Chandrasekhar derived a maximal mass ≃1.4M⊙ of a white dwarf. A white dwarf consists of degenerate electrons, i.e. Fermionic gas at low temperature described by a polytropic equation of state with polytropic index γ = 4/3 in the relativistic regime and with polytropic index γ = 5/3 in the non-relativistic regime.

The Chandrasekhar mass limit of a white dwarf is based on the maximal pressure provided by a degenerate Fermionic fluid against self gravity. The same principle applies to degenerate neutrons, i.e. to neutron stars. Landau[316] gives the following argument for a maximal mass; see, for example, Shapiro and Teukolsky[490].

S Persei

In the field of the Double Cluster in Perseus, one of the most spectacular objects in the whole sky, is a special type of red supergiant. It is a representative of a family whose periods of variation are far less certain than those of the Miras. S Persei is a semiregular variable star. The 5000 semiregular variables are a highly independent group of stars, too independent to predict accurately.

Compared to other variables we've looked at, S Per can be glacially slow. If it happens to be quiescent, you may not see much change over several months. While it does have a stated period and range, these figures are somewhat decorative in that they are based on many years of observations, and do not necessarily show the star's current behavior. From one month to another, it may not change at all, or it may surprise you. Observe this star at least once each 30 days.

To find S Persei, use the chart in Figure 17.1, by going north from the cluster NGC 869 (No. 869 in Dreyer's 1888 New General Catalog), until you pass the 6.2 magnitude star 7 Persei, then continuing north to 8 Persei, of 6.1 magnitude. Take care with the next step, which is a jump to the northeast by about one degree.

What happens to observations once an observer has submitted them to a variable-star organization like the AAVSO? It is possible to see how a particular observation compares to other data, and how it fits into measuring how a star is behaving.

According to Elizabeth Waagen, long-time assistant to the director of the AAVSO, here are the steps involved in processing an observation.

Reporting observations

(1) After making an observation, you can send it to AAVSO through its website www.aavso.org, using a program called “WebObs.” (That's how I do it.) Alternatively, you can send in observations via email. Emailed observations are automatically checked by the AAVSO for errors or omissions. A third method is the classic paper report form which, when received at AAVSO headquarters, is entered into the AAVSO database.

(2) All observations sent electronically can be viewed on the website www.aavso.org. Click on “Access Data” and “Light Curve Generator” or go directly to http://www.aavso.org/data/lcg/. Soon you will see a plot of recent observations that will show a star's light curve, the actual story of the star's behavior.

The light curve that you examine of recent data on the AAVSO website is a “quick look” representation of the data. It might come with a notice that the data have not been “validated,” meaning that the data points have not yet passed the AAVSO's strict quality control. Each one is plotted against others and added to the star's light curve.

The International Astronomical Union (IAU) was founded in 1922 to “promote and safeguard astronomy … and to develop it through international co-operation.” There are currently (2005) 9,014 individual members in 87 countries. The IAU is funded through the adhering countries, and is administratively “lean.” The total staff consists of a secretary and an assistant. The officers serve voluntarily, usually with support from their academic institutions. Almost all of the funds supplied from the dues are used for the development of astronomy.

One of the 40 IAU “commissions,” or interest groups, is Commission 46, formerly called “The Teaching of Astronomy,” and more recently, at the 2000 General Assembly, renamed “Astronomy Education and Development.” It is the only commission that deals exclusively with astronomy education; a previous Commission 38 (“Exchange of Astronomers”), which allocated travel grants to astronomers who need them, and a “Working Group on the Worldwide Development of Astronomy,” have been absorbed by Commission 46. The 40 commissions, and the many working groups, were recently organized into 11 scientific divisions. Commission 46 is part of a 12th division, “Union-wide Activities,” which deals with issues of concern to all IAU members.

The commission's mandate is “to further the development and improvement of astronomy education at all levels, throughout the world.” In general, the commission works with other scientific and educational organizations to promote astronomy education and development; through the national liaisons to the commission, it promotes astronomy education in the countries that adhere to the IAU; and it encourages all programs and projects that can help to fulfil its mandate.

Premise

Astronomy plays an essential role in human culture: there is nothing quite like the study of astronomy to capture the imaginations of our students, to make them understand phenomena and introduce them to the fundamental ideas and methods of science and mathematics.

