An introduction to astronomy: designed as a textbook for the use of students in college

Front matter

Class

Book XI i£

Tig.l

Preface To The Revised Edition

This work was revised by its author in 1S54, at which time were introduced notices of the recent discoveries in Astronomy. The changes made in the present edition are mostly of a different character. "While there have been added brief accounts of still later discoveries, and of new methods of observation, it has been especially my aim to give more clearness to certain descriptions and demonstrations, which my experience as a teacher has shown me to be perplexing to the learner. The discussion of central forces is entirely remodeled, and the great law of gravitation throughout the solar system is deduced, by a more direct and less cumbrous mode of reasoning, from the three laws of Kepler, which are taken as facts established by observation.

To those numerous teachers who approve the general design of Professor Olmsted in the preparation of this work, as set forth in his preface, and who have themselves tested the utility of that design, it is hoped that the changes now made will commend themselves as improvements.

E. S. SNELL.

Amherst College, March, 1861.

Author's Preface

Nearly all who have written Treatises on Astronomy, designed for young learners, appear to have erred in one of two ways ; they have either disregarded demonstrative evidence, and relied on mere popular illustration, or they have exhibited the elements of the science in naked mathematical formulas. The former are usually diffuse and superficial ; the latter, technical and abstruse.

In the following Treatise, we have endeavored to unite the advantages of both methods. We have sought, first, to establish the great principles of astronomy on a mathematical basis ; and, secondly, to render the study interesting and intelligible to the learner, by easy and familiar illustrations. We would not encourage any one to believe that he can enjoy a full view of the grand edifice of astronomy, while its noble foundations are hidden from his sight ; nor would we assure him that he can contemplate the structure in its true magnificence, while its basement alone is within his field of vision. W T e would, therefore, that the student of astronomy should confine his attention neither to the exterior of the building, nor to the mere analytic investigation of its structure. We would desire that he should not only study it in models and diagrams, and mathematical formulas, but should at the same time acquire a love of nature herself, and cultivate the habit of raising his views to the grand originals. Nor is the effort to form a clear conception of the motions and dimensions of the heavenly bodies, less favorable to the improvement of the intellectual powers, than the study of pure geometry.

But it is evidently possible to follow oat all the intricacies of an analytical process, and to arrive at a full conviction of the great truths of astronomy, and yet know very little of nature. According to our experience, however, but few students in the course of a liberal education will feel satisfied with this. They do not need so much to be convinced that the assertions of astronomers are true, as they desire to know what the truths are, and how they were ascertained ; and they will derive

VI

from the stud)' of astronomy little of that moral and intellectual elevation which they had anticipated, unless they learn to look upon the heavens with new views, and a clear comprehension of their wonderful mechanism.

Much of the difficulty that usually attends the early progress of the astronomical student, arises from his being too soon introduced to the most perplexing part of the whole subject,— the planetary motions. In this work, the consideration of these is for the most part postponed until the learner has become familiar with the artificial circles of the sphere, and conversant with the celestial bodies. We then first take the most simple view possible of the planetary motions by contemplating them as they really are in nature, and afterwards proceed to the more difficult inquiry, why they appear as they do. Probably no science derives such signal advantage from a happy arrangement, as astronomy ; — an order, which brings out every fact or doctrine of the science just in the place where the mind of the learner is prepared to receive it.

ANALYSIS.

PRELIMINARY OBSERVATIONS.

Article.

Astronomy, and its divisions 1

Descriptive, physical, practical 1

History. — Ancient nations who cultivated astronomy 2

Pythagoras — his time — his views. ... 2

Alexandrian school — Hipparchus. . . . 2

Ptolemy — the Almagest 2

Copernicus, Tycho Brahe, Kepler, Galileo, Newton, La Place 2

Astrology — Natural— Judicial 8

Accuracy aimed at in astronomy. .... 4 Truths not always to be proved when

stated 5

Coperniean system — its doctrines. ... 6

Plan of the work 7

PAET I. THE EARTH.

