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Practical Astronomy with your Calculator or Spreadsheet, 4th ed.

Posted by Michael Coren   11/06/2011 04:25PM

Practical Astronomy with your Calculator or Spreadsheet, Fourth Edition
by Peter Duffett-Smith and Jonathan Zwart
Published by Cambridge University Press, 2011.
Publisher's price $40 USD ($34.40 USD on Amazon).

Review by Michael Coren

This is the fourth edition of a volume that was first published in 1979 as Practical Astronomy with your Calculator. As suggested by the modified title and explained in the preface, the biggest change from previous editions is the inclusion of spreadsheets for nearly every calculation. The spreadsheets are available for free download at the publisher's web site ( The book also includes an introduction showing the basics of how to use a spreadsheet program, with mention of both Microsoft Excel and the freely distributed OpenOffice Calc.

One other obvious change from previous editions is a larger page size, approximately 7-1/2 by 9-3/4 inches (190 by 245 mm).

The computations in the book are divided into five sections:
- Time - including Julian dates, date of Easter, Universal Time (UT), Sidereal Time (ST), Ephemeris Time (ET), etc.
- Coordinate systems - including horizon coordinates (Alt-Az), equatorial coordinates, ecliptic coordinates, coordinate conversions, precession, nutation, geocentric parallax, etc.
- The Sun - position, distance, angular size, sunrise, sunset, twilight, etc.
- The planets, comets, and binary stars - Orbits, calculating positions, perturbations, distance, angular size, phases, etc.
- The Moon and eclipses - The Moon's orbit, position, motions, phases, angular size, moonrise and moonset, eclipses, etc.

(The complete Table of Contents can be viewed on Amazon using the "Look Inside" feature.)

This is not a textbook on celestial mechanics, and it makes no pretense of being one. Although there is a good deal of explanatory information and diagrams, particularly in the discussions of orbits, the calculations themselves are generally presented in a cookbook fashion, and the math is mostly limited to high school trigonometry (sines and cosines). The authors themselves state right in the preface that the calculations are "recipes," and that they mostly consider only the essential factors and ignore many of the smaller corrections needed for the most accurate results. If you're planning a mission for NASA, I would suggest you seek out more comprehensive algorithms. On the other hand, when the authors compare the results of their worked examples to the USNO/HMNAO Astronomical Almanac, they are typically accurate to within a few arc minutes or better in those instances, which in my experience is good enough to give many amateur GOTO systems a run for their money.

In addition to the spreadsheets that perform the calculations as described in the book, many of the calculations have additional spreadsheets that provide "more precise" solutions. These latter computations are included in a library of macros. The book documents how to use these macros in your own spreadsheets, but the specific algorithms used to obtain these "more precise" results are typically not discussed in the book. Looking at the source code for the macros doesn't provide much insight, since they mostly consist of lots of constants and sinusoidal expressions. This is not a criticism of the book, or the spreadsheets, since even Jean Meeus' Astronomical Algorithms presents many of these formulas as lengthy tables of sinusoidal coefficients. These formulas give precise numerical answers, but they have been derived from extensive empirical analysis rather than a closed form solution to the n-body gravitational problem (which rarely if ever exists). I suppose that's just the way the most precise calculations are done these days.

I found the sections on generalized coordinate transformations and precession calculations using matrices, which first appeared in the third edition (1988), to be particularly interesting. Besides abstracting the computations to a single method that is well suited to a high-level programming language, the inclusion of these sections is acknowledgement of the increased use of personal computers, as well as the ability of many contemporary programmable calculators to do matrix manipulation. A brief but sufficient overview of matrix multiplication is included for those who are not familiar with it.

Naturally I have a few critiques, but these are fairly minor and are really more of a wish list.

