The approach of gamma Virginis to its spring 2005 periastron, as seen and measured in the 12½-inch at Hanwell, 1998-2004. This swoop through periastron was the most spectacular binary-star event of the century.

Christopher Taylor's Astro-notes 
... and a bit more.   Welcome to this personal astro-notes website – thank you for taking an interest!

What this website is about
Its content 
Use of mathematics and physics
The author
Attributions and acknowledgements

What this website is about
 Astronomy! More specifically, a personal ‘take’ on the science of astronomy, its history, principles and observational practice, based on the writer’s more than 55 years’ experience of doing, studying, lecturing on and for many years teaching the subject.

The material here, mostly text, with some photos, diagrams and personal observational drawings, is broadly aimed at explaining some of the basic principles of astronomy & astrophysics, together with the directly relevant physics and mathematics, for a readership of late school-years and early university students, amateur astronomers and  other interested parties. The observational material, at least, should be easily accessible to all, whether having any scientific background or none, but most has been included here to tell some specific story about the science involved.
Its content:
This website is in the earliest stages of construction, so the choice of content yet put up is particularly limited and random. There is, however, a very large backlog of similar material waiting to go up and this work is ongoing, further sets of existing notes being put up here whenever time allows. These sets of notes have been compiled over the years (most are dated) either purely out of personal interest as an exercise in thinking through a topic from first principles in order to clarify the writer’s own understanding, or as teaching notes and lecture-handouts done for specific occasions. They have for the most part been written pretty much at random whenever the writer’s thoughts happen to have turned to the topic in question, with no aim then or now to compile a complete, systematic course in astronomy. The author has strictly only presumed to write on those subjects which particularly interest him, on which he is confident he can write with some authority, and concerning which he has a particular view or way of doing things which may conceivably be of interest to others – which is not all of astronomy!

 The sets of notes already in hand nevertheless cover an extremely wide range of topics, from the early history of astronomy right down to current cosmology, via optical principles of telescopes, image-formation and limits of optical resolution; instrument testing and construction; the practicalities of astronomical observation; fundamental astronomy; dynamical & other mathematical astronomy; gravitation, Newtonian and post-Newtonian; optical spectroscopy as applied to astronomy; elementary stellar astrophysics; simple mathematical developments of the basic principles of atomic physics needed for the last two topics; quantum mechanics; relativity; the observation and measurement of visibly-revolving binary stars; and many other things…

Use of mathematics and physics:
Some of these notes are at least slightly mathematical but many contain no ‘sums’ at all, and where significant mathematics is used it is clearly set out from first principles, nowhere going beyond what should be common knowledge to any first-year undergraduate in the physical sciences. Mostly, even in the more mathematical passages, fairly harmless school mathematics (graphs, quadratic equations and other elementary algebra, etc) is all that is involved. The emphasis in all cases is on clear understanding and rigorous logical deduction as directly as possible from well-grounded mainstream physical principles. Mathematics should never be allowed to obscure the physics or the astronomy. Simplicity is the essence.

Little if any even of this more overtly educational material is merely a boring recitation of commonplace textbook content, but a completely independent development of the particular topic from scratch, from the same first principles (of course) as the textbooks use. These sets of notes are generally the result of the writer having sat down with nothing more than blank paper and pen to answer the question “What is the clearest, logically most direct and elegant1 way of explaining this topic?” Existing published accounts of that then-current topic are never consulted in developing the main arguments and derivations. Where the resulting method differs markedly from the consensus of the textbooks (e.g. in the mathematical theory of Lagrangian Points), I have prefaced the notes with a critique of that consensus explaining why I nevertheless believe that not to be best-possible as a way of developing the subject. The reader may, of course, agree or disagree.

1 Especially where significant mathematics is used. Some textbook mathematics in the physical sciences is repulsively ugly and needlessly complicated.