Chapter I. — Of the figure and size of THE EARTH, AND THE DOCTRINE OF THE SPHERE

Figure of the earth — proofs 8

Dip of the horizon 9

Its relation to height — table 10

The exact form 11

Dimensions of the earth 12

How found 13, 14

Erroneous ideas of up and down 15

Sections by a plane 17

Axis of a circle — poles 18, 19

Great circles bisect each other 20

Secondaries 21

Measure of inclination. 22

Terrestrial and celestial spheres ..... 23

Horizon— rational and sensible 24

Zenith and Nadir. 25

Vertical circles — meridian, prime vertical , 26

Co-ordinates for the horizon, amplitude, or azimuth — altitude, or zenith distance 27

Axis and poles of the earth 28

Equator— equinoctial 29

Its secondaries— the meridians, or

hour circles 30

Latitude — polar distance 31

Longitude , , 32

The ecliptic — inclination to the equator 33

Vernal and autumnal equinoxes 34

Solstices— signs of the zodiac 85

Article.

Colures — equinoctial, solstitial 36

Co-ordinates to the equinoctial — right

ascension, declination 37

Co-ordinates to the ecliptic, celestial

longitude and latitude 37

Parallels of latitude 38

Tropics 39

Polar circles 40

Zones 41

Zodiac 42

Elevation of the pole 43

Elevation of the equator 44

Polar distance 45

Chapter II. — Diurnal revolution — Artificial GLOBES — ASTRONOMICAL PROBLEMS, Circles of Diurnal Ee volution 46

Sidereal day defined 47

Appearance of the circles of diurnal

revolution at the equator 49

A Right Sphere defined 49

A Parallel Sphere 50-52

An Oblique Sphere 53

Circle of Perpetual Apparition ...... 54

Circle of Perpetual Occupation 55

How are the circles of daily motion cut by the horizon in the different

spheres 56

Explanation of the peculiar appearances of each sphere, from the revolution of the earth on its axis. .. .57-60 Artificial Globes — terrestrial and celestial 61

Meridian — how represented — how

graduated 62

Horizon — how represented — how graduated 62

Hour Circles — how represented 63

Hour Index described 64

Quadrant of Altitude — its use 65

To rectify the globe for any place. ... 66 Problems on thk Terrestrial Globe —To find the latitude and longitude

of a place 67

To find & place, its latitude and longitude being given 68

To find the bearing and distance of

two places 69

To determine the difference of time of

two places 70

The hour being given at any place, to tell what hour it is in any "other part

of the world 71

To find the antoeci, periceci, and antipodes 72

Vlll

ANALYSIS.

Art.

To rectify the globe for the sun's place 73

The latitude of the place being given, to find the time of the sun's rising and setting 74

Problem.? on the Celestial Globe. —

To find the right ascension and declination ... 75

To represent the appearance of the heavens at any time 76

To find the altitude and azimuth of a star , 77

To find the angular distance of two stars from each other 78

To find the sun's meridian altitude, the latitude and day of the month being given 79

Chapter III. — Parallax — Refraction — Twilight. Parallax defined — diurnal 80

True place 81

Relation of parallax to the zenith distance, and distance from the center

of the earth 82

To find the horizontal parallax from

the parallax at any altitude 83

Amount of parallax in the zenith and

in the horizon 83

Effect of parallax upon the altitude of

a body 84

Mode of determining the horizontal

parallax of a body 85

Amount of the sun's hor. par 86

Use of parallax 87

Refraction. — Its effect upon the altitude of a body 88

Its nature illustrated 88

Its amount at different angles of elevation 89

How the amount is ascertained 90-91

Sources of inaccuracy in estimating

the refraction 92

Effect of refraction upon the sun and

moon when near the horizon 93

Oval figure of these bodies explained. 94 Apparent enlargement of the sun and

moon near the horizon 95

Twilight.— its, cause explained 96

Length of twilight in different latitudes 97

How the atmosphere contributes to diffuse the sun's light 98

Chapter IV.— Time. Time defined 99

What period is a sidereal day 100

Uniformity of sidereal days 100

Solar time, how reckoned 101

Why solar days are longer than sidereal 101

Apparent time defined 102

Mean time 103

An astronomical day 103

Equation of time defined 104

When do apparent time and mean

time differ most 104

When do they come together 104

Art.

