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schiff j basic mathematical insights astrophysics 2025

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Textbook in PDF format This book will show how it is possible to explore the Universe not only with telescopes but also with Mathematics. Moreover, this book aims at explaining the equations governing the behavior of the stars, planets, and galaxies, which are very accessible to the average undergraduate who has studied some Mathematics in school. We will also probe into unseen black holes to determine their mass as well as investigate other intriguing celestial phenomena such as dark matter and dark energy, the expansion of the Universe, and explore via Einstein’s Theory of Relativity, the very foundations of space and time itself. You will discover that both Special and General Relativity are absolutely essential for the functioning of the Global Positioning System (GPS), which illustrates how astrophysical ideas can impact everyday lives. Lastly, this book provides insight into how Mathematics allows us to see and hear how the Universe ticks. Each chapter is a front row seat for those who wish to listen to some of the most beautiful music expressed by the Universe, Mathematics. Preface Acknowledgements 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 Down to Earth Size of Earth Age of the Earth Orbiting Earth Escaping Earth Mass of Earth 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 Newton´s Laws Newton´s Three Laws of Motion Gravity Gravitational Potential Energy Virial Theorem Jean´s Criterion Escape Velocity Roche Limit Tidal Forces 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 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 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 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 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 Epilogue: Are We Alone? Drake Equation Appendixes Method of Least Squares/Linear Regression Exponential Growth/Decay Wien´s Displacement Law from Planck´s Law Wien´s Approximation Law Stefan-Boltzmann Law Gravitational Potential Energy Python Computer Programs Apsidal Precession Einstein Ring Multiply-Lensed Objects Gaussian Curvature Second Friedmann Equation from First Friedmann Equation Terminology Further Reading Index

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