Spherical Astronomy

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Paperback | 30 December 1985

At a Glance

Paperback
536 Pages

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22.86 x 15.24 x 3.02

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This is an introductory textbook on spherical and positional astronomy. It is entirely suitable for use by students with no prior knowledge of classical astronomy. At the same time, it is sufficiently comprehensive to make it a useful background reference book for anyone engaged in practical astronomy. The first three chapters sketch essential background: mathematical techniques and coordinate systems. Successive chapters then give treatments of refraction, aberration, stellar parallex, precession, nutation and proper motion. An entire chapter is devoted to astrographic plate measurements. The gravitational two-body problem is solved and applied to solar system dynamics. Novel areas include a full treatment of binary star orbits and two chapters on developments in radio astronomy. Worked examples and problems to be solved by the reader ensure that this is a valuable textbook.

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Non-Fiction Science Astronomy, Space & Time Physics Applied Physics Astrophysics

Preface	p. xi
Basic formulae
Introduction	p. 1
Spherical geometry - great circle arcs	p. 1
Spherical polar coordinates	p. 6
Spherical trigonometry - basic formulae	p. 8
Terrestrial latitude and longitude	p. 12
Right ascension and declination	p. 14
The displacement of a star on the celestial sphere	p. 16
The celestial sphere
Introduction	p. 22
The alt-azimuth system	p. 23
Hour angle and declination	p. 25
Sidereal time and right ascension	p. 30
The ecliptic and ecliptic coordinates	p. 32
Apparent and mean solar time	p. 35
Galactic coordinates	p. 40
Setting a telescope	p. 43
The reference frame
Inertial frames of reference	p. 48
Precession, nutation and proper motion	p. 49
The origin of the reference frame	p. 58
Selective review of special relativity	p. 62
General relativity	p. 70
General relativistic treatment of parallax, aberration and light deflection	p. 75
Geocentric coordinates
Introduction	p. 82
Approximate refraction formulae	p. 82
Refraction in a radially symmetric atmosphere	p. 87
The refraction constants and refraction tables	p. 93
Geocentric coordinates of the observer	p. 96
Geocentric parallax	p. 101
The effect of geocentric parallax on right ascension and declination	p. 106
Diurnal aberration	p. 109
Direct measurements of right ascension and declination
Introduction	p. 113
Errors of the meridian circle	p. 114
The removal of instrumental effects	p. 117
Reduction to the apparent place	p. 122
Polar motion	p. 124
The Danjon astrolabe and the photographic-zenith tube	p. 128
Two-body orbital motion
Basic equations	p. 137
Kepler's equation for a bound orbit	p. 139
Kepler's three laws	p. 143
The solution of Kepler's equation	p. 144
The equation of the centre	p. 147
Components of a planet's velocity	p. 148
Elliptic and hyperbolic orbits	p. 149
Comparison of general relativity with Newtonian theory	p. 151
The Kepler solution in general relativity	p. 153
The relativistic advance of perihelion	p. 156
Planetary and satellite orbits
The orbit in space	p. 162
Calculation of an ephemeris	p. 165
Planetary masses	p. 167
Planetary perturbations	p. 169
The orbit of the moon	p. 171
Calculation of osculating elements	p. 176
Preliminary orbit determination	p. 178
Heliocentric and barycentric coordinates
Introduction	p. 184
The motion of the earth	p. 184
Annual parallax	p. 187
Annual aberration	p. 189
Low precision formulae for parallax and aberration	p. 190
Planetary aberration	p. 193
General relativistic light deflection	p. 196
The direction of the null geodesic	p. 200
Relativistic derivation of the apparent place of a star	p. 202
Summary	p. 204
Precession and nutation
Introduction	p. 208
Luni-solar precession	p. 208
Planetary precession	p. 211
General precession	p. 214
Rigorous formulae	p. 217
Rotation matrices	p. 220
Approximate formulae	p. 222
Nutation	p. 225
The effect of nutation on a star's coordinates	p. 230
Time
Astronomical and physical concepts of time	p. 236
Sidereal and solar time	p. 240
Ephemeris and universal time	p. 242
Modern dynamical time-scales	p. 245
The Julian and the Besselian year	p. 249
Ephemeris transit	p. 251
Proper and coordinate time	p. 253
The computation of light-time - radar delays	p. 255
Proper motion and radial velocity
Components of stellar motion	p. 259
Intrinsic changes in proper motion	p. 262
Precessional changes in proper motion	p. 265
Barycentric radial velocity	p. 268
Pulsar timing	p. 271
The red-shift in general relativity	p. 272
Systematic effects in proper motion and radial velocity	p. 276
The cosmological red-shift	p. 279
Mean and apparent coordinates
Terminology	p. 284
The annual and secular variations	p. 286
A star's true place	p. 288
A star's apparent place	p. 290
Vector derivation of a star's apparent place	p. 295
The apparent place of a planet	p. 299
Star catalogues	p. 303
Astrographic plate measurements
Central projection	p. 307
Standard coordinates	p. 310
Centring error	p. 313
Refraction and annual aberration	p. 315
The plate constants	p. 319
Principles of plate reduction	p. 322
The method of dependences	p. 325
Direct use of rectangular coordinates	p. 328
Stellar distances and movements
Some astrophysical background	p. 333
Measurement of parallax and proper motion	p. 339
Distances of nearby stars	p. 342
The solar motion	p. 346
Statistical parallax	p. 350
Galactic coordinates	p. 353
Oort's constants	p. 356
The effect of galactic rotation on proper motions	p. 358
Elements of radio astronomy
Introduction	p. 362
Radio interferometry	p. 366
A radio transit instrument	p. 370
Phase ambiguity	p. 372
North-south interferometer	p. 374
The interferometer of general orientation	p. 378
Polar motion	p. 380
Aperture synthesis	p. 382
Rotational synthesis	p. 385
Radio astrometry
Introduction	p. 389
Twelve-hour connected interferometry	p. 390
Very long baseline interferometry	p. 392
Source directions and baseline vectors	p. 397
Media effects	p. 400
Relativistic effects	p. 405
The radio and stellar reference frames	p. 409
Planetary phenomena and surface coordinates
The apparent motion of an inferior planet	p. 415
The apparent motion of a superior planet	p. 418
Stationary points	p. 420
Planetary phases	p. 422
Planetographic coordinates	p. 425
Planetographic coordinates of a point on the disc	p. 429
Heliographic coordinates	p. 430
Heliographic coordinates of a sunspot	p. 433
Selenographic coordinates	p. 434
Eclipses and occultations
Classification of eclipses	p. 439
Conditions for a lunar eclipse	p. 441
Conditions for a solar eclipse	p. 443
Ecliptic limits	p. 444
Frequency and recurrence of eclipses	p. 448
Besselian elements of a solar eclipse	p. 450
Solar eclipse calculations	p. 453
Eclipse magnitudes	p. 457
Occultations by the moon	p. 459
Binary stars
Introduction	p. 465
Orbital elements of a binary system	p. 467
The Thiele-Innes method	p. 470
The Lehmann-Filhes method	p. 474
The masses of visual binaries	p. 478
Spectroscopic binary masses	p. 481
The binary pulsar	p. 484
Tensor methods
Introduction	p. 491
Tensors	p. 493
The metrical tensor	p. 496
Geodesics	p. 498
Curved spacetimes	p. 499
Astronomical constants
Fundamental constants	p. 502
Planetary data	p. 503
Answers to the numerical problems
References	p. 509
Index	p. 511
Table of Contents provided by Syndetics. All Rights Reserved.

Spherical Astronomy

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