Effect of a change in the place of the earth's perihelion 104

Causes of the inequality of the solar days 105

Explain the first cause, depending on the unequal velocities of the sun. . 105

Explain the second cause, depending on the obliquity of the ecliptic. .106-108

When does the sidereal day commence , 109

The Calendar.— Astronomical year defined 110

How the most ancient nations determined the number of days in the year Ill

Julius Caesar's reformation of the calendar explained Ill

Errors of this calendar 112

Reformation by Pope Gregory 112

Rule for the Gregorian calendar 112

New style, whenadopted in England. 113

What nations still adhere to the old style 113

What number of days is now allowed between old and new style 114

How the common year begins and ends 115

How leap year begins and ends 115

Does the confusion of different calendars affect astronomical observations 116

Chapter V. — Astronomical Instruments and Problems — Figure and Density of the Earth. How the most ancient nations acquired

their knowledge of astronomy 117

Use of Instruments in the Alexandrian School 117

Ditto, by Tycho Brahe 117

Ditto, by the Astronomers Royal 117

Space occupied by \" on the limb of

an instrument 117

Extent of actual divisions on the limb/ 118

Vernier defined 118

Its use illustrated ^ 119

Chief astronomical instruments eau-

merated 120

Observations taken on the meridian. 120

Reasons of this. 120

Transit Instrument defined 121

Ditto, described 121

Method of placing it in the meridian. 122

Line of collimation defined 123

System of wires in the focus 123

Astronomical Clock— how regulated . . 124

What does it show 124

How to test its accuracy 124

Rate and error 124

American method 125

Mural Circle — its object 126

Describe it 126

How the different parts contribute to

the object 126

Use of the Mural Circle for arcs of

declination 127

Altitude and Azimuth Instrument defined 128

Its use 12S

ANALYSIS.

IX

Art.

Describe it 128

Sextant described 129

How to measure the angular distance

of the moon from a star. .■ 129

How to take the altitude of a heavenlybody 129

Use of the artificial horizon 130

In what consists the peculiar value of

the sextant . 130

Astronomical Problems. — Given the sun's right ascension and declination, to find his longitude and the

obliquity of the ecliptic 132

Napier's rule of circular parts 132

Given the sun's declination to find his rising and setting at any place whose

latitude is known 133

Given the latitude of a place and the declination of a heavenly body, to determine its altitude and azimuth when on the six o'clock hour circle. 134 The latitudes and longitudes of two celestial objects being given, to find

their distance apart 135

Figure and Density of the Earth — reason for ascertaining it with great

precision 136

How found from the centrifugal force. 137 From measuring an arc of the meridian 138 From observations with the pendulum 139

From the motions of the moon 140

From precession 141

Density of the earth 141

How ascertained by Dr. Maskelyne.. 141 Why an important element 141

Chapter I. — The Sun — Solar Spots — Zodiacal Light. Figure of the sun 143

Angle subtended by a line of 400 miles 143

Distance from the earth 144

Illustrated by motion on a railway car. 144 Apparent diameter of the sun — how

found 145

How to find the linear diameter 145

How much larger is the sun than the

Its density and mass compared with

the earth's 146

Weight at the surface of the sun 146

Velocity of falling bodies at the sun. 146

Solar Spots. — Their number 147

Size 147

Description 147

What region of the sun do they occupy 147

Proof that they are on the sun 148

How we learn the revolution of the

sun on his axis 148

Time of the revolution 148

Apparent paths of the spots 149

Inclination of the solar axis 149

Sun's Nodes — when does the sun pass

them? 150

Faculae 151

Art.

