Nguồn ngoài

Celestial Mechanics

This book presents a treatment of celestial mechanics, integrating numerical methods, geometry, and Newtonian gravitation to model and predict celestial motion. It progresses from mathematical foundations to orbital theory, ephemeris computation, perturbations, and the analysis of planetary systems and binary stars, tightly linking theory with observational astronomy.

Astronomy Cosmology Physics

Tác giả: Jeremy Tatum
Nhà xuất bản: University of Victoria
Nguồn: LibreTexts
Giấy phép: CC BY-NC
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

Đọc trực tuyến Tải PDF (nguồn mở)

Mục lục· 181 mục

01: Numerical Methods
1.01: Introduction
1.02: Numerical Integration
1.03: Quadratic Equations
1.04: The Solution of f(x) 0
1.05: The Solution of Polynomial Equations
1.06: Failure of the Newton-Raphson Method
1.07: Simultaneous Linear Equations N n
1.08: Simultaneous Linear Equations N n
1.09: Nonlinear Simultaneous Equations
1.10: 1.10-Besselian Interpolation
1.11: Fitting a Polynomial to a Set of Points - Lagrange Polynomials and Lagrange Interpolation
1.12: Fitting a Least Squares Straight Line to a Set of Observational Points
1.13: Fitting a Least Squares Polynomial to a Set of Observational Points
1.14: Legendre Polynomials
1.15: Gaussian Quadrature - the Algorithm
1.16: Gaussian Quadrature - Derivation
1.17: Frequently-needed Numerical Procedures
02: Conic Sections
2.01: The Straight Line
2.02: The Ellipse
2.03: The Parabola
2.04: The Hyperbola
2.05: Conic Sections
2.06: The General Conic Section
2.07: Fitting a Conic Section Through Five Points
2.08: Fitting a Conic Section Through n Points
03: Plane and Spherical Trigonometry
3.01: Introduction
3.02: Plane Triangles
3.03: Cylindrical and Spherical Coordinates
3.04: Velocity and Acceleration Components
3.05: Spherical Triangles
3.06: Rotation of Axes Two Dimensions
3.07: Rotation of Axes Three Dimensions. Eulerian Angles
3.08: Trigonometrical Formulas
04: Coordinate Geometry in Three Dimensions
4.01: Introduction
4.02: Planes and Straight Lines
4.03: The Ellipsoid
4.04: The Paraboloid
4.05: The Hyperboloid
4.06: The Cylinder
4.07: The Cone
4.08: The General Second Degree Equation in Three Dimensions
4.09: Matrices
05: Gravitational Field and Potential
5.01: Introduction
5.02: Gravitational Field
5.03: Newton's Law of Gravitation
5.04: The Gravitational Fields of Various Bodies
5.4.01: Field of a Point Mass
5.4.02: Field on the Axis of a Ring
5.4.03: Plane discs
5.4.04: Infinite Plane Laminas
5.4.05: Hollow Hemisphere
5.4.06: Rods
5.4.07: Solid Cylinder
5.4.08: Hollow Spherical Shell
5.4.09: Solid Sphere
5.4.10: Bubble Inside a Uniform Solid Sphere
5.05: Gauss's Theorem
5.06: Calculating Surface Integrals
5.07: Potential
5.08: The Gravitational Potentials Near Various Bodies
5.8.01: Potential Near a Point Mass
5.8.02: Potential on the Axis of a Ring
5.8.03: Plane Discs
5.8.04: Infinite Plane Lamina
5.8.05: Hollow Hemisphere
5.8.06: Rods
5.8.07: Solid Cylinder
5.8.08: Hollow Spherical Shell
5.8.09: Solid Sphere
5.09: Work Required to Assemble a Uniform Sphere
5.10: Nabla Gradient and Divergence
5.11: Legendre Polynomials
5.12: Gravitational Potential of any Massive Body
5.13: Pressure at the Centre of a Uniform Sphere
06: The Celestial Sphere
6.01: Introduction to the Celestial Sphere
6.02: Altazimuth Coordinates
6.03: Equatorial Coordinates
6.04: Conversion Between Equatorial and Altazimuth Coordinates
