Posts Tagged ‘Gravity’

Physics Textbook on Cosmology and Gravitation

March 15, 2018

M.V. Berry, Principles of Cosmology and Gravitation (Bristol: Institute of Physics Publishing 1989).

Yesterday came the news of the death of the great British physicist and cosmologist, Stephen Hawking at the age of 76. Hawking had suffered for most of his adult life from motor neurone disease, since he was diagnosed with it in his early 20s. He was given only three years to live, but instead managed to live out a very full lifespan working on his theories of the origin of the universe and Black Holes. He was a great ambassador for science. His book, A Brief History of Time, was a bestseller when it appeared in 1980s, although he admitted that it was probably a book few finished. And he showed that it was still possible for a disabled person to do cutting edge research, provided they had the necessary technical and medical support. In his case, it was his wheelchair and the machine that allowed him to speak, first of all by keying in the words, then by twitching just a single muscle. Some of the praise seemed a bit too fulsome to me. Like when they started saying that he was the greatest scientist since Newton and Einstein. I don’t think he was. And Hawking on his own didn’t unlock the secrets of universe or Black Holes, as the Beeb’s presenters also claimed. As for his great sense of humour, well, it existed, as his appearance on shows like The Simpsons demonstrated, but my memory of it is marred by him turning up with the TV critic, Victor Lewis Smith, telling fart jokes and laughing on the 1990s series, Inside Victor Lewis Smith. But it really was inspiring to see how he was a great hero to the ‘A’ level students at a science fair yesterday, and how he had inspired them to become interested in science.

One of the complaints Richard Dawkins has made about popular science programmes is that they’re too ‘dumbed-down’. He points out that they have to have lots of explosions, and they mustn’t include equations, in case that scares people off. There’s a lot with which I don’t agree with Dawkins. I’m not an atheist, and have argued on this blog against him and the other militant atheists. But he is right here. Scientists writing the popular science books have said that they’ve been told by their publishers to leave equations out, because every equation in a book damages sales.

I think this is the wrong attitude to have. It’s why I’ve put up this piece about the above book by M.V. Berry. It’s an undergraduate physics textbook, which does contain the fundamental mathematical equations for this area of physics. Its contents include

1. Introduction

2. Cosmography
2.1 What the universe contains
2.2 The cosmic distance hierarchy and the determination of galactic densities
2.2.1 Parallax
2.2.2 Distance from velocity measurements
2.2.3 Distance from apparent luminosity
2.2.4 Weighing galaxies
2.3 The red shift and the expansion of the universe.

3. Physical base of general relativity
3.1 The need for relativistic ideas and a theory of gravitation.
3.2 Difficulties with Newtonian mechanics: gravity
3.3. Difficulties with Newtonian mechanics: inertial frames and absolute space.
3.4 Inadequacy of special relativity.
3.5 Mach’s principle, and gravitational waves.
3.6 Einstein’s principle of equivalence.

4 Curved spacetime and the physical mathematics of general relativity.
4.1 Particle Paths and the separation between events
4.2 Geodesics
4.3 Curved spaces
4.4 Curvature and gravitation.

5 General relativity near massive objects
5.1 Spacetime near an isolated mass.
5.2 Around the world with clocks.
5.3 Precession of the perihelion of Mercury
5.4 Deflection of light
5.5 Radar echoes from planets
5.6 Black Holes

6 Cosmic Kinematics
6.1 Spacetime for the smoothed-out universe
6.2 Red shifts and horizons
6.3 Apparent luminosity
6.4 Galactic densities and the darkness of the night sky.
6.5 Number counts

7 Cosmic dynamics
7.1 Gravitation and the cosmic fluid
7.2 Histories of model universes
7.3 The steady state theory
7.4 Cosmologies in which the strength of gravity varies

8 In the beginning
8.1 Cosmic black-body radiation.
8.2 Condensation of galaxies
8.3 Ylem.

Appendix A: Labelling astronomical objects
Appendix B: Theorema Egregium
Solutions to odd-numbered problems
Useful numbers.

there’s also a bibliography and index.