Theory of the spots 151

Zodiacal Light. — Where seen 152

Its form 152

Aspects at different seasons 152

1 ts motions 152

Its nature 152

Chapter II. — Apparent Annual Motion of the Sun — Seasons — Figure of thb Earth's Orbit. Apparent motion of the sun 153

How both the sun and earth are said

to move from west to east 154

Nature and position of the sun's orbit,

how determined 155

Changes in declination, how found. . 155

Ditto, in right ascension 156

Inferences from a table of the sun's

declinations 156

Ditto, of right ascensions 156

Path of the sun, how proved to be a

great circle 156

Obliquity of the ecliptic, how found. . 157

How it varies 157

Great dimensions of the earth's orbit. 158

Earth's daily motion in miles 158

Ditto, hourly, ditto 158

Diurnal motion at the equator per hour 158 Seasons. — Causes of the change of

seasons 159

How each cause operates 159

Illustrated by a diagram 160

Change of seasons had the equator

been perpendicular to the ecliptic. . 161 Figure of the Earth's Orbit. — Proof that the earth's orbit is not circular. 161

Radius vector defined 162

Figure of the earth's orbit, how obtained 162

Relative distances of the earth from

the sun, how found 163

Perihelion and Aphelion defined 164

Variations in the sun's apparent diameter 164

Angular velocities of the sun at the

perihelion and aphelion 165

Ratio of these velocities to the distances 165

How to calculate the relative distances of the earth from the sun's daily motions 165

Product of the angle described in any given time by the square of the distance 167

Space described by the radius vector

of the solar orbit in equal times. . . 168 How to represent the sun's orbit by a diagram 168

Chapter III. — Central Forces — Gravitation. Two forces in curved motion 170

Centripetal and centrifugal 170

Kepler's laws 171

First law — second — third 171

First principles in mechanics and astronomy identical 171

Kepler's first law proved 172

ANALYSTS.

Art.

Its converse 173

Measure of velocity in an orbit 174

Modification for those nearly circular. 174

Centrifugal force 175

First law of central force in circular

orl.it 176

Second ditto 177

Law of gravity in an elliptical orbit. . 178

Proof. 179

Same law for different orbits— proof. . 181 Bodies on the earth compared with

Same law explains disturbances 182

Gravity as quantity of matter. . .... 182

Projectiles 183

"Why parabola, not ellipse 183

Time of complete revolution of a projectile 183

Different forms of projectile paths. . . 184

Place of perigee and apogee 184

Annual and diurnal rotation by one

impulse 185

Effect of impulse on the system 186

Two bodies supposed 186

Motion of center 186

Motion of each body 186

Epicycloids, two forms 186

Where retrograde motion 186

How center can be kept at rest 186

Why planet returns from aphelion. . . 187

Why it departs from perihelion 187

Change in centrifugal force, compared with that in centripetal 187

Chapter IV. — Precession of the Equinoxes — Nutation — Aberration — Mean and True Places of the Sun.

Precession of the equinoxes defined. . 188

Why so called 188

Amount of precession annually 189

Eevolution of the equinoxes 189

Revolution of the pole of the equator

around the pole of the ecliptic 190

Changes among the stars caused by

precession 190

The present pole-star not always such. 190 What will be the pole-star 13,000 years

hence? 190

Cause of the precession of the equinoxes 191

Explain how the cause operates 191

Proportionate effect of the sun and

moon in producing precession 192

The law of compound rotations 192

Tropical year defined 193

How much shorter than the sidereal

year 193

Use of the precession of the equinoxes

in chronology 193

Nutation, defined 1 94

Explain its operation 194

Cause of nutation 194

Aberration, defined 195

Illustrated by a diagram 195

Amount of aberration 195

Effect on the places of the stars 195

Motion of the Apsides — the fact

stated 196

Art.

