Astronomy Weekend Success | Captain Slogg | New Courses in Physics and Astronomy | Lost Horizon | Newton and the Vortices | Sizing The Earth From Your Garden | Jim Crutchfield - Theoretical Physicist | Quanta and Continuum | Evidence of Black Holes

# Astronomy Weekend Success

*CAPTAIN SLOGG* *by Fizz*

## New Courses in Physics and Astronomy

#### by Dr Stuart Freake

# LOST HORIZON

#### by Brian Steadman

# Newton and the Vortices

#### by Fiona Vincent

# Sizing The Earth From Your Garden

#### by Ray Ash

### Leading Lights of Contemporary Science

## Jim Crutchfield - Theoretical Physicist

#### by Max Little

### QUANTA AND CONTINUUM

### Observational Evidence of Black Holes

*Satisfied FUSION astronomers and their tutors from UCL Mill Hill and the OU.*

FUSION's first Weekend Practical Event - aimed primarily at students of *S381 - The Energetic Universe* - was held on Saturday, 22nd March at the University of London Observatory in Mill Hill, and was a resounding success.

We began with a tour of the observatory and its five telescopes - one of which was trained on the Sun, enabling us to see some wonderful arc-shaped prominences and flares. It's all very well learning about these things on *S281* (or *S282* as it's now called) and even seeing pictures of them; but to see them for real is a truly mind-blowing experience - or at least it was for me. Then it was down to work for the afternoon on various "here's one I prepared earlier" daytime experiments based on data taken previously at the Observatory and elsewhere.

Computers featured heavily in these experiments, but the data was real enough. The experiments are an essential part of the course for students at universities like *UCL* - real time observing is only one element of the practical component of an astronomy or astrophysics degree. My own experiment was an investigation of the equivalent widths of H* lines in the spectra of various stars. It complemented the *S381* syllabus very nicely, with plenty of spreadsheet work and references to the Saha and Boltzmann Equations. I didn't finish it on the night (that's one of the hazards of being the organiser!) but sat down on Easter Monday to complete the calculations and was decidedly chuffed to find that at least some of my measured points fell somewhere near the theoretical graph of equivalent width against spectral class! Others did experiments based on how a CCD camera works, observation of prints from the *Palomar Observatory Sky Survey*, and the construction of a Hertzsprung-Russell diagram for an open cluster.

After a delicious buffet tea it was time to open up the domes and do some real observing. Although this was the climax of the whole event, I had not allowed myself to assume it would really happen, as only one in four nights is clear in Mill Hill. But the gods were smiling on us for once and it was a brilliantly clear night. We were allocated to the telescopes in groups of three. My group encountered some teething problems with our telescope - it had recently been modified by insertion of a movable mirror to permit naked-eye alignment before switching over to the CCD camera, but light kept leaking in from somewhere - but that was all part of the educational experience as far as I was concerned, and after all I did (just) achieve my ambition of actually seeing a galaxy!

A small group of us stayed over at a nearby youth hostel, and rounded off the weekend with a walk on Hampstead Heath, a tour of University College (courtesy of *UCL* undergraduates Laura Pickard and Mischa Stocklin, and Dr Mike Forshaw) and lunch at the British Museum.

Thanks to Nexus, the Royal Astronomical Society and the OU Department of Physics and Astronomy for generous donations towards the cost of the event, to Dr Mike Dworetsky and staff at the Observatory, and to all the *OU* students who came along and made it all possible. Feedback from those attending suggests the others enjoyed it as much as I did, give or take the odd bit of warm clothing.

We hope to make this an annual event, so watch out for an announcement in a future newsletter!

*Jim Grozier.*

"Go away and think more radically about proposals for new courses!" That was the message from Steve Swithenby, Dean of Science when the Faculty considered proposals for new and revised courses for 2006. The reason is clear: the *OU* is not meeting its targets for student numbers and so the Higher Education Funding Council is likely to claw back part of the *OU's* grant. To restore the grant we need to attract more students - and that means producing different types of courses that appeal to students who aren't currently studying with the *OU*. Simply producing more of the same types of physics and astronomy courses won't do the trick - they would provide more choice for students, but we would end up with fewer students per course and consequent reductions in 'efficiency'. Even attracting additional students to physics and astronomy courses from other areas of science or from other faculties doesn't help the *OU* as a whole. We need to open up 'new markets' for courses.