I’m not claiming to understand the equations. I struggled at both my ‘O’ level maths and physics, and what I know about science and astronomy I learned mostly through popular science books. But in the mid-1990s I wanted to see at least some of the equations scientists used in their explorations and modelling of the universe. One of the popular science books I was reading said at the time that this book was at the level that people with ‘A’ level maths could understand, and this didn’t seem quite so much a jump from my basic maths skills. So I ordered it. I’m afraid I can’t say that I’ve read it properly, despite the fact that I keep meaning to. Some of the equations are just too much for me, but I can follow the explanations in the text. I’m putting this notice of the book up here, in case there are any budding Stephen or Stephanie Hawkingses out there, who want to go a bit further than the pop-sci explanations, and see for themselves what the maths behind it all is like.

The Beeb also said in their eulogy for the great man, that Hawking hoped that the people reading his A Brief History of Time would come away with one point, even if they hadn’t finished it: that the universe is governed by rational law. Actually, this ideas isn’t unique to Hawking by a very, very long way. It actually comes from the Middle Ages, and is the assumption that makes science possible. Hawking was an agnostic, I believe, and many scientists are atheists. But this assumption that the universe is governed by rational laws ultimately comes from Christian theology. The founds of modern science in the Renaissance pointed to the passages in the Bible, in which God’s Wisdom creates the universes and establishes the boundaries and courses of natural phenomena, like the tides and stars. And the anarchist of science, Feuerabend, pointed out that the assumption that the laws of the universe all form a consistent whole come from Christian doctrine, quoting the 13th century theologian and philosopher, Thomas Aquinas: ‘We must believe that the laws of the universe are one, because God is one.’

Hawking has passed away, but it’s clear that he has inspired many more people to become interested in this rather arcane branch of the sciences. I hope this continues, despite the Tories’ attack on education and science and research for its own sake.


The French Astronomer Who Gave His Name to the Captain of the Enterprise?

December 28, 2016

More space/ SF stuff.

Looking through the 1982 Yearbook of Astronomy, edited by Patrick Moore, I found on the chapter for July a very brief biography of the 17th century French astronomer, Jean Picard. The piece ran

1982 is the anniversary of the death of Jean Picard, a celebrated French astronomer. He was born at La Fleche, in Anjou, on 21 July 1620; he studied for the priesthood, and was ordained, but his main interest was in astronomy. In 1645 he was appointed Professor at the College de France, and took a leading part in the establishment of the Paris Observatory. His most famous piece of research was undertaken in 1669-70, when he made a new and more accurate determination of the radius of the Earth. it has been said that it was this which allowed Isaac Newton to complete his work on the theory of gravitation, though in fact Newton’s earlier hesitation was due to the fact that one link in his chain of argument was incomplete. Jean Picard died as the result of an accident on 12 July 1682. (pp. 103-4).

Reading that, I wonder if he was the inspiration for Patrick Stewart’s character in Star Trek: The Next Generation, Captain Jean-Luc Picard. I’ve also got a feeling that another Francophone space scientist may also have inspired the name and character. Professor Calculus in the Tintin books by Herge is based on a real French scientist, who ascended to the edge of space in a high altitude balloon in the last century. I can’t remember the scientist’s name, but I’ve got a feeling it was also Picard.

Of course, it could all be coincidence. But considering the high standard of TV drama set by the series, it really wouldn’t surprise me if the creators and producers had done their historical research, and decided to create the Picard character partly as a tribute to these scientists.

Vox Political: Kipper and Conservative MP Douglas Carswell in Row with Scientists over Tides

September 20, 2016

This piece by Mike over at Vox Political is a real gem, as it encapsulates the profound anti-intellectualism and sheer bone-headed stupidity of the Tories and the Kippers. Mike has posted up a piece commenting on a report in the Independent that Douglas Carswell, the former Tory and now Kipper MP for Clacton, has got into a row with Britain’s scientists over the origins of tides. Conventional science holds that they’re caused by the Moon. Carswell, however, believes they’re caused by the Sun, and has challenged a top scientist at Sussex University’s Science Policy Research Unit over the issue.

The report also notes that this bizarre claim was made after Michael Gove declared that the British people were tired of experts after he failed to name one economist, who thought that Brexit would be good for Britain.

The title of Mike’s piece just about sums up the astonishment Carswell’s claim must cause in everybody, who has any idea about science: Both Tories and Kippers Have Made Douglas Carswell an MP. Read This and Asky Why?

