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A recent look at the UK University Admissions web page, www.ucas.ac.uk, showed there to be no fewer than 754 physics courses offered at 57 universities. The numbers give an exaggerated estimate of the profusion of courses as most universities offer both three year and four year degrees, which count as separate courses. Even so, this means that, on average, each university is offering physics in about seven flavours from Physics with Administration to Physics and the Universe!

It is not difficult to find the reason for the amazing range of courses. Universities are increasingly short of funding and need to fill every available place. This is at a time when the number of students studying physics at post-16 level is falling and the number applying to go on to study physics at university level has fallen from 3139 in 1994 to only 2655 in 2000. Physics is seen by many teenagers as a difficult and complex course of study at university level. This, coupled with the fact that scientists are poorly paid, leads many students to consider non-physics courses.

One of the growth areas in physics courses has been the addition of Astronomy (47 courses), Astrophysics (30 courses) and, more recently, Space Science (44 courses). These are areas where students already have an ignited interest though the publicity associated with the Hubble Space Telescope and other space missions. When the Physics with Astrophysics course at Birmingham was started in 1980, only about six other UK universities offered any courses in astronomy or astrophysics. Now, nearly every university offers such a course in an attempt to attract increased numbers of students.

What happens when physics departments fail to attract enough students? A shortage of students is one of the main reasons why many physics departments are running with a financial deficit. In addition, physics courses with significant laboratory work are expensive to operate, both in terms of manpower and equipment. Often the government's unit of resource is inadequate. In the past, universities often subsidized such departments but, in the present financial climate, they are increasingly expecting departments to `balance their books'.

One solution would be to abolish laboratory work altogether. This would reduce the number of academic staff needed to teach the course and there would be no need for funding for laboratory equipment or technical support. This has already happened in some branches of engineering where Health and Safety has decreed that high voltages and large motors are too dangerous to be operated by undergraduates. In this case, the `experimental' work is done by simulation on a PC.

A less drastic solution is the design study. In this, students work in a group and use material provided and that available on the World Wide Web to produce a detailed design, for example, a space mission. This is all well and good and may provide the opportunity to use their physics knowledge to learn the management skills of planning, group working and presentation, but the reality is that design studies never fail, whereas real experiments all too often do so. I do hope that UK funding of universities does not lead down the road of Physics with no Laboratory.

Universities in the UK are certainly short of funding, but there may be some room for optimism. The government has signalled the possibility of `top-up fees', which enables higher fees to be charged for certain courses. The Science Research Investment Fund (SRIF) has allowed universities to improve facilities to allow them to compete on a world scale. In science in particular, students are attracted to universities by their research programmes, but I hope that the teaching ideas for astronomy and space science included in this issue of European Journal of Physics will be used by other universities around the world to attract able students into the exciting world of science.

We describe an unusual undergraduate course that has been running successfully for over ten years and is built around a two-week field trip to Tenerife. The purpose of the visit is twofold: firstly to spend a week working in collaboration with students from the Universidad de La Laguna and secondly to spend a week at the Observatario del Teide carrying out astronomical observations. This paper is concerned primarily with the second of these two activities.

This paper describes how the design of a scientific satellite can be used to provide both a stimulating and effective subject for a physics based group study. The group study divides the satellite into distinct subsystems and small teams of two or three students carry out the detailed design of each subsystem. The aim is to produce a complete satellite system design along with the choice of launch vehicle, orbit and communications system so that all the mission requirements can be met. An important feature of the group study is that it is a student led activity with staff acting as mentors. The development of key skills and important learning outcomes from the group study is discussed along with the method for assessment, structuring and resourcing the study.

We describe an undergraduate experiment that can be used to place the Sun in context with the properties of our nearest stellar neighbours. Using stars selected on the basis of their trigonometric parallaxes and spreadsheet software, the Hertzsprung–Russell diagram and luminosity function are constructed for stars within 16 pc, showing that the Sun is at least 25 times more luminous and 2.5 times more massive than a median field star. The experiment serves as an excellent means of practising transferable skills and introduces the concepts of selection effects and systematic bias in astronomical measurements. The sample of nearby stars is demonstrably incomplete. The missing stars tend to be intrinsically faint, leading to an overestimate of the median stellar luminosity.

The aim of this course is to provide direct experience of collaboration with other European astronomy/space science students and to gain an insight into the establishment of ESA space science programmes. The first half of the course takes place in Southampton. The Southampton students work as a team to track a past ESA space science mission from initial conception through to final realization and operations. This is achieved through the study of the high quality documentation available in the form of ESA reports. Each student has well defined responsibilities within the team. The second half of the course takes place in Tenerife, at the University of La Laguna. Again the students are expected to complete a team study of a space science mission. This time, however, there are important differences: the study teams are now international, approximately half Southampton and half University of La Laguna students; and this time they are expected to design a completely new space astronomy mission with clearly specified scientific objectives and operational constraints.

In this paper I describe a student-led group project undertaken as part of the physics and astrophysics degree at the University of Birmingham, on the subject of finding extrasolar planets. The group project involves exposing the student to exciting new astrophysics, in the context of a research-like environment. The main focus of the study is on the student group developing plans for an optimal strategy for a planet-finding programme. To do this, the students have to study the techniques involved in planet finding and parameters of the likely planets and synthesize a strategy from this. The subject of planet finding is scientifically very approachable and is a young and fast-moving field; consequently it gives rise to lively, varied and interesting project work.

Problem-based learning (PBL) can be integrated into the curriculum in many different ways. We compare three examples of PBL in undergraduate astrophysics programmes, and discuss the strengths and weaknesses of the various approaches.