Before thinking about how we might do that, let's briefly look at where we stand now with physics and astronomy at the *OU*. The table below shows the current array of courses, with the two new courses planned for 2004 shown in italic.

**Level 1**

S103 Discovering Science

SXR103 Practising Science

S151 Mathematics for Scientists

S194 Introducing Astronomy

S196 Planets: An Introduction

S197 How the Universe works

MST121 Using Mathematics

**Level 2**

S207 The Physical World

SXR207 Physics by Experiment

S282 Astronomy

S283 Planetary Science*SXR208 Observing the Universe*

MS221 Exploring Mathematics

MST207 Mathematical Methods

**Level 3**

SM355 Quantum Mechanics

SMT356 Electromagnetism

S357 Space, Time and Cosmology

S381 The Energetic Universe

MXR355 Quantum Mechanics: Experiments, Applications and Simulations

SMXR356 Electromagnetism: Experiments, Applications and Simulations*SXP390 Project course*

MST322 Mathematical Methods and Fluid Mechanics

We're rewriting the *Electromagnetism* course for 2006 and plan to rewrite the *Quantum Mechanics* course for 2007 (we had intended the new courses to come out in 2004 and 2005, but the *OU's* financial situation caused a two-year postponement). We'd also like to revise the cosmology block of *S357* for 2005/6. If all of this goes ahead, then in 2007 all of our physics and astronomy courses will date from 2000 or later. In addition, *MST207* is currently being revised, with a separate residential school course, and *MST322* will soon be replaced by a new theoretical physics course.

Now this array of courses provides more than enough points for a named degree in Physical Science, or in Natural Sciences with Physics. So if we add courses, then we need to be aiming at different markets, and we are probably talking about students who wouldn't necessarily contemplate doing a degree in physics or astronomy. They may want to study one or two courses for professional development. They may want something that provides some of the physics underpinning for an area in which they have a general interest.

Suggested new courses include:

**Applications of computing in physics/science.** This would develop skills with use of computer algebra and mathematical modelling software in the context of investigating real physics problems.

**'The digital Universe'** - a course at level 1 or 2 where the computer takes the pain out of the mathematics by providing simulations, but there is a strong emphasis on the physics principles underpinning the simulations.

**The science of science fiction.**

**History/philosophy of science/physics/astronomy** - written to appeal to arts students as well as scientists.

**The science of business,** or the physics of business. This would teach modelling and analysis skills that are normally taught in a science context, and highlight parallels between business and science problems where a scientific approach can assist in developing a business solution. Probably at level 1.

**Forensic science,** or science and law. This could provide the science required to understand modern forensic techniques, and could be used for professional development of people in the legal profession.

**Physics for health science.** There may be a need to teach some basic physics to health service workers. This could fit in with the *OU's* developing links with the NHS.

**Physics (or science) for archaeology.** This could appeal to amateur archaeologists, English Heritage members, the audience for TV programmes related to archaeology.

**Physics of sport.**

**Space science.** A level 3 course that could discuss propulsion systems, orbits, communications, measuring techniques, etc.

**Environmental science** - possible areas include weather, or climate change.

So far I've only mentioned undergraduate courses. What about the Science MSc programme? At present the module with the largest physics content is *S809 Medical Imaging,* which is essentially a medical physics course. There is a proposal for another medical physics module, on radiotherapy, and if these two modules were combined with the project module it could provide an attractive medical physics MSc. There is also a proposal to produce a couple of astronomy and planetary science modules; one of these would be concerned with observational astronomy and the other with life in the Universe. One advantage of augmenting the MSc programme is that a large proportion of the students are new to the University, and also that it provides a route for *OU* graduates to continue their studies.

So what sort of physics and astronomy courses do you think that we should be producing in the next few years? What courses would YOU like to study? What courses would attract new students to the *OU*? We'd welcome your views - either by email *(
This e-mail address is being protected from spambots. You need JavaScript enabled to view it
)* or regular mail (Dr Stuart Freake, Director of Teaching, Department of Physics and Astronomy, Walton Hall, Milton Keynes MK7 6AA).