Direction of this motion Iy6

Time of revolution of the line of apsides 196

Present longitude of the perihelion. . . 196

Cause of advance of apsides 196

Anomaly defined 197

Anomalistic year, its length 197

Slow change in duration of the seasons. 198 Mean and True Places of the Sun. . 199

Mean Motion defined 199

Illustrated by surveying a field 199

Mean and true longitudedistinguished 199

Equations defined 200

Their object 200

Mean and True Anomaly defined 200

Equation of the center 200

Explain from the figure 200

Chapter V. — The Moon — Lunar Geography — Phases of the Moon — Her Revolutions. Distance of the moon from the earth. 201

Her mean horizontal parallax 201

Her diameter 201

Volume, density, and mass 201

Shines by reflected light 202

Appearance in the telescope 202

Terminator defined 203

Its appearance 203

Proofs of mountains and valleys. .... 20D

Form of the valleys 204

Ring-mountains— bulwark plains 204

Lava-lines seen at full moon 205

Water, clouds, vegetation 205

Explain the method of estimating the

height of lunar mountains 206

Has the moon an atmosphere? 209

Improbability of identifying artificial

structures in the moon 210

Phases of the Moon, their cause... 211 Successive appearances of the moon

from one new moon to another 211

Syzygies defined 211

Explain the phases of the moon from

figure 46 212

Revolutions of the Moon. Period

of her revolutions about the earth.. 213

Her apparent orbit a great circle 213

A sidereal month defined 213

A synodical do. 213

Length of each 213

Why the synodical is longer 213

How each is obtained 213

Inclination of the lunar orbit 214

Nodes defined 214

Why the moon sometimes runs high

and sometimes low 215

Harvest moon defined 216

Ditto explained 216

Explain why the moon is nearer to us

when on the meridian than when

near the horizon . 217

Time of the moon's revolution on its

axis 218

How known 218

Librations explained 219

Diurnal libration 21 9

Length of the lunar days 220

ANALYSIS.

XI

Earth never seen on the opposite side of the moon ' 220

Appearances of the earth to a spectator on the moon . . 220

"Whv the earth would appear to remain fixed 220

Path of the moon in space 221

How much more is the moon attracted toward the sun than toward the earth? 222

"When does the sun act as a disturbing force upon the moon ? 222

"Why does not the moon abandon the earth at the conjunction ? 222

The moon's orbit concave toward the sun 223

Chapter VI. — Lunar Irregularities. Specify their general cause 225

Unequal action of the sun upon the

earth and moon 225

Oblique action of earth and sun 225

Gravity of the moon toward the earth

at the syzygies 226

Gravity at the quadratures 226

Explain the disturbances in the

moon's motions from figure 48 228

Figure of the moon's orbit 230

How its figure is ascertained 230

Moon's greatest and least apparent

diameters 230

Her greatest and least distances from

Perigee and Apogee defined 230

Eccentricities of the solar and lunar

orbits compared 230

Moon's nodes, their change of place. . 231 Rate of this change per annum. ...... 231

Period of their revolution 231

Irregular curve described by the

moon 232

Cause of the retrograde motion of

nodes 232

Explain from figure 50 232

Svnodical revolution of the node destined 233

Its period 233

The Saros explained 233

The Metonic Cycle. 234

Golden Number 234

Revolution of the line of apsides 235

Its period 235

How the places of the perigee may be

found 235

Moon's anomaly defined. 235

Cause of the revolution of the apsides, 236 Amount of the equation of the center. 237

Ejection defined 238

Its cause explained 239

Variation defined 240

Its cause 240

Annual Equation explained 241

How these irregularities were first discovered 242

How many equations are applied to

the moon's motions ? 242

Method of proceeding in finding the

moon's place . » 242

Successive degrees of accuracy attained . . 242

Periodic and secular irregularities distinguished 243

Acceleration of the moon's mean motion explained 243

Its consequences 243

Lunar inequalities of latitude and parallax 244