ASTROLAB is a laboratory course for first year students on a physics and astrophysics degree programme at the University of Birmingham, UK. The laboratory runs for nine weeks with 5 h sessions. For the first seven weeks the students, working in pairs, perform experiments taken from a list of 20 experiments, with data obtained from observatories around the world. The data take the form of images, spectra and astronomical catalogues. In the final two weeks the students undertake a problem-based learning activity, a simple project in astronomy or astrophysics. The laboratory has been running for more than 20 years, and is judged as being very enjoyable and successful by students and staff.

OBSLAB is an observatory based laboratory for third year students on a physics and astrophysics degree programme at the University of Birmingham, UK. The students work in groups of four at the university observatory, where they obtain spectroscopic data using a computer controlled telescope and CCD detector. Much of the 72 h allocated to the project involves research, planning observations, data reduction and analysis and only about two nights are actually spent at the telescope. The laboratory has been running for more than 20 years and provides students with a unique opportunity to obtain their own real data.

A new derivation of the strength of Dirac's magnetic monopole is presented which does not require an explicit form of the magnetic induction in terms of g, the magnetic pole strength. The derivation essentially uses a modification of Faraday's law of induction and quantization of angular momentum.

The motion of a cylinder on an inclined plane, acted upon by a torque along its axis, is studied theoretically and experimentally. It is shown that the potential for the centre-of-mass exhibits the features of a fold catastrophe potential, the control parameter being related to the strength of the torque. This parameter determines whether or not the system experiences stable equilibrium positions. If it does, and depending on the initial conditions, it may perform oscillations around an equilibrium position, or it may cross a no-return point and roll down. A cylinder with a magnet inside, placed on an inclined plane in a region where a uniform magnetic field is present, is a real example of such a system. We constructed that system and report the data obtained in a set of experiments.

We consider the period of a simple pendulum in the gravitational field of the spherical Earth. Effectively, gravity is enhanced compared with the often used flat Earth (FE) approximation, such that the period of the pendulum is shortened. We discuss the FE approximation, and show when the corrections due to the spherical Earth may be of interest.

An inquiry among national experts on physics education research and teaching has been carried out using a questionnaire that deals with the organization of physics teacher training and the main tasks and research activities of professionals in physics education. The goal was to collect data on a European scale on physics teacher training at universities by professionals as well as on research activities by professionals in the field of physics education. Results are presented based on answers from 22 European countries.

The isotope ²²²Rn belongs to the ²³⁸U decay chain and can be obtained from natural mineral sources. The fact that radon is a gas and its radionuclide daughters get implanted on surrounding materials allows a set of different experiments in radiation physics. These experiments range from isotope decay time measurement to alpha, beta and gamma spectroscopy. To solve the radioactive decay chain equations, a simple iterative method is used as an alternative to the exact analytical solution.

Analogies in physics are unusual coincidences that can be very useful to solve problems and to clarify some theoretical concepts. Apart from their own curiosity, analogies are attractive tools because they reduce the abstraction of some complex phenomena in such a way that these can be understood by means of other phenomena closer to daily experience. Usually, two analogous systems share a common aspect, like the movement of particles or transport of matter. On account of this, the analogy presented is exceptional since the involved phenomena are a priori disjoined. The most important equation of capillarity, the Young–Laplace equation, has the same structure as the Gullstrand equation of geometrical optics, which relates the optic power of a thick lens to its geometry and the properties of the media.

This paper focuses on the early history of the fine-structure constant, largely the period until 1925. Contrary to what is generally assumed, speculations concerning the interdependence of the elementary electric charge and Planck's constant predated Arnold Sommerfeld's 1916 discussion of the dimensionless constant. This paper pays particular attention to a little known work from 1914 in which G N Lewis and E Q Adams derived what is effectively a numerical expression for the fine-structure constant.

Various properties of Keplerian orbits traced by satellites that are launched from one and the same spatial point with different initial velocities are discussed. Two families of elliptical orbits are investigated, namely the sets of orbits produced by a common direction but different magnitudes of the initial velocities, and by a common magnitude but various directions of the initial velocities. For the latter family, the envelope of all the orbits is found, which is the boundary of the spatial region occupied by the orbits.

W J M Rankine coined the term 'potential energy' 150 years ago. This paper examines why he introduced it, the evolution of its interpretation, and the extent to which it has stood the test of time.

The echo produced when a light 'pulse' from a stellar source (e.g. a nova or supernova) is reflected by circumstellar or interstellar material can appear as a luminous ring expanding at a rate that can be superluminal, i.e. having an apparent motion within the source, transverse to the observer's line of sight, at a speed greater than that of light. 'Light-echo optics' applied to the star RS Puppis and its nebula suggests that when nebular features in peripheral regions of circumstellar-shell images are observed, superluminal effects are not evident; however, such observations can give the stellar distance from the observer. Light-echo optics for an interstellar plane sheet, inclined to the observer's line of sight, can be applied to Nova GK Persei 1901 and SN 1987A, which show superluminal effects. For SN 1987A, an intense thermal x-ray source should be produced in AD 2003, when the advancing supernova ejecta interact with a circumstellar ring, 250 light days in radius: the arc-shaped x-ray image, while not actually a 'radiation echo', should expand at a superluminal rate for about 75 days from the time of its first appearance, and also for the same time before the completion of its 'circuit' around the ring.

The paper discusses the problem of the Lorentz contraction in accelerated systems, in the context of the special theory of relativity. Equal proper accelerations along different world lines are considered, showing the differences arising when the world lines correspond to physically connected or disconnected objects. In all cases the special theory of relativity proves to be completely self-consistent.