Everybody, even the non-scientist, has heard of black holes. *OU* students who have done *S357 - Space, Time and Cosmology, *should have a good idea of what a black hole is - an infinitely compressed mass of stuff (the *singularity*) surrounded by an *event horizon* from which nothing, not even light, can escape. A great amount of theoretical work has been done on black holes, and astronomical observations seem to confirm their physical existence. The solution of Einstein's field equations which describes black holes was discovered, according to the text books, by Karl Schwarzschild.

Schwarzschild was in the German army on the eastern front in 1915 where he contracted a fatal disease. His two papers on relativity were written during the subsequent period of illness. He died on 11 May 1916. Any physicist reading Schwarzschild's papers today will be amazed to find no mention of what we now call black holes. The first paper (January 1916) describes spacetime surrounding a spherical mass, and the second (February 1916) describes the mass itself. There is not the slightest whiff of an event horizon and its bizarre properties. At the time, nobody expected matter to collapse to a singularity but even if the matter in Schwarzschild's solution does collapse, there is still no event horizon. There is just a *naked* central singularity surrounded by a vacuum spacetime. So where did the theory of black holes and event horizons come from?

Schwarzschild's vacuum solution was the first exact solution of Einstein's equations and he sent it to Einstein. The latter replied "I have read your paper with the greatest interest. I had not expected that one could formulate the exact solution of the problem so simply." To formulate his solution, guided by physical considerations, Schwarzschild naturally chose to use spherical polar coordinates. It turned out that the radial coordinate was an unknown function *f(r)*, *r* being the usual radial coordinate in spherical polars. There was also an unavoidable discontinuity in the metric functions of the solution and the choice of *f(r)* amounted to deciding where in space this discontinuity should appear. Schwarzschild sensibly chose that the discontinuity should coincide with the coordinate origin so that the metric functions were continuous for all *r *>* 0*. That is why there is no event horizon in his solution.

In January 1917, the illustrious mathematician Hilbert published a paper on the subject. In reviewing Schwarzschild's work, he declared that Schwarzschild's choice of *f(r)* was not to be recommended and that it was simpler to put *f(r) = r*. Simpler maybe, but now the discontinuity formed a spherical surface at *r = *2G*m/c*^{2} (where G is the gravitational constant, *c* the speed of light and *m* the mass of the black hole) and the famous event horizon was born. Hilbert was probably unconcerned, thinking that the discontinuity would be covered by the spherical mass and not appear in the vacuum part of the solution. However, work in the 1930s, especially that of Oppenheimer and Snyder, concluded that a sufficiently large non-rotating mass must collapse to reveal the event horizon. Ironically, the event horizon is often said to be located at the Schwarzschild radius!

So which solution is better, Schwarzschild's or Hilbert's? Mathematically, both are acceptable but physically Schwarzschild's solution is by far the simpler, and for more reasons than are pursued here. Current observations supporting the existence of black holes cannot distinguish between them. At astronomical distances, the effects of matter falling into a black hole and matter falling into a naked singularity will look the same. Of course, 99% of the physics community and writers of text books in General Relativity believe in black holes, and they may be right, but total consensus in science can be an unhealthy situation. One recent heretical view is in the paper *Reconsidering Schwarzschild's original solution* by Antoci and Liebscher (Astron. Nachr. 322 (2001) 3, 137-142). It can be found on Antoci's website at the University of Pavia (http://matsci.unipv.it/persons/antoci), together with translations of Schwarzschild's papers.

For years there have been a few black hole dissenters, not writers in green ink, but serious physicists. I'll end with a little personal dissent! Most accounts of black holes say that you can't tell when you fall through an event horizon, that nothing remarkable happens there. They also say that when matter reaches a certain density, no known force can stop it collapsing to a singularity. During research for my PhD I found that you can detect the event horizon as you fall through it. I didn't know at the time that this had already been discovered by Karlhede, Lindstrom and Aman in 1981, and it is still a little-known fact today. I also studied the rotating dust cloud, discovered to be a solution of Einstein's equations by Bonnor in 1977. Density of the dust increases towards the centre of the cloud, tending to infinity as the centre is approached. In other words the density of the dust can be arbitrarily large. What mysterious exotic force prevents collapse of the rotating dust cloud? Rotation!

Today we take it for granted that the movement of the planets around the Sun is almost entirely explained by Isaac Newton's famous law of gravity. (Only the motion of Mercury's perihelion is not quite as Newtonian physics would predict; the strong gravitational field so close to the Sun means that a tiny relativistic correction is needed.) But Newton's discoveries were not universally accepted by his contemporaries.

