Mechanics of the Solar System : An Introduction to Mathematical Astronomy.

Cover -- Dedication -- Title Page -- Copyright -- Contents -- Introduction -- Chapter 1 Time and Space in Astronomy -- 1.1 Time -- 1.2 Universal Time -- 1.3 The solar year -- 1.4 The modern calendar -- 1.5 Julian Day numbers -- 1.6 Sidereal time -- 1.7 Flamsteed and the RGO -- 1.8 The celestial sphere -- 1.9 Coordinate systems -- 1.10 Ecliptic and equatorial coordinates -- 1.11 Transformation of coordinates between the ecliptic and equatorial systems -- 1.12 Equatorial coordinates of the Sun -- 1.13 Parallax -- 1.14 Angular separation -- 1.15 Celestial line-ups -- 1.16 Terrestrial coordinates -- 1.17 Directions of cardinal points in terms of a &amp -- A -- 1.18 Rising and setting -- 1.19 Stellar transits across a local meridian -- 1.20 Exercises -- Chapter 2 Planetary Motion -- 2.1 Ancient and modern conceptions of the Cosmos -- 2.2 Kepler and Newton -- 2.3 Properties of a planetary orbit -- 2.4 The mean anomaly -- 2.5 Orientation of the orbit -- 2.6 Determination of the ecliptic coordinates of a planet -- 2.7 Non-periodic orbits -- 2.8 Exercises -- Chapter 3 The General Kepler Problem -- 3.1 Introduction -- 3.2 Determination of the anomaly -- 3.3 An approximation for ϕ in a periodic orbit -- 3.4 Conclusion -- 3.5 Examples -- 3.6 Exercises -- Appendix -- Chapter 4 Calculation of the Position and Velocity of a Planet -- 4.1 Calculation from orbital elements -- 4.2 Comets -- 4.3 Calculation from VSOP -- 4.4 Geocentric position and velocity vectors -- 4.5 Time derivatives of geocentric coordinates -- 4.6 Exercises -- Chapter 5 Geocentric Observation -- 5.1 Relative motion -- 5.2 A schematic model -- 5.3 Geocentric orbits -- 5.4 Special events -- 5.5 Realistic calculations -- 5.6 Sample results for two planets -- 5.7 Planetocentric data -- (i) Planetocentric declination of the Sun and Earth -- (ii) Longitude of the Planet's central meridian.

(iii) The angles P &amp -- Q -- 5.8 Exercises -- Chapter 6 Corrections to the Apparent Position of a Planet -- 6.1 Method of calculation -- 6.2 ΔT -- 6.3 Aberration -- 6.4 Nutation -- 6.5 Conclusion -- 6.6 Stellar aberration -- 6.7 Exercises -- Chapter 7 Precession -- 7.1 The Earth as a very large top -- 7.2 Low accuracy calculation of the effects of precession 121 -- 7.3 The precession matrix -- 7.4 Equatorial coordinates -- 7.5 The Eulerian angles method -- 7.6 Instantaneous rate of precession -- 7.7 Reduction of orbital elements to a standard epoch -- 7.8 Exercises -- Chapter 8 Solar Transits of the Inner Planets -- 8.1 Rare events -- 8.2 Anatomy of a transit -- 8.3 Transits in history -- 8.4 Method of calculation -- 8.5 Transit systematics -- Mercury -- Venus -- 8.6 Topocentric effects and visibility of transits -- 8.7 Determining the size of the Solar System -- 8.8 Exercises -- Appendix -- Chapter 9 Seven Assorted Topics -- 9.1 Lagrange and the restricted three-body problem -- 9.1.1 Introduction -- 9.1.2 Lagrangian mechanics -- 9.1.3 The restricted three-body problem -- 9.1.4 Equilibrium points -- 9.1.5 Stability -- 9.1.6 The normal modes at L1, L2 &amp -- L3 -- 9.1.7 The points L4 and L5 -- 9.1.8 Discussion -- Appendices A, B -- 9.2 Orbital elements from the position and velocity vectors of the planet -- 9.2.1 Calculation of the orbital elements -- 9.2.2 Time dependence of the orbital elements -- 9.3 The anomalous motion of Mercury -- 9.3.1 Perihelion precession -- 9.3.2 New theory of gravity: GR -- 9.3.3 Application to Mercury -- 9.4 MOID -- 9.4.1 Oumuamua -- 9.5 Simple theory of the EOT -- 9.5.1 Qualitative argument -- 9.5.2 Lowest order calculation -- 9.6 Apparent and absolute visual magnitude -- 9.6.1 Stellar parallax -- 9.6.2 Stellar visual magnitude -- 9.6.3 Visual magnitude of a planet -- 9.7 Celestial navigation -- 9.7.1 Lunar distance.

9.7.2 Stellar altitudes -- Chapter 10 Mathematical Notes -- 10.1 Vectors -- 10.2 Matrices -- 10.3 Rotations of the coordinate axes -- 10.4 Non-commutation of finite rotations - experimental proof -- 10.5 The G-matrices -- 10.6 More about vector products -- 10.7 Angular velocity -- 10.8 General forms for finite rotations -- References -- Solutions to the exercises.

This book develops methods of computing astronomical phenomena from basic ideas. The position of a celestial body is defined by a vector, with components referred to a system of coordinate axes. The relations between various systems in regular use by astronomers are described. In cases where two systems differ in spatial orientation, they are related by a rotation matrix. These matrices are discussed in considerable detail in the mathematical notes. _x000D_ Other topics discussed include: Kepler's Laws and the dynamics of planetary motion, Precession and Nutation, transits of Venus and Mercury, Lagrange points._x000D_ While no previous knowledge of Astronomy is necessary, it is assumed that the reader is familiar with elementary algebra, trigonometry and calculus.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.