Physics topics

by Dr. J. B. Tatum


Stellar Atmospheres

Celestial Mechanics

Classical Mechanics

Geometric Optics

Electricity and Magnetism

Heat and Thermodynamics

Physical Optics

Max Fairbairn's Planetary Photometry

Integrals and Differential Equations

Quadric Surfaces

Celestial Mechanics (last updated: 2023 January 16)

Part I. Mathematical Preambles

Chapter 1.    Numerical Methods

1.2Numerical Integration
1.3Quadratic Equations
1.4The Solution of f(x) = 0
1.5The Solution of Polynomial Equations
1.6Failure of the Newton-Raphson Method
1.7Simultaneous Linear Equations, N = n
1.8Simultaneous Linear Equations, N < n
1.9Nonlinear Simultaneous Equations
1.10Besselian Interpolation
1.11Fitting a Polynomial to a Set of Points. Lagrange Polynomials. Lagrange Interpolation.
1.12Fitting a Least Squares Straight Line to a Set of Observational Points
1.13Fitting a Least Squares Polynomial to a Set of Observational Points
1.14Legendre Polynomials
1.15Gaussian Quadrature - the Algorithm
1.16Gaussian Quadrature - Derivation
1.17Frequently-needed Numerical Procedures

Chapter 2.    Conic Sections

2.2The Straight Line
2.3The Ellipse
2.4The Parabola
2.5The Hyperbola
2.6Conic Sections
2.7The General Conic Section
2.8Fitting a Conic Section Through Five Points
2.9Fitting a Conic Section Through n Points

Chapter 3.    Plane and Spherical Trigonomtry

3.2Plane Triangles
3.3Cylindrical and Spherical Coordinates
3.4Velocity and Acceleration Components
3.5Spherical Triangles
3.6Rotation of Axes, Two Dimensions
3.7Rotation of Axes, Three Dimensions. Eulerian Angles
3.8Trigonometrical Formulas

Chapter 4.    Coordinate Geometry in Three Dimensions

4.2Planes and Straight Lines
4.3The Ellipsoid
4.4The Paraboloid
4.5The Hyperboloid
4.6The Cylinder
4.7The Cone
4.8The General Second Degree Equation in Three Dimensions

Chapter 5.    Gravitational Field and Potential

5.2Gravitational Field
5.3Newton's Law of Gravitation
5.4The Gravitational Fields Around Various Bodies
5.4.1Gravitational Field Around a Point Mass
5.4.2Gravitational Field on the Axis of a Ring
5.4.3Plane discs
5.4.4Infinite Plane Laminas
5.4.6Solid Cylinder
5.4.7Hollow Spherical Shell
5.4.8Uniform Solid Sphere
5.4.9Bubble Inside a Uniform Solid Sphere
5.4.10Field Inside a Nonuniform Sphere
5.4.10.ADifferentiated Planet
5.4.10.BUndifferentiated Planet
5.4.10.B.iDensity Increases Uniformly With Depth
5.4.10.B.iDensity Increases Nonuniformly With Depth
5.5Gauss's Theorem
5.6Calculating Surface Integrals
5.7Pressure at the Centre of a Uniform Solid Sphere
5.8Gravitational Potential
5.9Nabla, Gradient and Divergence. Poisson's and Laplace's Equations
5.10The Gravitational Potential Near Various Bodies
5.10.1Potential Near a Point Mass
5.10.2Potential on the Axis of a Ring
5.10.3Plane Discs
5.10.4Infinite Plane Lamina
5.10.5Hollow Hemisphere
5.10.7Solid Cylinder
5.10.8Hollow Spherical Shell
5.10.9Uniform Solid Sphere
5.10.9.APotential Inside and Outside
5.10.9.BWork Required to Assemble a Uniform Sphere
5.11Legendre Polynomials
5.12Gravitational Potential in the Vicinity of any Massive Body

Part II. Celestial Mechanics

Chapter 6.    The Celestial Sphere

6.2Altazimuth Coordinates
6.3Equatorial Coordinates
6.4Conversion Between Equatorial and Altazimuth Coordinates
6.5Ecliptic Coordinates
6.6The Mean Sun
6.9The Length of the Year

Chapter 7.    Time

Chapter 8.    Planetary Motions

8.2Opposition, Conjunction and Quadrature
8.3Sidereal and Synodic Periods
8.4Direct and Retrograde Motion, and Stationary Points

Chapter 9.    The Two Body Problem in Two Dimensions

9.2Kepler's Laws
9.3Kepler's Second Law from Conservation of Angular Momentum
9.4Some Functions of the Masses
9.5Kepler's First and Third Laws from Newton's Law of Gravitation
9.6Position in an Elliptic Orbit
9.7Position in a Parabolic Orbit
9.8Position in a Hyperbolic Orbit
9.9Orbital Elements and Velocity Vector
9.10Osculating Elements
9.11Mean Distance in an Elliptic Orbit

Chapter 10.    Computation of an Ephemeris

10.2Elements of an Elliptic Orbit
10.3Some Additional Angles
10.4Elements of a Circular or Near-circular Orbit
10.5Elements of a Parabolic Orbit
10.6Elements of a Hyperbolic Orbit
10.7Calculating the Position of a Comet or Asteroid
10.8Quadrant Problems
10.9Computing an Ephemeris
10.10Orbital Elements and Velocity Vector
10.11Hamiltonian Formulation of the Equations of Motion

Chapter 11.    Photographic Astrometry

11.2Standard Coordinates and Plate Constants
11.3Refinements and Corrections
11.3.1Parallaxes of the Comparison Stars
11.3.2Proper Motions of the Comparison Stars
11.3.4Aberration of light
11.3.5Optical Distortion
11.3.6Errors, Mistakes and Blunders

Chapter 12.    CCD Astrometry

Chapter 13.    Calculation of Orbital Elements

13.4Kepler's Second Law
13.7Geocentric and Heliocentric Distances - First Attempt
13.8Improved Triangle Ratios
13.10Higher-order Approximation
13.11Light-time Correction
13.12Sector-Triangle Ratio
13.13Resuming the Numerical Example

Chapter 14.    General Perturbation Theory

14.2Contact Transformations and General Perturbation Theory
14.3The Poisson Brackets for the Orbital Elements
14.4Lagrange's Planetary Equations
14.5Motion Around an Oblate Symmetric Top

Chapter 15.    Special Perturbations

15.2Orbital Elements and the Position and Velocity Vector
15.3The Equations of Motion

Chapter 16.    Equivalent Potential and the Restricted Three-Body Problem

16.2Motion Under a Central Force
16.3Inverse Square Attractive Force
16.4Hooke's Law
16.5Inverse Fourth Power Force
16.6The Collinear Lagrangian Points
16.7The Equilateral Lagrangian Points

Chapter 17.    Visual Binary Stars

17.2Determination of the Apparent Orbit
17.3The Elements of the True Orbit
17.4Determination of the Elements of the True Orbit
17.5Construction of an Ephemeris

Chapter 18.    Spectroscopic Binary Stars

18.2The Velocity Curve from the Elements
18.3Preliminary Elements from the Velocity Curve
18.5Refinement of the Orbital Elements
18.6Finding the Period
18.7Measuring the Radial Velocity

Appendix A.    Miscellaneous Problems

Appendix B.    Solutions to Miscellaneous Problems

Texts © 2000 - 2013 Dr. J. B. Tatum
Web page design and code © 2002 - 2013 Jason Stumpf