Kepler, Galileo, Newton, Einstein: not a bad roll-call

The following is an edited extract from notes which I give to students before going through the derivation for the rather intimidating equation below.

You have just arrived at an equation which bookmarks a seminal moment in the history of science.


Around this time (16th century) an astronomer called Johannes Kepler discovered empirically (i.e. by analyzing data on the motion of planets) that the square of the periodic time of these planets (time for one complete orbit around the sun) is proportional to the cube of their distance from the sun.
Kepler actually stole the necessary data from a colleague, Tycho Brahe, but that’s nothing new in the world of Science. We will conveniently ignore that for now.

Later on Newton came along and was able to demonstrate this relationship mathematically, by combining a well known equation for circular motion on Earth with his own universal law of gravitation. We are about to follow in his footsteps and see exactly what he did and how he did it. Do not under-estimate the importance of this exercise (yes you have to know it for exam purposes, but that’s not why I consider it important).

This event had two very important consequences.
1. It showed that Newton’s Law of Gravitation must be valid in its own right, which was very important in securing Newton’s reputation as a giant of science, both at the time and for posterity.
2. Even more importantly, it demonstrated that ‘the heavens’ followed the same rules of science as those which operated here on Earth.
This meant that they were a legitimate area of study, and so Astronomy (which in turn led to Cosmology) was given an added respectability. Just to give a sense of what people believed at the time, Kepler had to spend much of his time during this period defending his mother of charges of being a witch.

I can think of no modern discovery which compares with this. Even if we discovered life on Mars it really wouldn’t be that big a deal. For up to this point the heavens were considered off-limits – the realm of God or the gods or whatever you’re into yourself. But now they could be shown to be just another series of objects which followed set rules, much like cogs in a complicated clock. So God was being pushed into the wings. You could see why neither Martin Luther or the Vatican Church would have been keen fans.

Kepler was following on the work of Nicolas Copernicus (known to science students down the ages as ‘copper knickers’), who in turned showed that the Earth revolved around the Sun, not the other way around.
Galileo’s run in with the Church was because he supported Copernicus’ view, so Galileo never actually made that discovery but was happy to use it to make fun of the church authority figures of the time. I think we all know how that worked out for him.

This was really the dawn of science, and progress was hindered by medieval views of the astronomers themselves. It took Kepler many years to realise that the orbit of the planets was elliptical in nature, not circular. He had assumed initially that the motion had to be circular because a circle was a perfect shape (harping back to the teachings  of Pythagoras and Aristotle, among others) and therefore would have been more pleasing to God who obviously had created the planets in the first place.

Similarly Newton, despite being heralded as one of our greatest ever scientists, spend up to 90% of his time trying to date the creation of Earth by tracing who gave birth to who in the bible.

But then Newton had another problem. He realised that Kepler was correct in stating that the planets traced out elliptical orbits, but even Newton’s equations didn’t fully match the path of the heavenly bodies; according to Newton’s equations the planets should slowly but exonerably drift from their current pathways. He couldn’t figure out why this didn’t happen – after all, his equations seemed to be perfect in every other way. And Newton believed that he was getting his ideas directly from God. Which doesn’t leave much room for admitting you made a mistake.

We now know that while Newton’s equations are very accurate, we actually need Einstein’s Theory of General Relativity to explain why they don’t precisely describe the motion of the planets.
It’s interesting to note that Newton’s explanation was that God must step in every so often to gently nudge the planets back into their preferred orbits. Now as you now know, invoking a deity to explain discrepancies in scientific observations is the antithesis of Science. So perhaps Newton wasn’t actually so mighty after all. This is partly why he is sometimes referred to as the last sorcerer rather than the first scientist.

So now we’re up to Einstein. His general theory of relativity suggested that the universe was expanding, but just like all of his predecessors he was a man of his time, and this coloured how he saw the world. It was believed at the time that the universe had always been the way it is now (this is referred to as the ‘Steady State’ theory). Einstein figured that there must be some mistake in his paper so he introduced what he called a ‘cosmological constant’ which basically amounted to a fudge factor which altered the implications of his calculations and prevented the universe from expanding.

Which was all very well until Hubble (he of the ‘Hubble’ telescope) showed that the universe was actually expanding after all.

Einstein referred to this as his greatest ever blunder.

So there you have it. This has been my attempt to put some context on the derivation that we are about to carry out. It is our chance to repeat one of the greatest moments in the history of science.

So you have two options; you can consider this exercise to be a pain in the ass or you consider it an incredible privilege to be in a position where you can follow in the footsteps of giants.

I think we know which option I go with.

And don’t be afraid to tell your parents this tonight; they may well throw their eyes up to heaven but if they do that’s a slight on them – not on you.


We are star-stuff: teaching about the elements

We had fun with these resources yesterday so I thought I would share them.

First up, where did all the stuff that makes up you and me come from?

Hold up your hand: You are looking at stardust made flesh. The iron in your blood, the calcium in your bones, the oxygen that fills your lungs each time you take a breath – all were baked in the fiery ovens deep within stars and blown into space when those stars grew old and perished. Each one of us was quite literally made in heaven. Modern science has shown us that we are more intimately connected to the stars than anyone dared to guess.”

The author of this magical piece, as far as I establish, is Marcus Chown, but if anyobdy can confirm or correct I would appreciate it.

