Theoretical Astronomy Relating to the Motions of the Heavenly Bodies Revolving Around the Sun in Accordance with the Law of Universal Gravitation: Embracing a Systematic Derivation of the Formulae for the Calculation of of the Geocentric and Heliocentric Places, for the Determination of the Orbits of Planets and Comets, for the Correction of Approximate Elements, and for the Computation of Special Perturbations ; Together with the Theory of the Combination of Observations and the Method of Least Squares

Framhlið kápu
J.B. Lippincott, 1896 - 662 síður
 

Valdar síður

Efni

Determination of the Position in Space
81
Transformation of Spherical Coordinates
87
Reduction of the Elements from one Epoch to another
99
Interpolation
112
Variation of the Right Ascension and Declination
125
Equations of Condition
127
Case of Hyperbolic Motion
134
Variation of the Longitude and Latitude
143
The Elements referred to the same Fundamental Plane as the Geocentric Places
149
Numerical Example
159
CHAPTER III
166
Determination of the Curtate Distances
181
Determination of the Node and Inclination
192
Numerical Example
199
Correction of Approximate Elements by varying the Geocentric Distance
208
CHAPTER IV
220
Corrections for Parallax
227
Formula for the Curtate Distances
228
Determination of the Curtate Distance for the Middle Observation
236
Position indicated by the Curvature of the Observed Path of the Body
242
Final Correction for Aberration
257
Numerical Example
265
Correction of the First Hypothesis
278
Determination of the Curtate Distances
289
Numerical Example
295
Method for the Final Approximation
307
Variation of Two Geocentric Distances
315
Variation of the Node and Inclination
325
Determination of the Elements of the Orbit by means of the Coordinates
332
Final Correction of the Elements
338
Modification for Hyperbolic Motion
346
CHAPTER VII
360
The Measure of Precision and the Probable Error
366
Weights of Observed Values
372
Normal Equations
378
Determination of the Weights of the Resulting Values of the Unknown Quanti
386
Separate Determination of the Unknown Quantities and of their Weights
392
Determination of the Heliocentric or Geocentric Place
471
Change of the Osculating Elements
477
Fundamental Equations
483
Determination of the Components of the Disturbing Force 489
489
Determination of the Place of the Disturbed Body
495
Variation of the Node and Inclination
502
Change of the Osculating Elements
516
Case of very Eccentric Orbits
523
Numerical Example
529
Correction of the Assumed Value of the Disturbing Mass
535
Near Approach of a Comet to a Planet
546
Effect of a Resisting Medium in Space
552
Angle of the Vertical and Logarithm of the Earths Radius
561
For converting Intervals of Mean Solar Time into Equivalent Intervals of Sidereal Time
563
For converting Intervals of Sidereal Time into Equivalent Intervals of Mean Solar Time
564
For converting Hours Minutes and Seconds into Decimals of a Day
565
For finding the True Anomaly or the Time from the Perihelion in a Parabolic Orbit
566
For finding the True Anomaly in a Parabolic Orbit when v is nearly 180 611
vii
For finding the Time from the Perihelion in a Parabolic Orbit 612
viii
For finding the True Anomaly or the Time from the Perihelion in Orbits of Great Eccentricity 614
viii
CHAPTER
viii
For finding the True Anomaly or the Time from the Perihelion in El liptic and Hyperbolic Orbits 618
x
For the Motion in a Parabolic Orbit 619
xi
Fundamental Equations
xiii
For the Limits of the Roots of the Equation sin 2 m sin z 622
xiv
For finding the Ratio of the Sector to the Triangle 624
xvi
For finding the Ratio of the Sector to the Triangle 629
For Elliptic Orbits of Great Eccentricity 632
For Special Perturbations 633
Elements of the Orbits of the Comets which have been observed 638
Elements of the Orbits of the Major Planets 648
Constants c 649
EXPLANATION OF THE TABLES 651
APPENDIX Precession 657
Aberration 659
Intensity of Light 660
Numerical Calculations 662

Aðrar útgáfur - View all

Theoretical Astronomy Relating to the Motions of the Heavenly Bodies ...
James Craig Watson
Heildartexta - 1869
Theoretical Astronomy Relating to the Motions of the Heavenly Bodies ...
James Craig Watson
Heildartexta - 1885
Theoretical Astronomy Relating to the Motions of the Heavenly Bodies ...
James Craig Watson
Heildartexta - 1868
View all »

Common terms and phrases

accuracy already angle applied approximate elements approximate values ascending node ascension and declination assumed values auxiliary axis becomes calculation centre of gravity comet computed correct value cos² cosi denote determined differences differential coefficients directly distance disturbed body disturbing force dx dy dy dz earth eccentric anomaly eccentricity ecliptic and mean ephemeris equa equations of condition error Eurynome expressed in seconds formulæ found by means fundamental plane geocentric places given heavenly body heliocentric co-ordinates hyperbolic hyperbolic motion integration intervals logarithms mass mean anomaly mean equinox multiply observed places obtain orbit parallax perihelion perturbations positive radius-vector reduced referred respect retrograde motion right ascension second member sin² Substituting system of elements Table tions true anomaly unknown quantities variations velocity απ

Bókfræðilegar upplýsingar

TitillTheoretical Astronomy Relating to the Motions of the Heavenly Bodies Revolving Around the Sun in Accordance with the Law of Universal Gravitation: Embracing a Systematic Derivation of the Formulae for the Calculation of of the Geocentric and Heliocentric Places, for the Determination of the ...
Bindi 408 of Harvard Widener Library astronomy preservation microfilm project
HöfundurJames Craig Watson
ÚtgefandiJ.B. Lippincott, 1896
Original fromla Biblioteca de Catalunya bókasafnið
Digitized19 apr. 2010
Length662 síður
  
Export CitationBiBTeX EndNote RefMan