The discovery of TV Corvi

On April 11, 1963, a group of visitors stood in the small gallery facing the largest telescope at Kitt Peak National Observatory at the time, the 84-inch reflector. After the tour guide explained the operation of the great telescope, he asked if there were any questions. One 14-year-old certainly had one. “How does an astronomer get permission to use this telescope?” he asked. “This telescope at the National Observatory,” the guide hissed, “is available only to qualified personnel.”

I was that 14-year-old. Two years later, on December 17, 1965, I began my project to search the sky. On that night, my goal was to begin a search of the sky that might yield a comet, or possibly a nova. A quarter century later, I found a nova, but it did not involve my use of a telescope.

On February 9, 1986 – coincidentally the perihelion date of Halley's Comet – I was in the basement archives at Lowell Observatory poring through hundreds of paper envelopes that Clyde Tombaugh used to store his photographic plates. It was a part of a biography I was writing about the man who had discovered Pluto. These plate envelopes had been replaced with modern archival envelopes, but the originals, complete with Clyde's detailed notes of observation, were still stored in a filing cabinet.

There is an interesting cartoon that shows two small boys and a dog. In the first panel, one boy says to the other “I taught Stripe (the dog) how to whistle!” In the second panel, the other boy replies “I don't hear him whistling!” In the third and final panel, the first boy says “I said I taught him; I didn't say he learned it”.

This cartoon emphasizes the difference between teaching and learning. Research shows that, in the most traditional methods of teaching, the amount of learning may be zero. Of course, there is more to teaching than the learning of facts. In fact, there is an old saying that “education is that which remains after the facts have been forgotten.” So it can include the intangible effects of an inspirational teacher.

There are many important challenges in the effective teaching and learning of astronomy, and most of them are amenable to research. One challenge is students' deeply rooted misconceptions about astronomical topics; non-expert teachers often share the same misconceptions. Some of these misconceptions are caused by the influence of religion or of popular culture. Others result from the three-dimensional nature of many astronomical concepts, or from the problems of moving from an observer-centered frame of reference to an external one, or from the enormous astronomical scales of size, distance, and time. Many of these concepts are intrinsically difficult, and the work of Piaget and others seemed to show that these concepts require students to have reached the appropriate stage of intellectual development - secondary school, for instance.

Buried deep in the richest part of the winter sky is the magnificent constellation of Orion the Hunter, a group of stars that have a closer relationship than the chance positioning of most constellations. Except for Betelgeuse, most of the bright stars in Orion are roughly the same distance from us. Orion is far more than just a place in the sky, named for a figure from mythology. Orion is a cosmic production plant, whose different divisions show us how stars are made.

The process of star formation is very complicated, but here we can see how it takes place. Young stars in the belt of Orion represent a group of stellar children whose formation is essentially complete. The sword area is a cosmic nursery with some of the stars being less than a million years old. Some astronomers suspect that the area south of the sword, with its hydrogen-rich regions, given another several million years, will coalesce to produce new stars.

In the area where stars are in the process of birth, the highlight is M42, the Great Nebula. The darker your sky, the greater the thrill of such a sight. Here is a nebula whose visual appearance is stunning, whose delicate patterns are exquisite. With a 10 cm (4-inch) telescope, you can make out the beginnings of the complex light and dark gases that share the nebula.

Two of the most famous Mira variables in the sky, R Leporis and Chi Cygni, are challenging, but for different reasons: R Leporis is unusually red, and Chi Cygni lies in a rich field of stars.

R Leporis

Until you've seen R Leporis at maximum, you haven't seen red. Here is a star whose redness offers us a new interpretation of color, a transcendent presence of vivid hue from a great distance.

In my early years of stargazing, I was guided by an old book by J. B. Sidgwick called Introducing Astronomy. During hundreds of observing sessions it taught me faithfully, pointing out the constellations one by one, as well as the inspiring contents of each. I especially remember the description of M42 as exciting to read about as the nebula was to look at. Then I'd turn the page for Lepus the Rabbit, just to see what glories were hidden from me in the little constellation that couldn't quite hop above the treetops of my southern horizon. It was Introducing Astronomy that taught me about R Leporis, Hind's Crimson Star, that shone in the sky like a drop of blood. As much as I longed to see this star, I expected I never would until either the trees fell down or I moved to a better site. Since neither prospect seemed very likely in the slowly-moving world of my youth, I relegated R Lep to a growing list of objects I would never see.

