When the first edition of this book appeared in 1989, it offered no advice on observing with CCDs. Although CCD systems were available at the time to the professional community, they were very expensive, costing upwards of 70 000 US dollars. Today, CCDs are well within the reach of advanced amateur astronomers. A top-of-the-line system, the SBIG Research STL-11000M/CM, retails for about a sixth of that price, and it is far more capable than anything that was available in the 1980s.

With a CCD camera, your experience with variable stars will enter a whole new dimension. I realized this on a warm April night in 2004 when, as part of the spring meeting of the AAVSO, Wendee and I sponsored an evening observing session. I can't remember ever having so much fun. Two of the observers, including Tom Cragg visiting from Australia, were interested in checking on the state of T Pyxidis, one of their favorite recurrent novae. However, being pretty low in the southwest, the star was impossible to see visually with any of the available telescopes that evening.

Just a year earlier, our attempt to study T Pyx would have ended there. But on that night we used only a 15 cm reflector plus a Meade 416 CCD, and found the field a few degrees above the southwest horizon. Being thoroughly familiar with the field, Cragg had no trouble finding T Pyxidis and estimating its magnitude as 17.3! It was easy, productive, and fun.

Hyperbolic spacetimes possess a local causal structure described by a light cone at every point. The metric obeys the second-order Einstein equations containing one parameter: the velocity of light. This suggests that infinitesimal perturbations of the metric itself propagate along the very same light cones. We have a separation theorem: gravitational radiation propagates in curved spacetime according to a four-covariant wave-equation, in response to which the metric evolves in the tangent bundle. The result is independent of the foliation of spacetime in spacelike hypersurfaces.

Recall that general relativity embodies the Newtonian gravitational potential energy embedded in the metric tensor. Gravitational radiation will be a novel feature which, for finite amplitudes, hereby carries off energy and momentum. As with waves in any field theory, the energy-momentum transport scales with the frequency and amplitude squared.

Gravitational radiation is a spin-2wave, characterized by rotational symmetry over π in the plane orthogonal to the direction of propagation in the spin-classification of M. Fierz and W. Pauli [184]. The lowest-order mass-moment producing gravitational radiation, therefore, is the quadrupole moment. In this chapter, we derive the classical expressions for quadrupole emissions.

The topic of including astronomy as part of a general curriculum is first addressed by Nassim Seghouani in a poster entitled The project of teaching astronomy in Algeria. Seghouani mentions that there is currently no teaching of astronomy in Algeria despite a glorious history in this domain. The Algiers Observatory, constructed in 1890, participated since its creation in many international projects, and it was the leading observatory in the international project “Carte du Ciel.” Today, and since 1985, research in astronomy in Algeria has started up again, and the country has firmly decided to invest in this domain. New instruments have been acquired lately, such as an 80-cm telescope. The introduction of astronomy and postgraduate astronomy courses is currently in progress, along with wider aspects attached to this project. The organization of summer schools as well as the introduction of astronomy teaching in secondary schools is also discussed.

Further global perspectives are provided by representatives from many of the countries created upon the dissolution of the former USSR, including a paper by Elchin S. Babayev. Babayev and his colleagues describe the current situation of astronomy education in Azerbaijan. Azerbaijan has a long history of contributing to astronomy, and has an under-utilized astronomical treasure in the Maragha Observatory, located in the south of Azerbaijan, originally established in the Middle Ages by astronomer Nasiruddin Tusi.

This part of the book contains stars that have not been described in earlier chapters. It is intended to help you plan an observing program by introducing you to a selection of interesting variable stars. By reading through these chapters, you should find some stars that you will enjoy watching. The finder charts are intended to help in finding the location of a variable star. Once you have decided on a program, I suggest that you visit the website www.aavso.org to see what charts are available for each star you choose. Be careful to plan in advance the best time and equipment for observing them. The order in which the different constellations are presented in each chapter represents a vague and somewhat arbitrary eastward movement across the sky.

For each star, I have included the range, period and a code that specifies level of difficulty:

1. – very easily found and estimated

2. – a good star for beginners

3. – some challenge, either in finding or in estimating

4. – quite difficult

5. – recommended only for advanced observers with larger instruments

Tables of the suggested variable stars, arranged by level of difficulty, appear at the end of each chapter in Part 3.

Different sources provide different values for maxima, minima, and ranges of many variable stars, especially those with uncertain variations. In most cases I have used the values given in the General Catalogue of Variable Stars by B. V. Kukarkin et al., Fourth Edition.