I have this taped to the outside of my lab door, and was delighted to see a first-year take it down into her notebook recently (not sure the senior years ever stop to even notice it, but maybe that says more about our education than anything else).

It turns out that pretty much all the hydrogen in and around us is here from the time of the Big Bang over 13 billion years ago, and most of the helium is also that old (although helium is still being created all around us in the form of nuclear radiation). These are the first two elements in the periodic table. These eventually formed stars and in the process (nuclear fusion) formed the next 24 elements (up to iron). But even the energies involved in the sun’s day-to-day activites aren’t great enough to produce elements heavier than iron. So where did all the other 90 elements come from? (and remember that all these elements are what you and I are made from today).

Eventually the fuel (and energy) to produce fusion runs out and thus begings the final steps of a star’s incredible journey. But even in death they have a sting. Most ‘dead’ stars don’t just sit there, no sirree bob. The phrase ” it’s better to burn out than fade away” cannot be more apt than when applied to the death knell of one of these incredible stellar objects. If the star has enough mass then after collapsing in on itself it ‘rebounds’ and sends out the mother of all shock waves, one which is so strong that it actually tears the sun itself apart – it has become a ‘supernova’. A supernova explosion can be as bright as 4 billion (yes billion) suns. Not surprisingly it can become the brightest thing in the night sky for days (the last documented one within out own galaxy seeems to have been in 1604, but the Chinese also had written about one a thousand years before that).  Not that the 1604 explosion actually happened in 1604; it actually happened 13,000 years previously – it just took that long for the light to get from there to here (‘there’ and ‘here’ also being relative terms). But I digress.

When the star explodes the energy it contains is now sufficient to create all the heavier elements above iron, from copper upwards.

So there you have it: we are stardust.

The Amerian physicist Neil de Grasse Tyson sums it up rather nicely:

The gentleman you saw briefly in the background is Carl Sagan

Sagan was like Richard Dawkins without the arrogance, indeed he was a much more successful communicator  because he delibertately chose to preach not just to the converted, but to all. He would not have been impressed with Dawkins:

People are not stupid. They believe things for reasons. The last way for skeptics to get the attention of bright, curious, intelligent people is to belittle or condescend or to show arrogance toward their beliefs.

Here is Sagan taking us on a whirlwind tour of the history of our planetary and biological evolution.

But of course there’s no chance that any of the good stuff here will ever appear on a syllabus near you.
It’s also pretty unlikely that, with the exception of Humphrey Jones over at the frogblog, many other science teachers get animated by this. It seems to be the humanities teachers who are more likely to tackle the mystery and wonder of science. I guess those teachers who are fascinated by the wonder in Science are happy enough to enthuse their own students and leave it at that.
For another day perhaps.

And now for something completely different:

Science really does seem to be coming back into fashion – no longer is it just for the nerds. Or maybe it still is for nerds, but nerds are now cool. Thank you Stephen Fry.
Here’s Daniel Radcliff’s version:

Finally, for something a little more light. And for bonus points, for what sitcom do this band have an even more catchy tune?

Wha’ is the stars, Joxer?

Boyle: An’, as it blowed an’ blowed, I ofen looked up at the sky an’ assed meself the question — what is the stars, what is the stars?

Joxer: Ah, that’s the question, that’s the question — what is the stars?
Boyle: An’ then, I’d have another look, an’ I’d ass meself — what is the moon?
Joxer: Ah, that’s the question — what is the moon, what is the moon?

“Juno and the Paycock”, Seán O’Casey (1924)

 From pretty much the time a baby can focus on the lights overhead he will notice the stars in the sky and wonder about them. Twinkle Twinkle Little Star has lasted through the years partly because it resonates with an innate curiosity in all of us to find out exactly what is up there. So you would think something about astronomy or better still cosmology would be on either the Junior Cert Science syllabus or the Leaving Cert Physics syllabus (or here’s a mad idea – why not both?). Not only is it not on either, but in the draft of the new Physics syllabus it doesn’t even get a mention.

Last year at a physics-teachers’ convention we were told that the draft could not be altered significantly and that therefore there would be no mention of stars, galaxies, the Big Bang, or indeed any reference to any of the incredibly exotic objects out there. There would, of course, be a consultation process but this seems to allow for no more than tinkering around the edges. Which begs the question why could we not have been consulted to begin with? Are we not to be trusted?

Presumably it’s still considered much more important to be able to measure the density of a stone than it is to explain the origin of the universe (interestingly you will find the Big Bang mentioned in the Religion syllabus).

 I suppose even if these topics did get mentioned we would somehow manage to distil the wonder out of them like we do pretty much everything else on the syllabus.

Did you know that there are objects in the sky which are about the size of the Earth but which have the mass of the Sun, and which can spin almost 1,000 times a second? Remember our Earth takes 24 hours to do one revolution and yet these guys can spin one thousand times a second! Mad I tell you. Oh, and they were discovered by an Irish woman (they are called pulsars; check out this cool video on YouTube)

 So what should students learn about the heavens? As always, put away the textbooks and look to our colleagues across the so-called ‘two cultures’ divide.

You want to know about galaxies? – sit up straight and listen to Monty Python.

Or how did it all begin? – Try The Barenaked Ladies.

Maybe if we want to attract students back into science we could do worse than start here.

Barenaked Ladies: It all started with the big bang

Monty Python: The Galaxy Song