**Kepler - the problem**

In 1609, at the age of 38, Johannes Kepler published his *Astronomia nova*, in which he announced his first two laws of planetary motion (see below); the third law followed in 1619. After years of effort, Kepler had at last succeeded in finding simple mathematical expressions to describe the observed motions of the planets. But he was still unable to explain them. Kepler could see that the Sun played a crucial role in the motions of the planets, but he could only postulate that it exerted some mysterious "magnetic" force on them.

**Descartes - the philosopher**

Kepler was an astronomer and a mathematician; he used mathematics as the obvious tool for investigating the natural world. His younger contemporary René Descartes was a philosopher, and for him mathematics was the key to building a complete system of human philosophy.

Descartes felt that human knowledge so far was a makeshift construction, like a building designed by many different architects. With no trace of false modesty, he proposed to redesign it entirely by his own efforts. He started with the basic premise "Cogito, ergo sum" (I think, therefore I am); from this, he aimed to work through metaphysics to physics, and thence to all other areas of knowledge, which he grouped broadly into medicine, mechanics or morals.

Some of Descartes' physical theories appeared in his *Principles of Philosophy* in 1644. To Descartes, there was no such thing as empty space. In his system, the universe was filled with a swirling fluid of tiny invisible particles. The planets and their moons were spun around in whirlpools or vortices in this fluid, which thus accounted for all their rotating and orbiting motions.

This theory explained the broad features of the Solar System: that the planets all orbit in the same direction in approximately the same plane. Descartes apparently hadn't read about Kepler's three laws, and so he didn't have to consider whether his vortices could reproduce in detail the actual motions of the heavenly bodies.

**Newton - the physicist**

It was a generation later that Isaac Newton provided the theoretical explanation for Kepler's laws. An unloved child, who grew into an unloving and unlovable man, he was nevertheless recognised by all his contemporaries as a mathematical genius. As a student at Cambridge he studied mathematics largely on his own initiative, though he did attend lectures by Isaac Barrow. By his early twenties he was producing original work on infinite series, and following a line of thought that would eventually lead him to the invention of the calculus.

During a year at home enforced by the Great Plague, Newton made his famous observation of a falling apple, and hypothesised that the Moon was held in orbit round the Earth by the same force of attraction. However, when he checked this by calculation, the figures didn't tally (because the accepted value for the mass of the Earth was incorrect) - so he let the matter drop.

Newton succeeded Barrow as professor of mathematics at Cambridge; much of his early work there was on optics. However, in the late 1670's the members of the newly-formed Royal Society were very interested in celestial mechanics. Robert Hooke, Christopher Wren and Edmond Halley were all studying Kepler's laws, and had deduced that the planets must be held by an attractive, inverse-square force centred on the Sun. But none of them could prove this mathematically.

In 1684 Halley asked Newton for help; Newton's response was the manuscript *De Motu Corporum*, which solved the problem completely. His interest re-kindled, Newton spent the next two years working intensively on mechanics. After much persuasion by the diplomatic Halley, he eventually published his results as the three books of *Philosophiae Naturalis Principia Mathematica* in 1686-7.

In this massive work, which we now call simply the *Principia*, Newton created an entirely new system of dynamics, and introduced the principle of universal gravitation. In modern terminology, he asserted that any two bodies attract each other with a force that is proportional to the product of their masses, and inversely proportional to the square of the distance between them.

For Newton, the whole of physics rested on mathematics. He demonstrated how the theory of gravity leads inevitably to Kepler's three laws. It also accounts for the behaviour of comets, the motion of the Moon (though that was not completely resolved for some years) and the shape of the Earth.

**The Debate**

Newton was well aware of Descartes' theory of vortices - and also of its shortcomings. He pointed out that Kepler's second law required that "the periodic times of the several parts of the vortices should observe the square of their distances from the Sun"; but for Kepler's third law to hold true, "the periodic times of the parts of the vortex ought to be as the 3/2th power of their distances." He also remarked that "comets are carried with very eccentric motions through all parts of the heavens indifferently, with a freedom which is incompatible with the notion of a vortex."

The theory of gravity, of course, explains all these motions accurately. In England especially, this work was hailed as a triumph. But many European readers had difficulty in accepting a mysterious force acting across the vast distances of empty space; Christian Huygens called the idea "absurd", and Gottfried Leibniz condemned it as "occult".

