Mathematical Astronomical Morsels I

Mathematical Astronomical Morsels IBy Jean Meeus. Product Information: 6. 00" by 9. 00", 400 pages, hardbound. From The Foreword Every time two full moons occur in the same month, pundits in the media take note. They explain that, according to folklore, the rare second one is called a blue moonwhence the saying, once in a blue moon. However, they have got it backwards, says Philip Hiscock of the Folklore and Language Archive, Memorial University of Newfoundland. The fabled blue moon,

By Jean Meeus.

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

From The Foreword

Every time two full moons occur in the same month, pundits in the media take note. They explain that, according to folklore, the rare second one is called a blue moon—whence the saying, “once in a blue moon.” However, they have got it backwards, says Philip Hiscock of the Folklore and Language Archive, Memorial University of Newfoundland. The fabled blue moon, meaning any rare or unusual occurrence, dates back at least 150 years in the English language. The link to lunar phases in a calendar month is quite recent. Hiscock traces it to an obscure children's book published in 1985, followed the next year by a question card in the game of Trivial Pursuit!

Meanwhile, hardly a week goes by in the Internet's astronomy areas without a total novice dropping in to ask, “What about the alignment of planets coming in May of the year 2000? Are we in danger of a tidal wave or a massive earthquake?” A replay seems brewing of the public alarm over the supposed syzygy of 1982 March 10, widely touted as something that occurs once every 179 years.

Pop-culture obsessions like these do not originate in the magazines for amateur astronomers, let alone in scientific journals or textbooks. But they say something important about our society. Here we have naive but sincere people, whose astronomical curiosity has been stirred for perhaps the first time in their lives. Their interest will soon wane unless a teacher, commentator, or writer they respect can step in with a meaningful response. Even worse, their end-of-the-world fears may escalate.

Jean Meeus's latest book explores the frequency of blue moons, planetary groupings, and a great deal more, as only this master of astronomical calculations could. He predicted the May 2000 alignment in an article for Sky & Telescope magazine in December 1961, but without spreading the doomsday concern, of course. He has brought together these and other tidbits from his voluminous writings, spanning nearly half a century, on every sort of celestial configuration, cycle, and curiosity. His wide following in America can now enjoy these penetrating analyses, many of which originally appeared only in Europe. The collection is much more than mere anthology. Each conclusion has been checked, and virtually every numerical result calculated afresh, with all the rigor we have come to expect.

This Belgian astronomer is particularly attracted to the rarest of all celestial occurrences—things almost impossible to find by paging through almanacs or scrolling through time with a computer's planetarium program. For example, he investigates how often a bright star or planet is occulted by the moon during a total lunar eclipse. He looks at how many times per century Jupiter can appear ""without a visible moon,"" all the Galilean satellites being either in front of the disk, behind it, or in eclipse. He goes on to examine another elusive event, one that the English amateur Horace Dall was lucky enough to photograph with his 15-inch reflector on 1956 April 21: the shadow of not one, not two, but three satellites crossing Jupiter's disk at once! This book lists the occasions when we, too, can hope to witness something similar during our lifetimes.

The detection of patterns and cycles is a theme pursued throughout. Most readers have probably heard about the Saros in connection with solar eclipses, or the eight-year cycle of Venus risings that is a cornerstone of the Maya calendar. But here we find evidence for the half Saros (about 3293 days), for which the author proposes the name Sar. A mysterious 586-year period also emerges among the lunar eclipses. It is so long a span that a few writers have fallen into a statistical trap. Using data for the entire 20th and 21st centuries, they have concluded that total lunar eclipses are more common than partial ones. Wrong! As Jean Meeus demonstrates with his beautiful diagram of eclipse clumps (page 104), the opposite is true over the long haul.

Many celestial cycles are fleeting, destined to fade away after a few iterations as others overlap them or start up afresh. It is a fallacy to think that you can recreate planetary motions for many years by spinning back or fast-forwarding a planetarium projector. Only someone with a profound grasp of astronomical motions and relationships could have produced an authoritative book like this.

