# Mathematical Astronomical Morsels III

**By Jean Meeus.**

**Product Information:** 6.00" by 9.00", 400 hardbound.

From The Foreword:

Welcome, once again, to the crossroads where astronomy, mathematics, and arcane knowledge meet. In this third volume of his Morsels series, Belgian astronomer Jean Meeus deals masterfully with a host of new questions about eclipses and planetary conjunctions — things that anyone from a curious child to a serious skywatcher might wonder about. The sky’s rhythms are not strictly repetitive, as he proves time and again by finding entertaining quirks in the motions of the Moon and planets.

In his Preface the author hints that some readers might accuse him of practicing “old” astronomy. Don’t let that fool you. The problems he tackles would have fascinated astronomers of the early 20th and prior centuries, but those poor souls faced a brick wall of computational difficulty. They had to work out all their answers laboriously, with a pencil and paper. Freed from that limitation, the author uses today’s computers to address each topic with a rigor and finesse beyond the wildest dreams of any old-time practitioner.

After winning worldwide acclaim for his trailblazing Astronomical Formulae for Calculators (Willmann-Bell, 1982) and Astronomical Algorithms (1991), he has harnessed the powerful techniques presented in these works, along with other methods from his repertoire, for the novel applications covered here. For some really long-term studies he has collaborated with Aldo Vitagliano (University of Naples), the creator of Solex, a remarkable program for solar-system motions that can be freely downloaded from the Internet.

I’m struck by the fact that we now live in “long gaps” between certain types of celestial occurrences, making it appear that they never occur. But that’s a mistake. For example, there is probably no one alive today who remembers seeing the planet Venus go south of the bright star Antares in 1914 or 1922, and we learn in Chapter 37 that Venus won’t repeat this performance until 2109. Similarly, Jupiter hasn’t occulted Saturn (as seen from Earth) since before the pyramids of Egypt were built; the next time will be in A.D. 7541, and it does so twice in that year!

As if to make up for these long waits, current generations of skywatchers are being specially treated to transits of Venus, rare though they are. Such transits have a nice way of coming in pairs, as in 2004 and 2012. But that will end about 1,800 years from now, after which a person will get exactly one chance in a lifetime to see a Venus transit — unless, by then, the human life expectancy exceeds 105 to 138 years.

Make no mistake, many of the intricate calculations described in this book were beyond our grasp just a few years ago. Or maybe someone attempted them and gave the wrong answers, with no one being the wiser. The French public adored Camille Flammarion, a charismatic champion of astronomy in the late 19th and early 20th centuries. The erroneous value he promulgated for the longest possible total solar eclipse still turns up occasionally today, as we find out in Chapter 10.

Many surprises lurk in these pages. As schoolchildren we learned that a solar eclipse can occur only at a New Moon, and a lunar eclipse at a Full Moon. It is also true (as more advanced courses teach) that an extreme apogee or perigee of the Moon can happen only near one of these same two phases. So it’s intriguing to discover in the book’s first chapter that an extreme apogee or perigee can never coincide with an eclipse.

Did you know that the shape of a solar eclipse track depends on the calendar month in which it occurs, and that in the arctic regions there can be an eclipse of the midnight Sun? Moreover, our star can indeed come to a halt in the daytime sky, as if obeying Joshua’s biblical command, “Sun, stand thou still.” It does so routinely, twice each day, as viewed from the surface of the planet Mercury!

When three planets form a nearly perfect line in space, who but an Albert Einstein (or a Jean Meeus) would have foreseen that the velocity of light plays a vital role in what is (or is not) seen by observers on the two end planets? Chapter 46 cites six actual dates when one observer would see an occultation by the middle planet, and the other a near miss, due to a difference in the travel time of light to each observer.

Only a curmudgeon could say that investigations like these, having no obvious purpose, are not worth pursuing. Let’s be glad the great astronomer Joseph Louis Lagrange didn’t have that attitude, back in 1772, when he first described how a tiny body (now called a Trojan asteroid) could permanently trail behind or lead the way for a major planet going around the Sun. Lagrange worked at a time when not a single asteroid of any type, let alone a Trojan, had been spotted in a telescope. Many hundreds of Trojans are known today, and we learn in Chapter 24 that the statistics of their orbits have certain peculiarities yet to be explained. Perhaps this purely “recreational” book will inspire a budding theoretician to make a future advance in celestial mechanics.

