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An Elementary Treatise on the Planetary…
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An Elementary Treatise on the Planetary Theory. With a collection of…

by Charles Hartwell Horne Cheyne

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Indeholder "Preface to the first edition", "Note on changes in the Second Edition", "Chapter I. Introduction", " 1. Necessity of approximate methods", " 2. Deviations of the planets from elliptic motion", " 3. Elements of the orbit", " 4. Plane of the orbit", " 5. The Sun and planets considered to attract as if they were collected into their respective centres of gravity", " 6. Principle of Superposition of Small Motions, when admissible", " 7. Difference between the Lunar and Planetary Theories", " 8. Component of the disturbing force in any direction. Disturbing function", " 9. Meaning of the symbol dR/ds", " 10. Disturbing function independent of any particular system of co-ordinates that may be employed", " 11. Transformation of the expression for B? 7 ", " 13. To explain how R may be expressed in terms of the time and the elements of the orbit", " 14. Relations between the partial differential coefficients of R", "Chapter II. Formulæ for calculating the elements of the orbit", " 18. Equations of motion", " 19. Definition of the term fixed in the plane of the orbit", " 21. Principle of the method of the Variation of Parameters", " 22. Application of this method to the equations of motion", " 23. Definition of the instantaneous ellipse", " 24. To obtain formulas for calculating the elements", " Process explained", " Mean distance", " Excentricity", " Longitude of perihelion", " Node and inclination", " Epoch", " Mean motion", " 39. Recapitulation of formulæ for calculating the elements", "Chapter III. Development of the disturbing function", " 42. Expansions of r_1, r_1', theta_1, theta_1', z and z'", " 43. Substitution of these in the expression for R", " 46. Form of the terms in the development of R", " 47. Determination of that part of R which is independent of the time explicitly", " 50. Order of magnitude of the periodical terms", " 52, Proof that (a^2 + a'^2 - 2*a*a'*cos(phi))^(-1) can be expanded in a series of cosines of multiples of phi", " 53. Calculation of the coefficients", " 58. Simplification of the expression for F", "Chapter IV. Secular variations of the elements of the orbit. Stability of the planetary system", " 60. Definition of the term secular", " 61. Formulæ for calculating the secular variations", " 62. Approximate method of calculation", " 63. Stability of the planetary system", " Stability of the mean distances", " Stability of the excentricities and inclinations", "Chapter V. Secular variations of the elements continued. Integration of the differential equations", " 72. Integration of the equations for the excentricity and longitude of perihelion", " 74. Stability of the excentricities", " 76. Examination of the expression for the longitude of perihelion", " 77. When the apsidal line oscillates, to find the extent and periods of its oscillations", " 78. Geometrical interpretation of the equations which give the secular variations of the excentricity and longitude of perihelion", " 79. Integration of the equations for the inclination and longitude of the node", " 80. Stability of the inclinations", " 81. Examination of the expression for the longitude of the node", " 82. When the line of nodes oscillates, to find the extent and periods of its oscillations", " 83. Inclination of the orbits of two mutually disturbing planets to each other approximately constant", " 84. Geometrical interpretation of the equations which give the secular variations of the node and inclination", " 85. Integration of the equation for the longitude of the epoch", " 86. Secular acceleration of the Moon's mean motion", " 87. Formulae for calculating the node and inclination of the plane of a planet's orbit relatively to the true ecliptic", " 88. Invariable plane of the Solar System", "Chapter VI. Periodic variations of the elements of the orbit", " 89. Definition of the term Periodical Variations", " 91. Expressions for the periodical variations of the elements", " 92. Long inequalities", " 93. To select such terms in R as will produce the principal inequalities of long period", " 94. Relation between corresponding terms of the long inequalities in the mean motions of two mutually disturbing planets", " 95. Variations of elements whose periods are very long", " 96. Distinction between secular and periodic variations", " 98. Periodic variations in radius vector", " 99. Periodic variations in longitude", " 100. Example of the processes of this Chapter", "Chapter VII. Direct method of calculating the inequalities in radius vector, longitude, and latitude", " 102. Direct method contrasted with that of the proceding chapters", " 103. Equations of motion", " 105. Equation for the perturbation in radius vector", " 106. Equation for the perturbation in longitude", " 107. Equation for the perturbation in latitude", " 108. Integration of the equation for the perturbation in radius vector", " 109. First approximation to the value of σr", " 110. Omission of the arbitrary term", " 112. Certain terms to be neglected", " 113. Second approximation to the value of σr", " 114. Calculation of perturbations in longitude", " 115. Determination of the constant g", " 116. Long inequalities", " 117. Integration of the equation for the perturbation in latitude", "Chapter VIII. On the effects which a resisting medium would produce in the motions of the planets", " 118. Possibility of the existence of a very rare medium", " 119. Equations of motion", " 120. Formula for calculating the mean distance", " 121. Formula for calculating the excentricity", " 122. Formula for calculating the longitude of perihelion", " 123. Formula for calculating the longitude of the epoch", " 124. Transformation of the above formulae", " 125. Assumed form of the density", " 126. Effect of the medium upon the elements, the orbit being supposed nearly circular", " 127. The medium though insensible to the planets may yet affect the motions of comets", "Problems", "Appendix", " On the form of the equations of Art. 39", " Note to Arts. 31 and 33", " Example of numerical calculation", " On the methods of calculating the masses of the planets", " On the construction of Astronomical tables".

Smuk lille bog, der gennemgår, hvordan man beregner planetbaner og ellers har styr på at regne på halvlange aritmetiske udtryk. ( )
  bnielsen | Dec 13, 2016 |
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