For the Cartesians - the followers of Descartes - everything in a rational universe had to be pushed or pulled by forces acting in direct contact; it seemed to them that "the Newtonians retained the astrological emanations and astral forces of the mediaeval universe" (David Harrison, Darkness at Night).

Nevertheless, Newtonianism became quite fashionable in France; the writer Voltaire learned about it in the salon of Mme. du Châtelet. When he visited England in 1734, Voltaire wrote: "A Frenchman arriving in London finds things very different, in natural science as in everything else. He has left the world full, he finds it empty. In Paris they see the universe as composed of vortices of subtle matter, in London they see nothing of the kind... For your Cartesians everything is moved by an impulsion you don't really understand; for Mr Newton it is by gravitation, the cause of which is hardly better known."

The theory of gravity was just one of Newton's many achievements, but he was always unwilling to publish his results, and at the same time jealous for the credit of discovering them. For example, Newton certainly developed the technique of the calculus some years before Leibniz discovered it independently, but Leibniz published his version first. The argument between them, fuelled partly by nationalism, raged for many years.

In the same way, although Newton did not actually name Descartes when he attacked the hypothesis of vortices, it is clear that he regarded the man as a personal rival. As early as 1676, he had written to Hooke with attempted modesty, "If I have seen farther than Descartes, it is because I have stood on the shoulders of giants."

**The Debate Resolved**

Despite the philosophical difficulty of "action at a distance", and despite the fact that neither Newton nor anyone else could explain how gravity actually works, it became clear over the following decades that Newton's theory of gravity explained the natural world in a way that no other theory could.

Some aspects, like the motion of the Moon, were difficult to analyse completely: in the 1740's, Leonhard Euler was still struggling with this, and wondering if vortices were needed to explain it. The problem is that the Moon is attracted almost equally by the Earth and by the Sun; it's not enough to consider the Earth-Moon system alone, or to treat the Sun's influence as a minor perturbation.

In fact there is no exact mathematical solution for such a "three- body problem". But eventually ways were found of approximating the Moon's motion to any required degree of accuracy. Descartes' vortices were finally laid to rest.

**Kepler's Three Laws (in modern terminology)**

1. The planets move in ellipses, with the Sun at one focus.

2. The orbital speed of a planet varies such that the radius vector sweeps out equal areas in equal times.

3. The squares of the orbital periods of the planets are proportional to the cubes of the semi-major axes of their orbits.

*Originally printed in "Scottish Astronomers' Group Magazine", Winter 1999.*

This is an experiment which any *FUSION* member can do at home on Sunday 22 June. By compiling all our results we can hope to arrive at an accurate value for the size of the earth using simple calculations. This will be a variation on an original experiment by the Greek mathematician Eratosthenes. Our measurements will need to be simultaneous like his were.

**Historical Overview**

Eratosthenes taught in Alexandria in 200 BC. He learned that at the summer solstice the sun was exactly overhead at a place called Syene where its rays touched the bottom of a deep well. Simultaneously the sun was 7 1/5 degrees south of the zenith at Alexandria. He knew that the exact distance from Syene to Alexandria was 5,000 stadia and from simple mathematics was able to calculate the earth's size to within 5%. Eratosthenes correctly assumed that Alexandria was 7 1/5 degrees of latitude north of Syene

**Explanation of the Basic Maths**

The angular difference between two places' latitudes is proportional to their distance apart in a north-south direction. In other words the angle subtended at the centre of a circle is proportional to its arc. The difference in latitude between two places is given by the Sun's angle, after allowing for longitude. Circumference of earth = 360/7.2 x 5,000 stadia = 250,000 stadia or 24,660 miles approximately.

**How to Take a Reading on Sunday 22 June 2003**

Choose a vertical object like a shed, fence post or something you can easily measure using a flexible rule. Measure its vertical height and the length of its shadow on the ground at regular intervals between 11am and 3pm. Then divide its height by the minimum shadow length. Use the Tan^{-1} button on your scientific calculator to get the Sun's angle. This is the angle we start with (it equals 113.5 degrees minus your latitude). That is all you need to do; though as we are all good, conscientious physicists, it would be nice if you could include an estimate of the errors in your measurements (see below). Using a good road atlas (or GPS receiver), find your distance north/south and east/west of Greenwich and send your results to *FUSION*. The results will be compiled and published in the next Newsletter. If it's overcast on 22 June we will try again on 29 June at the same time. Good luck!

