon. Do they know what it is made from? How can we see it? Does it always look the same? Why do you think that? How do people on Earth find out about the Moon?
  2. Introduce vocabulary: Following this the students are given a pencil and worksheet, the teacher holds up a picture of the Moon and asks for the name for its shape (full moon, gibbous moon, half moon, crescent moon, new moon). Some students will know some of the names. They copy the word down and sketch a picture of the moon in that phase. Repeat until all 5 are done.
  3. Memorise shapes: The students put down their pencils and worksheets and try to make the moon phase shapes with their arms or bodies (depending on how much space you have). The teacher leads by saying a phase and the children have to find a way to make themselves resemble the shape.
  4. Observe the shadow face/illuminated face: in pairs, the students come and look for the dividing line between the bright face and the shadow face of the gym ball “moon”. They look from the front, side and behind and link the shape of the bright surface that they can see to the shape of the Moon at different times of the month.
  5. Observation experiment: The rear side of the worksheet has a chart where the children can write the day or the week, whether they could see the moon (due to cloud cover), was it visible at day or night and what shape it had. They go away and complete this during the week – realistically in children aged 6-7 most will do 3 or 4 observations out of a possible 7.
  6. Make a prediction: The final task on the worksheet is to make a prediction about what shape the Moon will have in a few days time. The students are using the pattern they have seen in their observations and linking it to the order of the phases introduced in the class activity.


FOLLOW UP: It was left to the class teacher to follow up this activity throughout the week with reminders and a discussion on their results the following week. The vocabulary of the phases of the moon can be easily incorporated into their continued work on the Solar System topic; in written work describing a trip to the moon, in art work, as part of maths learning about shape (sphere, hemisphere, crescent etc) and fractions (whole, half, quarter).


So how do I think it went? I have never taught science to such a young group of children before and on the whole they were interested and well behaved.

The worksheet seems to be pitched at the right level, most students could read it and understood what to do however some students needed to be shown where to draw the picture and where to write the word. Some students took a little longer to write than others and there was discussion about how best to show shadow and a New Moon which was interesting, eventually they solved these issues for themselves.

The A4 pictures of the moon phases were large enough to be seen be everyone as I sat in front of the group.

They enjoyed standing up and making moon shapes with their arms over their heads, a big circle for a full moon, D shape for half moon, banana shape for a crescent and so on. If I had thought this through a bit more I could have taken them to the centre of the hall (we were in the main school hall) and made a bit more of this.

Some children really wanted to touch the ball and trace the line between the shadow and bright side, so if I repeated the lesson I would take some plasticine or a coil of rope for the ball to sit in so it didn’t wobble around so much on the stool.

The one thing I felt needed improving was the time when I showed the illuminated big ball to the pairs of students. Those waiting in their seats were not occupied enough. Partly this was due to were I had had to position the ball, the sun was very bright through the windows that afternoon and the corner of the hall was the only suitable dark enough spot even with the curtains pulled. That meant far fewer students than I had anticipated could walk around the ball at a time, I had planned for 8-10 students to walk and view both sides, front and back at the same time. One class teacher stepped in and led the group in practicing the shapes and tested them on the words while their classmates took turns to look at the ball. The other teacher didn’t and the students eventually became restless.

I would prepare a word search or pairing/matching game for this period of the lesson if I did it again to reinforce the vocabulary while they waited.

With one group we had a good discussion about how scientists find things out which led nicely onto the homework observation task. We ran out of time with the other group which meant the task was explained with less context. This bothered me but the students didn’t seem to mind. The students very much enjoyed asking questions about how scientists work, one asked me if scientists have rows with each other about who is right, which of course they do very politely via academic publications.

Additional Resources

moonphasepictures – Word document of A4 lack and white Moon phase photos

Phases of the Moon – students’ worksheet

The Great American Eclipse – critical thinking resource

Critical thinking is such an important skill and a fundamental tool in science. We do not believe, we prove beyond reasonable doubt. Increasingly inaccurate, deliberately false and manipulative information is being shared on social media and it becomes vital that our students and ourselves can think critically about what we are seeing. Just because it is on the internet doesn’t make it fact, even if lots of other people have “liked” it. Here I unpick a particular example from earlier this year which nearly tripped me up.

You can’t have missed the fact that a total solar eclipse tracked from sea to shining sea in the USA on 21st August 2017. There were some beautiful images posted of dramatic darkened skies. One in particular popped up on my social media timeline which at first glance was an impressive, nay even stunning image.

My first impression was followed by a jarring feeling of incongruity, something about this felt off. I have painted pictures of a moon over the sea and I know the sun and moon appear similar in size in the sky, that’s why eclipses happen after all. The sun-moon seemed a bit too big compared to the size of the waves, to the distance to the horizon. Then I clocked how bright it is, totality during an eclipse is so dark you can see the stars. Then I spotted the clouds appeared behind the sun-moon and finally every photo of the sun at the horizon I have ever seen shows visual distortion due to the much thicker atmosphere, like this one here;

yet the faked image shows a perfect circle just touching the sea. It looks beautiful but is completely fake, a quick google search revealed the height of the sun over the coast of  Oregon at totality was actually much higher and at 10.15am in the morning. So I call bullshit on this image.

Fake news is an increasingly common topic of discussion amongst people concerned by the way deliberate bias and propaganda or plain ignorance is infiltrating all of our contact with news and information online.In the UK the government curriculum changes in the sciences were designed to increase scientific literacy in students by exposing them to topics deemed contentious by the media like GMOs, mobile phone radiation risk, use of vaccines and training the students to question the sources and reliability of the data used to back up outlandish claims against scientific advice.

One of the most beneficial aspects of studying science is of course the development of critical thinking skills. This faked image is a great way to engage students in this key skill.

Activity – Critical Thinking

Display the faked image (search faked eclipse photos) and its attribution (Oregon, USA) and ask the students do they believe it is real and why, is there anything a bit off about it, where is Oregon on a map and which way does the Earth rotate, and how could they check the veracity of the claim.

Follow up discussion can explore phenomena such as the distortion of the sun at the horizon, the light levels at totality, the size of the sun and moon in the sky etc.

A selection of faked and real photos could then be put up with students voting on which they think is real and why.

Follow-up activities:

Homework on an aspect of the discussion such as the mechanics of an eclipse and the relative sizes of the sun and moon in the sky, or following on with critical thinking skills a single side of writing on “how to spot fake eclipse photos”.