One of the International Astronomical Union's highest priorities is the worldwide development of astronomy. A substantial fraction of its resources is used for that purpose; the resources are administered through the IAU's Commission on Education and Development. At the 2000 General Assembly of the IAU in Manchester UK there was a three-day conference on “Astronomy for Developing Countries.” The proceedings were edited by Alan H. Batten, and published by the IAU in 2001. This book is the definitive guide to the topic. The IAU works closely with other organizations, such as the United Nations Office for Outer Space Affairs. This office has organized a series of workshops on basic space science, in various parts of the world, and astronomy is one of the topics covered. The government of Japan has generously provided small telescopes and planetariums to several developing countries. The Vatican Observatory organizes summer schools for graduate students and young astronomers from astronomically developing countries. The IAU International Schools for Young Astronomers (ISYA) take place every year or so somewhere in the world, and also involve graduate students and young astronomers. See www.astronomyeducation.org.

According to the StarGuides database maintained at the Strasbourg Observatory, there are approximately 100 countries in which there is some astronomical activity - either research or teaching, professional or amateur. In about 50 of these countries, astronomical activity is not sufficiently developed for the country to adhere to the International Astronomical Union (IAU), or there may be other factors that make IAU membership difficult. Their level of astronomy activity ranges from minimal to moderate.

R Leonis

On a bitter January night in frosty Montreal, I first watched R Leonis. A cold front had just passed through, leaving a crisp starry sky. Checking my variable-star chart, I began to look for R. It was frightfully cold. After an uncomfortable 45-minute search I finally found R Leonis as it rose through the haze and smog that hugged the eastern horizon. By this time I was so cold that even the simplest and smallest motions of the telescope were magnified into an agonizing exercise that taxed my whole being. I had finally found a faint magnitude 9.3 star, graced by two other stars – chambermaids assisting a stellar queen – at 9.1 and 9.6. It was so cold that the telescope tube froze to its mount and I couldn't even take the poor instrument inside! Quickly, observer minus telescope moved inside for some warmth. Never had hot chocolate tasted so good!

Still outside, hundreds of light years away, shone my new variable. On that frigid night, R Leonis taught me two important lessons. One was that variable star observing can be challenging and worthwhile. The other is that to observe variables properly, one must first acquire a feeling for them, a genuine concern for what they are doing, and a will to undergo some discomfort to remain in touch with them. You may not feel this the first cold night out, but you will as you get familiar with the variable's behavior.

Introduction

South Africa's recent history in education has been fairly turbulent as a result of previous government policies, especially in how it affected the education of black people. After the democratization of South African society, it became clear that there was a need to develop a new curriculum, and it was an ideal time to start with a “clean slate.” South Africa had the unique opportunity to make a major paradigm shift in education and make a total break with past structures. One of the aims of this new curriculum was to transform education. This transformation would be not only educational but also political: there was a need to empower previously disadvantaged (black) teachers. This process started in the early 1990s, and the implementation of a newcurriculum began in 1998.

The primary aim of continuum measurements is to obtain the photospheric temperature scale, but numerous other uses range from gravity measurement, chemical composition studies, the detection of companion stars and disks, through properties of broad-band photometric systems, and bolometric corrections. In the hotter stars, the shape of the continuum is molded by the bound–free absorption of neutral hydrogen. From the ground, we can measure only a small part of the Balmer continuum (912–3647 Å) long-ward of the ozone cut-off ∼3400 Å, the complete Paschen continuum (3647–8207 Å), and some of the Brackett continuum (8207–14 588 Å) which is badly cut up by terrestrial molecular absorption. The Balmer and Paschen discontinuities are useful as pressure diagnostics for late A and F stars, but they also depend on temperature. In cooler stars, where the negative hydrogen ion dominates, all continuum characteristics depend almost exclusively on temperature.

The spectrum measured with low resolution, e.g., 10–50 Å, is often called the “energy distribution.” In such situations, the spectral lines are included, and then measurements of the fraction of light removed by spectral lines is needed to regain accurate information on the position of the continuum.