The whole point of the exercise, and of putting up the results here, is that we all ‘tick’ mentally in different ways and an explanation which is a model of clarity to one reader may be impenetrable to another – so if you’re struggling with the textbooks, dear reader, try what’s here (if relevant), as it may just ‘click’ with you in a way that the books don’t (and textbook writers commonly have an awful habit of merely copying from each other!). Of course, equally, it may be the other way round, so if this is your first encounter with a topic and you find my version ‘clear as mud’, read a good textbook. Either way, it should do the trick.

Where derivations of important results start from physical principles and laws of nature, as generally they must, the writer uses only a minimal set of their most fundamental and general formulations. He has a deep dislike of long and convoluted arguments which lose sight of the original first principles, or which take short-cuts by invoking fancy theorems the reader is unlikely to have encountered: that way lies logical coercion of belief, not explanation.
So, all of this is the result of independent thought, starting from and ending at the same points as you will find in the textbooks, but sometimes following a significantly different route in between. Maybe you’ll like this road better, maybe not. What you will not find here is ‘Independent’ or ‘Alternative’ thinking which attempts to repudiate rigorously tested and well-established mainstream science: if you are seeking support for ‘Counter-Earths’, ‘cold Sun’ theories, non-Doppler explanations of the cosmological redshift, electromagnetic ‘explanations’ of gravity, and the like, you will have to look elsewhere. Nor does the writer touch, with the proverbial bargepole, the wilder speculations on the fringes of cosmology and theoretical physics, such as the multiverse and string theory. It will take a very great deal more work by the proponents of those notions, in producing concrete, testable predictions, to persuade this writer that their theories are anything more than articles of theological faith, rather than real science.

 It is planned also to include occasional sets of notes here dealing purely with applicable mathematics or physics but only where these have been motivated by, and are directly relevant to, some topic or problem in astronomy. Any reader uncertain about these things should begin with the gentle June 2020 piece Seasonal recurrence of Venus'es apparitions ... in the 'Astronomy and Easy Mathematics' section here, which gives a striking example of the very simplest of mathematics having really interesting, non-trivial astronomical consequences

The Author
Failed to see the great sun-grazer Comet Ikeya-Seki in 1965 despite high hopes and fairly determined attempts with the unaided eye; turned his first telescope on the night sky at Christmas 1966; first set up the massive, veteran 12½-inch Newtonian reflector 2 which he still uses, in November 1967; a few nights before Christmas 1968, he and his late father had a spectacular view in the 12½-inch of Apollo 8 on its way to the Moon 3 ; and made his first experiments in both stellar spectroscopy and aperture-mask interferometry on the 12½-inch in 1971-2 at about the time he went up to university. At Oxford he read Physics, scoring alphas in 1975 finals on both assessed practical lab-work – mostly in atomic spectroscopy – and in the Theoretical Physics option-paper, something of which he is inordinately proud.

2 See the ‘Telescopes’ page on  
3 See the author’s piece on Sky & Telescope website 

 During graduate research in the Clarendon Laboratory, Oxford in the later ‘70s the writer took up mathematics teaching at GCE ‘A’-level and beyond, which then became his day-job for the next 25 years. The writer was mathematics tutor of Harris Manchester College, Oxford through the ‘90s and has extensively taught most areas of mathematics up to undergraduate level.
Since 1997 Christopher T. has done a substantial amount of astronomy teaching, including regular evening classes, weekend residential courses and summer-school 1-week courses, for the departments of continuing education of both Oxford and Cambridge Universities:

Regular Oxford astronomy evening classes at O.U.D.C.E. each term throughout the academic years 1997-2004;
Exploring Stars and Planets in the department’s summer-school, August 2000-2003 (general astronomy);
Strange Universe in the same summer-school, August 2004-2006 (relativity, gravitation, quantum mechanics, black holes and cosmology, all non-technical);
Herschel’s Garden: the heavens as natural history in the Cambridge international science summer-school, July 2004 (stellar & galactic astronomy);
Unmasking the Universe again in Cambridge (Madingley Hall), August 2004 (first half of a week’s course taught jointly with Dr. Robin Catchpole, I.o.A.);
Dance of the Spheres, a Madingley weekend course, December 2005 ( classical celestial mechanics/dynamical astronomy from Newton to the present day – almost entirely without equations! This used a purely graphical method of ‘Oriented polar direction-fields’ based solely on the energy and angular-momentum principles, developed specially for the occasion by this author. This course was a runaway best-seller, the lecture-room full and a waiting list of a further dozen hopefuls – which astonished the lecturer.)
Herschel’s Garden again, this time as a Madingley weekend course, Sept. 2007;
Medieval Comets, plenary lecture at the Cambridge Medieval Studies summer-school, August 2008;
Time & Tide, a tale of our Moon and others, Madingley weekend course March 2012 (tidal dynamics in astronomy using the methods of Dance 2005, especially for the Earth-Moon system and the possible geophysical impacts on Earth’s history, life, etc);
The History of Astronomy a Madingley w/e course split with Prof. Mike Edmunds and Dr. Allan Chapman, in which Christopher T. did two lectures on the Herschels, November 2013.
Also, for the U.K. programmes of two US universities:
Einstein, celebrity & the eclipse of 1919, plenary lecture for ~ 100 students and faculty of the University of Georgia summer school at Trinity College, Oxford, July 2019;  and most recently,
Astronomy, an introduction, a full-semester 16-week ‘astronomy for liberal arts’ course for the Wroxton Abbey study-abroad campus of Fairleigh Dickinson University, New Jersey, January-May 2022.

All of the lectures for the above were compiled entirely by the author and all courses, with the exceptions of the 1997-2004 Oxford evening classes and the two shared Madingley weekends, were set up from scratch wholly by him.  A representative sample of the more interesting course-descriptions is included on this website. The writer is always potentially open to serious requests to run these or other possible new courses in the UK – if interested, please write to:
1, The Piggeries,
Hanwell Castle,
nr. Banbury
OX17 1HN

 In addition to these there have been one-off talks delivered at the Museum of the History of Science, Oxford, and at meetings of the British Astronomical Association (the BAA), The Society for the History of Astronomy (SHA), UK Space Council and several UK local astronomy societies. Also notes, letters and the occasional paper have appeared fairly regularly in The Observatory, the Journal of the BAA, the SHA Bulletin, the Newsletter of the BAA Historical Section, etc… and several substantial observational & historical papers are in the pipeline.

The author is also founder and Director of the Hanwell Community Observatory in north Oxfordshire (see ) and, after 55 years ‘at the eyepiece’, remains a very hands-on, practical astronomer known to some for his work on visual binary stars, and still very actively observing.

Society memberships:
BAA Winter 1967/8 – 1978; 1992 – the present.
Stratford-on-Avon Astronomical Society 1993 – the present (founder member).
SHA Summer 2002 – the present (founder member).
FRAS, 2011 – the present.      
Herschel Society 2018 – the present.
Life member of both Oxford and Cambridge university astronomical societies 1970s – the present.

Attribution & acknowledgments
You are welcome to use any material on this website but if copying or quoting content in any publication, printed or online, please give full acknowledgment of its source.
The author himself gratefully acknowledges the huge help provided by Dr. Stephen Wass of Polyolbion Archaeology in the construction and launching of this website, without which it would not exist


The writer’s 12½-inch reflecting telescope at Hanwell, Oxon, 2018. The corgi provides the scale

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Astronomy Courses
Astronomical Optics, First Principles
Atoms and quanta for astronomy
Gravity, Newtonian and post-Newtonian Telescopes, use, capabilities and evaluation
Astronomy, History of
Astronomy, Optical Techniques for
Binary stars, visual observing Mathematics for Astronomy Unanswered questions
Astronomy and Easy Mathematics Astronomical spectroscopy, visual, first steps in
Cosmology from first principles Practical Project Suggestions
Astronomy, Mathematical & Dynamical Astrophysics, simple stellar Earth-Moon system, tidal dynamics & ‘evolution’ Small-telescope astronomy