**Estimation of Errors**

(Δθ)^{2} = (*l*Δ*h*/(*l*^{2} + *h*^{2}))^{2} + (*h*Δ*l*/(*l*^{2} + *h*^{2}))^{2} = (Δ*h*)^{2}/(*l*^{2} + *h*^{2}) if Δ*l* = Δ*h*

Crutchfield received a BA in physics and mathematics from the University of California, 1979 and his PhD from the same university in 1983. Since 1985, up until he began work at the Santa Fe Institute in 1997, he worked in the physics department at the University of California. He started his career looking at some unsolved physical problems such as "Unexplained Helium Film Effect with Dielectric Resonators", but the overall theme that ran through this work were ideas drawn from statistical physics and the emerging field of "complex systems theory".

This field attempts to fully characterise mathematical laws that describe the behaviour of physical systems that don't just simply swing like pendulums, vibrate like clamped strings or spin like perfect planets in idealised orbits - nearly all systems encountered in everyday life! A major observation of this field is that systems that on the face of it are very simple can paradoxically exhibit a bewildering range of hard to follow trajectories.

For example, a magnetic pendulum which is free to swing hanging over two other fixed magnets can rest above either magnet: there are two possible equilibrium positions. Disturbed from rest equidistant from the two magnets, the pendulum quickly begins an extremely complicated motion, and eventually damps to rest over one of the magnets. But which one? The motion is Newtonian, but errors in measurement and the precise initial rod position are quickly amplified to make the motion and final position unpredictable.

**Unpredictability**

The subject of Crutchfield's PhD dissertation was the application of information theory to the study of two types of non-linear dynamical systems like the example above: those without extrinsically coupled random motion (noise) and those with. The first type of system can be called "deterministic", because all future states can be generated only from knowledge of any preceding state. The second class of systems cannot be predicted, because the noise introduced from the outside is amplified by the system leading to wildly differing future behaviour. His analysis showed that even in the unpredictably noisy system, by considering how the system's dynamics change with scale, fundamental aspects of the behaviour can be obtained in one overarching framework - a fractal information measure.

**Experimental mathematics**

Certainly all the systems that he considered in his PhD can be set up very easily, but still the complexity of such motion becomes quickly overwhelming unless powerful tools can be brought to bear on the problem. In his 1985 paper, *Experimental Mathematics: The Role of Computation in Nonlinear Science*, he wrote about the sorts of dedicated computer hardware and software that might be needed to aid the exploration of the possible trajectories generated by non-linear mathematical models.

Published by the Association of Computing Machinery, this paper is an early example of how computer science is gaining importance in mathematics, previously considered to be a purely "deductive" art. By setting up algorithms in hardware or software to emulate the trajectory of a chaotic system, the dynamical evolution can be explored under complete control, aiding the discovery of mathematical rules.

By the mid 1990's, Crutchfield had worked on an interesting array of problems in complex physics, and had published a series of papers on bridging the gap between the three theoretical domains of information, dynamical systems and computation. In his paper *Complexity: Order contra Chaos*, he describes how to define a complex process: as one that is not simply purely random or purely repetitive, but combines aspects of both novelty and familiarity.

**Artificial science?**

The stated aim of Crutchfield's latest research at the Santa Fe Institute, the Computational Mechanics Group, is to answer the question: "How can we detect and then quantify structure in natural processes?" They imply that structure can be captured by computational algorithms. For example, in *Pattern Discovery in Time Series* for the Journal of Machine Learning Research an algorithm is described that, given measurements of trajectories can obtain a simple representation in terms of "causal states".

This is valuable in that it requires no a priori specification of its structure - this is inferred entirely from the measurements themselves. This means that it contains the minimum number of assumptions necessary to model the trajectory, and as such might be termed a "minimal axiomatic system". It is not a far flight of fancy to imagine that this could, in the future, allow a purely automatic search for mathematical laws, given access to good measurements!