As I write these lines, Sky & Telescope magazine has just reinstated (after 36 years) the monthly question-and-answer section that so delighted me as a teenage subscriber living in rural Virginia. Today, as then, the magazine receives all sorts of innocent queries about the planets and the sky that are easy to pose but very tricky to answer with authority. For help in preparing our answers we consult various experts, run software simulations, and check the papers published in obscure journals. But I’ll let you in on a secret. On the bookshelf by my desk, right alongside its predecessors, I’m adding Jean Meeus’s latest Morsels as a prime editorial resource.

Roger W. Sinnott*Senior Editor, Sky & Telescope magazine***Table of Contents**

Notes on Dates and Time Reckoning

The Moon

1 Extreme perigees and apogees of the Moon - mystery solved

Eclipses

2 Years with five solar eclipses

3 Two eclipses in northern Siberia and the period of 10 years

4 Similar eclipse paths

5 Solar eclipses with long central lines

6 Solar eclipses: shapes of central lines

7 Annular-total solar eclipses

8 Broken-ring eclipses

9 About solar eclipses of type IV

10 The maximum duration of a total solar eclipse

11 The time interval between two successive solar eclipses

12 The shortest time interval between two totalities at the same place

13 Accumulating totalities

14 About crossing central lines

15 Large solar eclipses at the Poles

16 Where does greatest eclipse occur?

17 Just-missing partial ""eclipses""

18 About Saros and Inex series

19 Eclipse duos

20 Magnitude, ratio and obscuration

21 Lunar tetrads

22 About solar and lunar eclipses

23 Exotic eclipses

Planetary Motions

24 The Trojans

25 Asteroid 63252 and Comet Lexell

26 Iris and Metis

27 Close approaches between asteroids

28 Planets and the Latus Rectum

29 About the perihelia of Saturn

30 Planetary perturbations

31 True and apparent distances

32 Surface gravity and escape velocity

33 About the synodic period of a satellite

Planetary Phenomena

34 More than one opposition in one year?

35 The axial tilt of Mercury

36 The motion of the Sun in the sky of Mercury

37 Venus and Antares

38 Shadows on Jupiter

39 Jupiter with only one visible satellite

40 Jupiter: triple satellite phenomena

41 Transits of Venus and Mercury: some secular variations

42 Another list of Venus transits

43 Transits of Venus: local durations

44 Simultaneous transits

45 More simultaneous transits

46 Mutual occultations of planets (off-Earth)

On the Celestial Sphere

47 Can Venus be visible at midnight?

48 Simultaneous greatest elongations

49 Simultaneous inferior conjunctions

50 The planets' greatest declinations

51 Diurnal path and horizon

52 More sunshine near the Polar Circles

Varia

53 Pursuing the Sun

54 Galileo's first records of Jupiter's satellites

55 Planetographic and planetocentric latitudes

56 Friday the 13th

57 A sky full of moons?

Index

**About The Author**

Jean Meeus, born in 1928, studied mathematics at the University of Louvain (Leuven) in Belgium, where he received the Degree of Licentiate in 1953. From them until his retirement in 1993, he was a meteorologist at Brussels Airport. His special interest is spherical and mathematical astronomy. He is a member of several astronomical associations and the author of many scientific papers. He is co-author of Canon of Solar Eclipses (1966), the Canon of Lunar Eclipses (1979) and the Canon of Solar Eclipses (1983). His Astronomical Formulae for Calculators (1979, 1982, 1985 and 1988) has been widely acclaimed by both amateur and professional astronomers. Further works, published by Willmann-Bell, Inc., are Elements of Solar Eclipses 1951-2200 (1989), Transits (1989), Astronomical Algorithms (1991), Astronomical Tables of the Sun, Moon and Planets (1983 and 1995), Mathematical Astronomy Morsels (1997), More Mathematical Astronomy Morsels (2002) and Mathematical Astronomy Morsels III (2004). For his numerous contributions to astronomy the International Astronomical Union announced in 1981 the naming of asteroid 2213 Meeus in his honor.