Both Tories and Kippers have made Douglas Carswell an MP. Read this and ask: Why?

Quite. If you’re wondering whether the Moon does cause tides, Mike over in his piece has a clip of Brian Cox explaining the phenomenon.

I’ve a feeling that as far back as the ancient Greeks, it was known that the Moon caused tides. Certainly the great medieval philosopher and scientist Robert Grosseteste of Lincoln knew about it in the Twelfth century. As he was writing several centuries before Isaac Newton discovered the Law of Gravity, Grosseteste believed that they were caused by the Moon’s magnetism, rather than its gravitational effect on Earth. Still, you can’t expect too much of the people of that period, when science was still very much in its infancy. But it nevertheless shows the astonishing advances the people of the Middle Ages were capable of, simply using the most primitive of equipment, observation, and the power of their minds.

This simple fact, that the Moon causes the Earth’s tides, has been put in thousands of textbooks on astronomy and space for children since at least the beginning of mass education and popular science. Astronomy has been a popular hobby for amateurs since at least beginning of the 20th century, and I’ve no doubt probably as far back as the 19th. Generations of children have had the opportunity to learn that the Moon causes tides, along with other interesting and fascinating facts about space. Carswell, however, is clearly the exception, having rejected all that.

It all brings to my mind the conversation Blackadder has with Tom Baker’s bonkers sea captain, Redbeard Rum, in the epdisode ‘Potato’ from the comedy show’s second series. Trying to impress Good Queen Bess by sailing abroad as explorers, Blackadder, Percy and Baldrick plan to fake their expedition by sailing round and round the Isle of Wight instead until they get dizzy. They get lost instead as Rum believes it is possible to sail a ship without a crew. When they ask him if you really can, Rum replies, ‘Opinion is divided.’
‘So who says you don’t?’
‘So who says you do?’
‘Everybody else.’


This exactly describes Carswell’s attitude to space physics. Everybody else believes the Moon causes the tides, except him. I can see this causing yet another panic amongst scientists and ‘science educators’. Way back around 2009, the 150th anniversary of the publication of Darwin’s Origin of the Species, various scientists like Richard Dawkins were running around demanding better science education because polls showed a majority of the British public didn’t believe in it. This was partly a response to the growth in Creationism and Intelligent Design, though both of these views of evolution have had a very limited impact over here in Britain. That controversy seems to have quietened down, though the issue of the continuing need for improved science education has carried on with the persistence denial of climate change and anthropogenic global warming by the Right in both America and Britain. One of the sceptics of global warming and climate change over on this side of the Pond is Nigel Lawson. He’s even written a book about it, which I found the other day in another of Cheltenham’s secondhand book shops. Now that Carswell’s made this statement about the tides, which flies in the face of everything scientists have known since blokes like Aristotle, it wouldn’t surprise me if today’s leading science communicators, like Dawkins, Robert Winston, Alice Roberts, Brian Cox and the rest of them started worrying about this issue as well. And I wouldn’t blame them if they did.

As for Gove’s comment that ‘People in Britain are fed up of experts’, this also reminds me another comment by the American comedian, Bill Hicks. ‘Do I detect an air of anti-intellectualism in this country? Seems to have started about 1980 [the year Reagan was elected].’

If you’re worried that the Tories and UKIP don’t understand science, and are going to take us back to the Dark Ages, be afraid: you’re right. And heaven help the rest of us with them in charge.

Robert Jenkin: Science Demonstrates the Unimaginable Grandeur of God and His Creation

May 15, 2013

Although some Christians in the 17th century felt that the new scientific advances attacked and undermined Christianity, others believed the complete opposite. One of these was Robert Jenkin. In his The Reasonableness and Certainty of the Christian Religion, published in London in 1700, Jenkin stated that the new scientific advances not only demonstrated the power and majesty of God through His creation, they also showed how transcendent His works were. The Law of Gravitation seemed to have no rational explanation. It was nevertheless true, and a major scientific advance. It also showed how far beyond human understanding God’s construction and management of the cosmos was. He wrote:

‘Indeed infidelity could never be more inexcusable than in the present age, when so many discoveries have been made in natural philosophy, which would have been thought incredible to former ages, as any thing perhaps that can be imagined, which is not a downright contradiction. That gravitating attractive force, by whihc all bodies act one upon another, at never so great a distance, even through a vacuum of prodigious extent, lately demonstrated by Mr. Newton; the Earth, together with the planets, and the sun and stars being placed at such distances, and disposed of in such order, and in such a manner, as to maintain a perpetual balance and poise throughout the universe, is such a discovery, as nothing less than a demonstration could have gained it any belief. And this system of nature being so lately discovered, and so wonderful, that no account can be given of it by a hypothesis in philosophy, but it must be resolved into the sole power and good pleasure of Almighty God, may be a caution against all attempts of estimating the divine works and dispensations by the measures of human reason. The vastness of the world’s extent is found to be so prodigious, that it would exceed the belief not only of the vulgar, but of the greatest philosopher, if undoubted experiments did not assure us of the truth of it.’

In fact, gravitation only appeared inexplicable because Aristotelian science denied action at a distance. For the Aristotelians, for something to have an effect it had to be in physical contact with whatever it acted upon. This was not the case in Platonic philosophy, which considered that things could operate through a system of similarity and attraction/ repulsion. This, however, was associated with the occult. It was, for example, the explanation for the supposed effect the stars had on the creatures on Earth in astrology. Newton himself was very much aware how his theory contradicted Aristotelian notions of causation, and had indeed drawn his inspiration for the theory from Neoplatonism.

Modern physicists consider that gravitation is caused by sub-atomic particles of force called gravitons. In Star Trek, gravitons are the force used by the space ships’ tractor beams to tow other space ships and other objects. No gravitons have so far been detected. Some cosmologists believe that they are unnecessary to explain gravity. These scientists instead consider that gravity is the effect mass has when it bends the fabric of space-time, as described in Einstein’s Theory of Relativity. Whatever the precise explanation of gravity may turn out to be, one can agree with Jenkin that although its cause may have a rational explanation, that explanation in its turn demonstrates the wonderful construction of the universe by the Almighty.

Medieval Kingdoms of Infinite Space

April 27, 2013

There’s a little bit in an episode of Star Trek: The Next Generation, where Q says to Picard ‘What is it your beloved Shakespeare said? ”All the Galaxy’s a stage, and all its people only players’.
‘World’, Picard corrects him. ‘It’s world, Q’.
‘Well,’ retorts Q sniffily, ‘it’s what he would have put.’ Yet a century before Shakespeare, European Natural Philosophers were discussing the possibility of other worlds and extraterrestrial life.

Medieval philosophy and science was based very much on Aristotle. Aristotle believed gravity was a universal force produced by each element seeking its own place in the universe. Thus, things fall to Earth because Earth is their natural place. He ruled out the possibility that there were other worlds, because he felt that if there were, this would mean there was no natural place. Other ancient Greek philosophers, such as the Pythagoreans and Plato, had a different view of gravity. According to Joannes Stobaeus, writing in the 5th century AD, Heraclides of Pontus and the Pythagoreans believed that each star was a world consisting of an earth surrounded by air. Plato in the Timaeus believed that objects naturally sought to rejoin their own kind, in whichever world it was situated. During the fifteenth century there was a revival of interest in Platonism. The leading churchmen Nicole of Oresme and Nicholas of Cusa both believed that gravity was a local phenomenon, and that each star was a centre of attraction holding its constituent parts together through gravity. Nicholas of Cusa went even further, and believed that every star was inhabited, just like Earth. There’s a myth that it was the belief in an infinite number of inhabited worlds which led to the Church burning Giordano Bruno for heresy. It wasn’t. The Church did not have an issue with that. It was Bruno’s pantheism and belief in magic which led to his condemnaiton by the ecclesiastical authorities.

Nicholas of Cusa went even further than believing the universe was inhabited. He considered that while the universe was not infinite, it had no boundaries, and thus had no centre, therefore denying that the Earth was at the centre of the universe. It’s a profoundly modern conception of the nature of the cosmos, even if he shared the medieval belief that each world was surrounded by rings, each ring composed of one of the four elements. It makes you wonder what someone like Nicholas of Cusa would have produced if, rather than writing tale of Romance, they had written Science Fiction instead.


A.C. Crombie, Augustine to Galileo 2: Science in the Later Middle Ages and Early Modern Times 13th – 17th Century (Harmondsworth: Penguin 1959).