First, there are a number of computations that I think could benefit from the ability of spreadsheets to obtain numerical solutions through iteration, but the spreadsheets accompanying the book do not use this capability. The solution to Kepler's Equation, which is mentioned many times throughout the book and is part of every orbital computation (position of the Sun, Moon, Earth, planets, comets, etc.), would seem to be an obvious application to demonstrate an iterative spreadsheet solution.

Second, while the orbital elements for the planets in Table 8 have been updated for epoch 2010.0, including the removal of Pluto following its 2006 reclassification by the IAU (more on that later), Table 9, with the orbital elements for selected periodic comets, hasn't been updated since at least the second edition (1982), and likely the first. Most of the comets in the list have gone through at least one complete orbital period since the perihelion dates given in the table, and some have gone through multiple orbits. How accurately can one really calculate the position of Comet Encke's upcoming 2013 perihelion by extrapolating forward through 12 orbital periods from its 1974 perihelion using just the methods in this book? Don't these elements have osculations and other perturbations? Moreover, although I am not personally a close follower of comets, I would imagine that there are other periodic comets that one could argue would be of greater interest to amateur astronomers in 2011. Comets Hartley 2, Tempel 1, and Holmes come to mind. Are any amateurs really still tracking Comet Halley?

(Speaking of Table 8, there is an error in the orbital elements given for Uranus. Its value of ε, the heliocentric longitude at epoch 2010.0, is listed as 271.063148°, but I believe the correct value is 356.1354°, based on interpolating the USNO Table of Osculating Elements. I emailed the authors about this through the publisher's web site back in September, but as of early November I have not received any response and nothing has been posted in the errata section of the web site.)

Third, Pluto's 2006 reclassification by the IAU illustrates the fact that the outer Solar System has become a lot more crowded than it was just a decade ago, let alone in 1979 when the first edition was published. Beyond simply removing Pluto's orbital elements from the table of "planets," the authors could have used this new edition to add discussions of main belt asteroids and trans-Neptunian objects (TNOs). Ceres and Vesta frequently come close to naked-eye visibility, and some of the TNOs are well within the reach of modern amateur astrophotography techniques. Can these objects just be treated as planets with different orbital elements, or are there other factors to consider?

The final item on my wish list involves the Moon. The information that is in the book is well detailed, and describes the major corrections needed in computing its position and the complexities in computing moonrise, moonset, and eclipses. One notable omission, in my opinion, is a discussion of geometric librations. I don't think these computations are that difficult once you know the Moon's position and a couple of other factors, some of which are already addressed in the book.

While it was not my purpose in this review to do a side-by-side comparison with Jean Meeus' Astronomical Algorithms, such comparisons are unavoidable since the latter is perhaps the standard reference for amateurs. Briefly, the range of topics covered in this book is not as comprehensive, and the computations in this book are generally not as precise, as the ones in Astronomical Algorithms. If you own Astronomical Algorithms and are comfortable with using it, you won't gain much new from this book. However, what is here seems like it should be more than sufficient for the casual amateur's needs. Furthermore, while many of Meeus' examples show just the final numerical answers, the authors of this book walk you through all of the examples in step-by-step detail, showing you the intermediate results you should obtain.

Unlike the situation in 1979, the thought of doing these computations on a handheld calculator seems somewhat tedious in this age of GOTO scopes, tablet PCs, and app-loaded iPhones. Even using spreadsheets seems a roundabout way to obtain information that can be easily garnered from various web sites or basic planetarium software, much of which can either be downloaded for free or costs less than this book. Then again, there will always be people who enjoy being able to do the computations themselves, and this book definitely helps to fill a conspicuous gap between the precompiled tables found in monthly observing guides and college-level textbooks on celestial mechanics.

All in all, this book does a good job at what it sets out to do. The formulas and algorithms are presented clearly and with an appropriate level of detail, and the spreadsheets supplement the text by showing an additional way to perform the computations without having to resort to a scientific calculator or writing your own programs.

Standard disclaimer: No financial interest, don't know the guys, blah blah blah.

Clear skies!