Unlike other topics in astronomy or education, there is very little research specifically on pre-service astronomy education. Perhaps it is because so few teachers are called upon to teach astronomy specifically, or because their astronomy teaching is peripheral to their main interest (e.g., general science at lower levels or physics at higher levels). Previous IAU meetings have had little information on this topic. The 1988 IAU Colloquium 105 on the Teaching of Astronomy (Pasachoff and Percy, 1990) had no papers on this topic.

The northern hemisphere nights at this time of year are short but busy, for there is always something to do.

We begin with the most prominent feature of the northern sky, the “summer triangle” of Vega, Deneb, and Altair. In and around this triangle are many fine variables, including SS Cygni, a dwarf nova whose bimonthly explosions have made it one of the most popular variable stars of all.

A good star with which to begin is Beta Lyrae, a star offering nightly variation, and the parallelogram of Lyra offers two additional stars that work well as comparison standards. Next you can move to Aquila, whose Eta provides changes over a slightly longer period. We then can check on our old friends X and g Herculis and RR Coronae Borealis.

At this time of year we can turn our sights to Corona Borealis, the crown of Ariadne where our friends R and T Coronae Borealis lurk in the evening sky. We also can enjoy some of the Crown's more traditional long-period variables, like W, whose striking red color helps in finding.

Cygnus offers so many variables that you could hardly begin to see them in a single season. The constellation's most famous variable is Chi, a star lying in the middle of the Swan's neck. This season also features Sagittarius, whose collection of over 2500 variable stars surely must contain something of interest to a beginner. And there is: RY Sgr is a star like R Cor Bor.

The conference on which this book is based focused on astronomy education in the schools, where our society passes on knowledge and understanding to the younger generation in a systematic and formal way. In the proceedings of an astronomy education conference held in Maryland in 1996, however, Andrew Fraknoi wrote as follows:

Astronomers, their institutions, and their organizations actively promote understanding of astronomy through “outreach” in all of these ways. In the USA, such outreach has recently been formalized by NASA's requirement that major projects have Education and Public Outreach (E/PO) activities.

Introduction

Whatever the country, in general few teachers are educated in astronomy during their university studies, astronomy being an optional subject. So in-service training of schoolteachers is necessary either because astronomy is in the school curriculum or because the teachers themselves are introducing some aspect of astronomy in their lessons.

The following points will be developed:

• the context in which this training is taking place;

• the methods used for such training, taking into consideration the fact that astronomy will be taught if the teachers feel confident.

Examples of in-service training are taken from the French educational system because it is applied to a large body of teachers, the French curriculum being a national one, and also because in-service training in astronomy started 25 years ago through the non-profit association CLEA (Comité de Liaison Enseignants Astronomes: Teacher-Astronomers Joint Committee), created in 1977 as a consequence of the Education Commission's “Teachers Day” during the Grenoble IAU General Assembly in 1976.

In-service training has to be undertaken in two directions: one that intends to give the necessary background in astronomy-astrophysics and the other that will give to the teachers themselves the possibility of developing pedagogical resources for their needs, not forgetting that schoolteachers are also active in semi-scholarly activities: clubs, educational projects.

General relativity endows spacetime with a causal structure described by observer-invariant light cones. This locally incorporates the theory of special relativity: the velocity of light is the same for all observers. Points inside a light cone are causally connected with its vertex, while points outside the same light cone are out-of-causal contact with its vertex. Light describes null-generators on the light cone. This simple structure suffices to capture the kinematic features of special relativity. We illustrate these ideas by looking at relativistic motion in the nearby quasar 3C273.

Lorentz transformations

Maxwell's equations describe the propagation of light in the form of electromagnetic waves. These equations are linear. The Michelson–Morley experiment[372] shows that the velocity of light is constant, independent of the state of the observer. Lorentz derived the commensurate linear transformation on the coordinates, which leaves Maxwell equations form-invariant. It will be appreciated that form invariance of Maxwell's equations implies invariance of the velocity of electromagnetic waves. This transformation was subsequently rederived by Einstein, based on the stipulation that the velocity of light is the same for any observer. It is non-Newtonian, in that it simultaneously transforms all four spacetime coordinates.

Variation of the Sun! For many years the AAVSO has had a section for observation of the Sun, the logic being the star around which we revolve is a variable. In a stretched sense this may be true, but if we were to observe the Sun as we watch other stars, from light years away, we would find it shining at a constant brightness, without any indication whatsoever of its 11-year cycle of variation that we see manifested in sunspot activity.

