Basic Mathematical Insights into Astrophysics

Preface
Acknowledgements
Contents
Chapter 1: Measurement
	Scientific Notation
	SI Units
	Constants
	What´s the Angle?
	Solid Angles
	Light-Years/Parsecs
	Mass
	Density
	Temperature
	Logarithms
	Brightness/Stellar Magnitudes
	Galactic Orbital Velocities
	Method of Least Squares
	Standard Deviation
	Power Laws
		Mass-Luminosity Relation
		Main-Sequence Lifetimes
Chapter 2: Down to Earth
	Size of Earth
	Age of the Earth
	Orbiting Earth
	Escaping Earth
	Mass of Earth
Chapter 3: Let There Be Light
	Electromagnetic Radiation
	Frequency
	Energy
	Blackbody Radiation
		Wien´s Displacement Law
		Planck´s Law
		Wien´s Approximation Law
		Rayleigh-Jeans Law
			Ultraviolet Catastrophe
		Stefan-Boltzmann Law
	Inverse Square Principle
	Irradiance/Radiant Flux Density
	Hertzsprung-Russell Diagram
	Comments on H-R Diagram
	Eddington Luminosity
	Sérsic Profile
	Transit Method
Chapter 4: Newton´s Laws
	Newton´s Three Laws of Motion
	Gravity
	Gravitational Potential Energy
	Virial Theorem
		Jean´s Criterion
	Escape Velocity
	Roche Limit
		Tidal Forces
Chapter 5: Kepler´s Laws
	Ellipses
		Ellipticity
	Orbital Elements
	Kepler´s Laws
		Orbital Velocity
		Orbital Period/Mass
		Mass of Sagittarius A*
		Geostationary Satellites
	Lagrange Points
	Deviations from Kepler´s Laws Reveal Dark Matter
Chapter 6: Climbing the Distance Ladder
	Distance Formula
	Parallax
	Galaxy Distance via Cepheids
		Apparent vs Absolute Magnitude
		Period-Luminosity Relation
		Distance Modulus
	Type 1a Supernovae
	Tip of the Red Giant Branch
	Tully-Fisher Relation
	Galaxy Diameter
Chapter 7: Hubble´s Law of the Universe
	Doppler Effect/Redshift
	21-cm Neutral Hydrogen
	Hubble Parameter/Constant
	Lookback Time
	Expansion Scale Factor
Chapter 8: Relativity
	Special Relativity
	Two Postulates of Relativity
	Time Dilation
	Lorentz Dilation Factor
	General Relativity
	Time Dilation
	Global Positioning System
	Apsidal Precession
	Gravitational Redshift
Chapter 9: Black Holes
	Schwarzschild Radius
	M87´s Black Hole
	Central Velocity Dispersion
	Black Hole Density
	Schwarzschild Precession for Black Holes
	Hawking Radiation/Temperature
	Black Hole Luminosity
	Black Hole Evaporation
	Black Hole Entropy
Chapter 10: The Universe
	Einstein Field Equations (EFE)
	Geometry of Space
	First Friedmann Equation
	Eras Tour
	Second Friedmann Equation
	Critical Density
	Density Parameter
	Space is Flat
	Spacetime Metrics
	Minkowski Metric
	Schwarzschild Metric
	De Sitter Metric
	Friedmann-Lemaître-Robertson-Walker Metric
	Topology of the Universe
	Future of the Universe
	Equation of State Parameter
Chapter 11: Epilogue: Are We Alone?
	Drake Equation
Appendixes
	Appendix I
		Method of Least Squares/Linear Regression
	Appendix II
		Exponential Growth/Decay
	Appendix III
		Wien´s Displacement Law from Planck´s Law
	Appendix IV
		Wien´s Approximation Law
	Appendix V
		Stefan-Boltzmann Law
	Appendix VI
		Gravitational Potential Energy
	Appendix VII
		Python Computer Programs
	Appendix VIII
		Apsidal Precession
	Appendix IX
		Einstein Ring
	Appendix X
		Multiply-Lensed Objects
	Appendix XI
		Gaussian Curvature
	Appendix XII
		Second Friedmann Equation from First Friedmann Equation
Terminology
Further Reading
Index