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Introduction to the Mechanics of the Solar System
- 1st Edition - October 22, 2013
- Author: Rudolf Kurth
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 1 - 1 4 8 6 - 6
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 4 7 2 8 - 4
Introduction to the Mechanics of the Solar System introduces the reader to the mechanics of the solar system and covers topics ranging from the periods of the planets to their… Read more
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Request a sales quoteIntroduction to the Mechanics of the Solar System introduces the reader to the mechanics of the solar system and covers topics ranging from the periods of the planets to their flattening and its effects on the orbits of satellites. Kepler's three laws of planetary motion are also discussed, along with the law of gravity; the two-body problem; and perturbations in the motions of the moon and the planets. This book is comprised of four chapters and begins with an analysis of the kinematics of a single planet, focusing on the work of Johannes Kepler, particularly his determination of the orbits of the Earth and Mars and his formulation of his three laws of planetary motion. The following chapters explore systems of ordinary differential equations; determination of orbits using Laplace's method and Gauss' method; the equations of motion and their integrals; the perturbation equations of celestial mechanics; and Lagrange's solution of the three-body problem. The notations of the Earth and the moon are also considered. This monograph is intended for astronomers and astronomy students.
I. The Kinematics of a Single Planet
1. The Periods of the Planets
Kepler's Problem
Specification of Fixed Directions
Lower and Upper Bounds for the Period of a Planet
Approximate Determination of the Period
The Periods of Mercury and Venus
Observational Results
2. Kepler's Determination of the Orbits of the Earth and Mars: His First Law
Introductory Remarks
Kepler's Construction of the Earth's Orbit
His Construction of Mars' Orbit
Empirical Results
3. Kepler's Second and Third Laws
Kepler's Second Law
His Third Law
Applications
Summary
4. The Elements of a Planetary Orbit
The System of Co-ordinates
The Geometrical Elements
Transformations of Co-ordinates
The Kinematical Elements
5. The Computation of the Motion of a Planet
A direct Method
Derivation of Kepler's Equation
Its Analytical Solution
Successive Approximations
Relations between Eccentric and True Anomalies
The Vector of Position as a Function of the Elements and the Eccentric Anomaly
Its Analytical Properties
6. Orbital Determinations and their Improvement
Determination of the Elements from Two known Positions in Space
Determination from Known Position and Velocity Vectors
Determinations from Three Known Directions
Correction of Elements
The Influence of Observational Errors
The Earth's Motion
Aberration Time
7. Summary and Discussion
Exercises
Notes
II. The Dynamics of a Single Planet
1. The Law of Gravity and the Law of Motion
Postulates for the Concept of Force
Preliminary Formulation of Newton's Laws
Critical Remarks
Final Form of Newton's Laws
Summary
The Constant of Gravitation
2. Systems of Ordinary Differential Equations
The Principal Problem of Dynamics
Successive Approximations
Power Series
Application to the Two Body Problem
3. The Two Body Problem
The Integral of Area
The Energy Integral
The Relative Orbit
The Relative Motion
Parabolic Motions
Rectilinear Motions
The Relations between Period and Semi-major Axis
The Masses of the Planets
4. The Determination of Orbits
Laplace's Method
Gaus's Method
5. Summary
Exercises
Notes
III. The Dynamics of the Planetary System
1. The Equations of Motion and their Integrals
The Equations of Motion
Critical Note
Conservation of Momentum
The Center of Mass
Uniform Translations of the System of Co-ordinates
Conservation of Moment of Momentum
Generalization
Conservation of Energy
The Use of Known First Integrals
Relative Motions
2. Perturbations in the Co-ordinates
The Equations of Motion
Fourier Series Expansions
The Analytical Character of the Integrated Series
Gaus's Interpretation of the Secular Term
Determination of Neptune's Orbit
Perturbations in the Elements
3. Perturbations in the Elements
Variation of Parameters (Lagrange's Method)
Variation of Parameters (Poisson's Method)
Power Series of a Small Parameter
Jacobi's Variational Equations
Homogeneous Linear Systems
Inhomogeneous Linear Systems
Constant Coefficients
Small Oscillations
Periodic Coefficients
4. The Perturbation Equations of Celestial Mechanics
Survey
Poisson's Equation
Perturbation of the Major Axis
Perturbations of Eccentricity
Inclination and Nodal Line
The First Integral for the Direction of the Perihelion
Perturbation of the Direction of the Perihelion
Perturbation of the Perihelion Time
Summary
5. Perturbations in the Motions of the Planets
6. Perturbations in the Motion of the Moon
The Disturbing Force as a Function of Position
The Disturbing Force as a Function of the Time
Perturbation of the Semi-major Axis
The Perturbations of the Nodal Line, Inclination and Eccentricity
The Perturbation of the Apsidal Line
The Perturbation of the Solar Motion
7. The Perturbation of the Perihelion of Mercury
The General Formula
An Hypothesis about the Disturbing Force
8. Lagrange's Solution of the Three Body Problem
The Triangular Solution
The Rectilinear Solutions
9. The Problème Restreint
The Equations of Motion
Jacobi's Integral
Lagrange's Solutions
10. Summary
Exercises
Notes
IV. The Planets and the Moon as Rigid Bodies
1. Perturbations of the Orbits of Satellites caused by Flattening of the Planets
The Disturbing Force
Assumption of Rigid Body
The Displacement of the Periastron
The Rotation of the Nodal Line
2. The Rotation of the Earth
An Approximate Theory
The Exact Equation
Geometry of Rotations
Euler's Dynamical Equations
Euler's Geometrical Equations
The Free Motion of the Earth's Axis
The Equations for its Forced Motion
Precession and Nutation
Numerical Data
3. The Rotation of the Moon
Qualitative Considerations
Outline of a Quantitative Treatment
4. Summary and Conclusion
Exercises
Notes
Index
- No. of pages: 188
- Language: English
- Edition: 1
- Published: October 22, 2013
- Imprint: Pergamon
- Paperback ISBN: 9781483114866
- eBook ISBN: 9781483147284
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