Whether we worship it, plan our lives by its schedule, tan ourselves by its light, bask in its warmth, or study it, the Sun is a star whose importance cannot be overstated. And when we observe it through our telescope, we learn much about the the churning, changing nature of the star around which our planet turns.

An amateur astronomer and pharmacist of Dassau, Germany, Heinrich Schwabe, discovered the Sun's “variation” in 1843 through his long series of meticulous observations of its activity. After buying a small telescope, he began to search for a planet inside Mercury's orbit, hoping to find it transiting the Sun's surface. This “Vulcan” idea still lives and, as late as 1982, infrared searches have attempted to find such a planet. It has not been found. Schwabe's serendipitous discovery was the 11-year sunspot cycle.

The most obvious solar feature is the sunspots, magnetic storms on the solar surface that appear dark because they are cooler than the rest of the surface.

Astronomy is deeply rooted in almost every culture, as a result of its practical applications and philosophical implications. Nowadays, we determine time, date, and direction from clocks, calendars, compasses, and global positioning system (GPS) signals from the sky. In earlier times, these were determined by direct observation of the sky. Even today, the Islamic month and new year are based on direct observation, not on a calendar prepared in advance. One of us (JRP) lives and teaches in the most multicultural city in the world - Toronto. There, a large fraction of students come from Asian cultures that set their calendar by the sun and/or moon. The other (JMP) comes from another multicultural city, New York, where the lunar Jewish calendar still resonates in a large fraction of the population. The Christian calendar also approved by and named after Pope Gregory XIII in 1582, now often called 1582 CER (Common Era) but formerly ad (Anno Domini) 1582, also has many astronomical connections, and students may be interested to learn about these.

The connection between astronomy and religion, of course, can be problematic. In Part V, we included creationism under the heading of pseudoscience. But astronomy and religion need not conflict. Our astronomical colleagues in the Vatican Observatory are both astronomers and Jesuits. Over the years, they have developed a deep understanding of the possible relationships between science and religion, while maintaining a first-class astronomy research program (and a major collection of meteorites). Nevertheless, many humans are deeply influenced by their belief and faith in their religions, as well as by their culture. Many issues can be introduced through the history of astronomy.

What do you see when you look through a telescope? Is it the mountains and valleys of a lunar highland, or perhaps a thinly veiled Jovian storm? Or do you prefer the ghostly light of the distant galaxies, island universes adrift in a sea of space and time? Perhaps you see the fluctuations of stars in our galaxy, stars of all ages whose nightly appearance changes according to some cosmic drumbeat whose rhythm we try to unravel.

A variable star is simply a star that changes in brightness. Observing variable stars is both useful to science, and fun. It is a field that needs the observations that dedicated amateurs with small telescopes have the time and enthusiasm to make. It will reciprocate as you contribute to it, for the more you observe the more you will learn about your subjects of observation.

The purpose of this book is to inspire you to observe variable stars. Through its pages, I want to share my enthusiasm for these distant suns that change in brightness. Accordingly the book's approach is to emphasize the observing, and to keep the scientific explanations simple.

Why do variables attract us? The answer lies in the stars themselves. These innocuous objects attract our interest because of their behavior, not their appearance. Although they do not look fascinating at first glance, consistent watching will draw out their surprises.

R Coronae Borealis

Have you ever had a backwards day, when everything seemed to be happening in reverse, and things turned out to be precisely the opposite of what you expected? Such a day should end with your first observation of a “backwards nova,” a star called R Coronae Borealis.

Usually, a nova stays at minimum until the day of its mighty explosion. R Coronae Borealis does the opposite. It stays at maximum, a bright beacon around magnitude 6, and then without warning plunges eight full magnitudes to the depths of a magnitude 14 minimum. At its brightest it can be seen with a good pair of unaided eyes if the sky is dark enough. At minimum it will test the mettle of a 20 cm (8-inch) telescope.

R Coronae Borealis is not really a nova in reverse; it only acts like one, perhaps by surrounding itself at completely irregular intervals with a shell of carbon particles which absorb light. In late February of 1977, I returned from an evening out and the clouded sky was just beginning to clear. I decided to check the sky and observe just one variable for a total session of no more than ten minutes. I thought I would try R Coronae Borealis since the night before and for many months earlier it had been shining brightly at about magnitude 6. It often happens that my shortest observing sessions turn out to be the most productive.