Mathematical Astronomy Morsels

Description

Mathematical Astronomy Morsels. Jean Meeus's explores the frequency of blue moons, planetary groupings, and a great deal more, as only this master of astronomical calculations could. Here, he has brought together the best from his voluminous writings, spanning nearly half a century, on every sort of celestial configuration, cycle, and curiosity. The Moon 1 The instantaneous lunar orbit . . . . . . . . . . . . . . . . 11 2 The extreme values of the distance of the Moon to the Earth 14 3 The distribution of the Moon's perigee and apogee distances 17 4 What is the mean value of the Earth - Moon distance? 21 5 Extreme declinations of the Moon . 26 6 The librations of the Moon . . . 29 7 Months with five lunar phases 37 Eclipses and Occultations 8 The number of eclipses in a year . . . . . . 43 9 Solar eclipses : some periodicities . . . . . . 49 IO Curious and interesting facts about solar eclipses. 56 1 Regions of visibility of solar eclipses . . . . . . 62 12 When is the northem limit the southem one? . . 83 13 The frequency of total and annular solar eclipses fora given piace 88 14 Total and annular solar eclipses in dose succession at a given piace 93 15 Nearly-zenithal centrai solar eclipses . . . . . . . . . . 98 16 Curious and interesting facts about lunar eclipses 7 Total penumbral lunar eclipses . . . . . . . . . . 18 The half-saros . . . . . . . . . . . . 9 Series of occultations 100 108 110 113 3 4 MATHEMATICAL ASTRONOMY MORSELS 20 Occultations of bright stars by the Moon . . . . 124 21 Series of occultations of Satum . . . . . . . . . . . . . . . 134 22 Occultations of bright stars by the eclipsed Moon 139 23 Occultations of planets by the eclipsed Moon . . . . . . . . . 149 24 Occultations of planets by the eclipsed Sun . . 154 25 Occultations of bright stars by planets . . . . . . . . 159 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 orbitai inclinations of the four Galilean satellites 165 169 172 179 182 186 191 194 200 207 209 215 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 . . . . . . . . . . . . . . . . . . 223 233 240 246 262 269 279 281 TABLE OF CONTENTS 5 On the Celestial Sphere 6 Heliacal risings and settings . . . . . . . . 7 The positions of Uranus, Neptune, Pluto and Ceres at their discovery dates . . . . . . . . . . . . . 8 Ecliptic and galactic equator . . . . . . . . . . . . . 9 The equinoctial and solstitial points and the constellations . 50 The declination of Polaris . . . . 51 Alpha is not always the brightest 289 296 301 303 305 308 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 313 315 319 328 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 . . . . . . . 337 346 352 354 361 366 370 Index . . . . . .. . . . . . . . .. . . . . . . . . . . . . . . . 375