Some readers will see here an antidote to the claims of astrology. Others will gain a deep insight into the misuse of statistics, especially in such areas as the sunspot cycle and its relation to weather on Earth. But all of us can acquire plenty of ammunition to settle bets at star parties, test computer programs, and amaze our friends (or an astronomy professor) with some little-known surprises about the sky and calendar.

So why exactly does Christmas fall more often on a Tuesday than on a Monday? How many centuries will elapse before 10 successive Easters occur in April? What is the reason that total solar eclipses are more common for observers in the Northern Hemisphere than in the Southern? Turn these pages, and you'll find out!

Roger W. Sinnott
Senior Editor, Sky & Telescope magazine

Table of Contents

Notes on Dates and Time Reckoning

THE MOON
1. The Instantaneous Lunar Orbit
2. The Extreme Values of the Distance of the Moon to the Earth
3. The Distribution of the Moon's Perigee and Apogree Distances
4. What is the Mean Value of the Earth-Moon Distance?
5. Extreme Declinations of the Moon
6. The Librations of the Moon
7. Months With Five Lunar Phases
ECLIPSES AND OCCULTATIONS
8. The Number of Eclipses in a Year
9. Solar Eclipses: Some Periodicities
10. Curious and Interesting Facts About Solar Eclipses
11. Regions of Visibility of Solar Eclipses
12. When is the Northern Limit the Southern One?
13. The Frequency of Total and Annular Solar Eclipses for a Given Place
14. Total and Annular Solar Eclipses in Close Succession at a Given Place
15. Nearly-Zenithal Central Solar Eclipses
16. Curious and Interesting Facts About Lunar Eclipses
17. Total Penumbral Lunar Eclipses
18. The Half-Saros
19. Series of Occultations
20. Occultations of Bright Stars by the Moon
21. Series of Occultations of Saturn
22. Occultations of Bright Stars by the Eclipsed Moon
23. Occultations of Planets by the Eclipsed Moon
24. Occultations of Planets by the Eclipsed Sun
25. Occultations of Bright Stars by Planets
PLANETARY MOTIONS
26. The Barycenter of the Solar System
27. On the Passages of Earth in Perihelion
28. Periheloids and Apheloids
29. A Periodicity of 179 Years?
30. Planetary Quadrants and Planetary Sectors
31. How Often are the Planets Aligned?
32. On `Remarkable' relations between the Mean Motions of the Planets
33. Ceres and Pallas, and Other Couples
34. Seneca, Orthos, and Quetzalcoatl
35. Defining Asteroids of the Apollo and Amor Types
36. The Periodic Comet Encke and Jupiter
37. The Orbital inclinations of the Four Galilean Satellites
PLANETARY PHENOMENA
38. Planetary Motions: Approximate Periodicities
39. Opposition Loops
40. Opposition Places
41. Triple Conjunctions
42. Planetary Groupings
43. Periodicities in the Phenomena of the Satellites of Jupiter
44. Jupiter and Triple Shadow Phenomena
45. Jupiter Without Satellites
ON THE CELESTIAL SPHERE
46. Heliacal Rising and Settings
47. The Positions of Uranus, Neptune, Pluto and Ceres at their Discovery Dates
48. Ecliptic and Galactic Equator
49. The Equinoctial and Solstitial Points and the Constellations
50. The Declination of Polaris
51. Alpha is Not Always the Brightest
STATISTICS, ETC.
52. The Mean Frequency, Yes, but
53. Statistics: Danger!
54. Sunspots and the Weather
55. Solar Activity and the Brightness of Lunar Eclipses
VARIA
56. The Equation of Time
57. About the Equinoxes and the Solstices
58. The Weekday of Christmas Day
59. The Distribution of Easter Sundays
60. The Date of Easter - Some Interesting Data
61. Rounding Numbers
62. Predicting Sunspot Activity
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) and More Mathematical Astronomy Morsels (2002). For his numerous contributions to astronomy the International Astronomical Union announced in 1981 the naming of asteroid 2213 Meeus in his honor."