For more information about this interesting scientist who has pursued many varied topics including work on condensed matter physics, fluid dynamics, astrophysics, evolution and theoretical neurobiology, see www.santafe.edu/~chaos/.*FUSION astronomers at the Radcliffe 24-inch twin refractor.*

*Robert Palmer hoping for clear skies while working with the Palomar Sky Survey!*

*Yet more work with the Palomar Sky Survey.*

*Fred Muirhead and that Sky Survey!*

*Sunday morning survivors on Hampstead Heath.*

**Peter Napier Prizes for 2002**

A few years ago, the Physics and Astronomy Department received a legacy from Peter Napier, an *OU* graduate who had studied many of our physics courses. The Department decided to invest the money and use the income to fund two annual student prizes of £50 book tokens. One prize goes to the student with the best performance in *S207 The Physical World* and the other goes to the student with the best performance in one of the Level 3 physics or astronomy courses.

Like the National Lottery, prize winners have the option of declining publicity, and the 2002 winner for *S207* has exercised this option. So all I can say is that the student had previously obtained distinctions in *S267* *How the Earth Works, MST121 Using Mathematics* and *MS221* *Exploring Mathematics.*

The Level 3 prize has been awarded to Fenella Jackson for her superb performance on *S381* *The Energetic Universe*. This follows distinctions in both *SM355 Quantum Mechanics* and *SMT356 Electromagnetism*. In her letter accepting the prize, Fenella wrote about her experience studying with the *OU*:

"I started doing *OU* courses about ten years ago, when I gave up work to start a family. I started with the science foundation course which was brilliant, and now do a 30 point course each year. We've now four children, so finding the time to study - and staying awake while I do - has been a struggle, but the courses have been a real life-line to me, off-setting the mind-numbing tedium of some aspects of motherhood (nappies, colds, reading the same picture book 5,000 times, scraping the baby food off the walls...) And it even equipped me to answer some of their questions (Why is the sky blue? Why do rainbows go away? What is a black hole?...) And I can criticize science fiction programmes, and be knowledgeable in museums - so it's all really useful stuff!

I've done some earth-science courses, but seem to have gravitated towards physics and astronomy. I just wish there were (a) more courses left to do, (b) some courses taking the material even further (taught 4th level courses?) and (c) that I could remember something about the courses I took more than a year ago! At least the last point means that I can always go around again!"

So congratulations to both students on their brilliant performances!

*Stuart Freake*

**Can you swell the ranks?**

Past experience has shown that Summer Schools (and Revision Weekends) are ideal places to sign up new *FUSION* members. Would you like to promote *FUSION* membership at these events? All you have to do is take a clutch of *FUSION* leaflets and application forms with you - and this is the hard bit - make yourself known to your fellow students. The best way to do this is to ask one of the tutors to introduce you before a tutorial or lecture. You can then say a few words about the benefits of joining *FUSION*. Leaving forms and leaflets on a table en route to the dining hall can be very effective too. Let us know how you get on! Forms and leaflets can downloaded from our web site or obtained by writing to us at the address below.

**When can I start my PhD?**

Several members have asked if they have to wait until the end of the year, when they get their final course result(s), before being allowed to start (or even apply for) a PhD studentship. The answer depends on the attitude of the University, your funding council and the *OU*. If you AND someone at the *OU* are confident that you will get the final required course credit, the University may let you start in September providing your funding council offers a studentship pending the award of your *OU* degree at the end of the year.

**Letters to the Editor**

In addition to full blown articles, we would like to encourage members to contribute comments and ideas to a *Letters to the Editor* section. These can be emailed to *
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* or posted to the address on page 8.

**Thank you Peter!**

The *FUSION* Committee wish to thank Peter Fletcher for auditing our accounts to OUSA's satisfaction.

This Hubble Space Telescope image contains three main features: The outer white area is the core or centre of the galaxy NGC4261. Inside the core there is a brown spiral-shaped disk. It weighs 100,000 times the mass of the Sun. Because it is rotating the radii and speed of its constituents can be measured, and hence the weight of the object at the centre calculated. This object is around the size of the solar system, but weighs 1.2 x 10^{9} solar masses. This means that gravity is about one million times as strong as that of the Sun. Almost certainly this object is a black hole.

Newsletter published by *Fusion - The Open University Physics Society*, 92a Springfield Road, Brighton, East Sussex BN1 6DE, UK.*Please note that the views expressed in this newsletter do not necessarily reflect the views of the Society or editor.*

Articles for inclusion in the next issue should be sent to the address above or emailed to
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.

Last Updated (Wednesday, 13 March 2013 19:34)

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