6.05: Ecliptic Coordinates
6.06: The Mean Sun
6.07: Precession
6.08: Nutation
6.09: The Length of the Year
6.10: Problems
6.11: Solutions
07: Time
08: Planetary Motions
8.01: Introduction to Planetary Motions
8.02: Opposition Conjunction and Quadrature
8.03: Sidereal and Synodic Periods
8.04: Direct and Retrograde Motion and Stationary Points
09: The Two Body Problem in Two Dimensions
9.01: Kepler's Laws
9.02: Kepler's Second Law from Conservation of Angular Momentum
9.03: Some Functions of the Masses
9.04: Kepler's First and Third Laws from Newton's Law of Gravitation
9.05: Position in an Elliptic Orbit
9.06: Position in a Parabolic Orbit
9.07: Position in a Hyperbolic Orbit
9.08: Orbital Elements and Velocity Vector
9.09: Osculating Elements
9.10: Mean Distance in an Elliptic Orbit
10: Computation of an Ephemeris
10.01: Introduction to an Ephemeris
10.02: Elements of an Elliptic Orbit
10.03: Some Additional Angles
10.04: Elements of a Circular or Near-circular Orbit
10.05: Elements of a Parabolic Orbit
10.06: Elements of a Hyperbolic Orbit
10.07: Calculating the Position of a Comet or Asteroid
10.08: Quadrant Problems
10.09: Computing an Ephemeris
10.10: Orbital Elements and Velocity Vector
10.11: Hamiltonian Formulation of the Equations of Motion
11: Photographic Astrometry
11.01: Introduction to Photographic Astrometry
11.02: Standard Coordinates and Plate Constants
11.03: Refinements and Corrections
11.3.01: Parallaxes of the Comparison Stars
11.3.02: Proper Motions of the Comparison Stars
11.3.03: Refraction
11.3.04: Aberration of Light
11.3.05: Optical Distortion
11.3.06: Errors Mistakes and Blunders
12: CCD Astrometry
13: Calculation of Orbital Elements
13.01: Introduction to Calculating Orbital Elements
13.02: Triangles
13.03: Sectors
13.04: Kepler's Second Law
13.05: Coordinates
13.06: Example
13.07: Geocentric and Heliocentric Distances - First Attempt
13.08: Improved Triangle Ratios
13.09: Iterating
13.10: Higher-order Approximation
13.11: Light-time Correction
13.12: Sector-Triangle Ratio
13.13: Resuming the Numerical Example
13.14: Summary So Far
13.15: Calculating the Elementss
13.16: Topocentric-Geocentric Correction
13.17: Concluding Remarks
14: General Perturbation Theory
14.01: Introduction to General Perturbation Theory
14.02: Contact Transformations and General Perturbation Theory
14.03: The Poisson Brackets for the Orbital Elements
14.04: Lagrange's Planetary Equations
14.05: Motion Around an Oblate Symmetric Top
15: Special Perturbations
15.01: Introduction
15.02: Orbital elements and the position and velocity vector
15.03: The equations of motion
16: Equivalent Potential and the Restricted Three-Body Problem
16.01: Introduction
16.02: Motion Under a Central Force
16.03: Inverse Square Attractive Force
16.04: Hooke's Law
16.05: Inverse Fourth Power Force
16.06: The Collinear Lagrangian Points
16.07: The Equilateral Lagrangian Points
17: Visual Binary Stars
17.01: Introduction to Visual Binary Stars
17.02: Determination of the Apparent Orbit
17.03: The Elements of the True Orbit
17.04: Determination of the Elements of the True Orbit
17.05: Construction of an Ephemeris
18: Spectroscopic Binary Stars
18.01: Introduction to Spectroscopic Binary Stars
18.02: The Velocity Curve from the Elements
18.03: Preliminary Elements from the Velocity Curve
18.04: Masses
18.05: Refinement of the Orbital Elements
18.06: Finding the Period
18.07: Measuring the Radial Velocity