Astrophysics

As a branch of physics, astrophysics applies physical laws and principles to understand the nature of the universe and the celestial objects within it. It seeks to explain the birth, life, and death of stars, the formation and evolution of galaxies, the properties of planets and exoplanets, and the behavior of matter in extreme environments such as black holes and neutron stars. By analyzing data from across the electromagnetic spectrum, as well as from gravitational waves and cosmic particles, astrophysicists develop and test theories that describe the physical processes governing these cosmic phenomena, forming a foundational component of the broader field of cosmology.

1. Foundations of Astrophysics
   1. Fundamental Physical Principles
      1. Classical Mechanics
         1. Newton's Laws of Motion
            1. First Law (Inertia)
            2. Second Law (Force and Acceleration)
            3. Third Law (Action and Reaction)
            4. Applications to Celestial Bodies
         2. Law of Universal Gravitation
            1. Gravitational Force Equation
            2. Gravitational Potential Energy
            3. Gravitational Field Concept
            4. Tidal Forces
            5. Applications in Astrophysics
         3. Kepler's Laws of Planetary Motion
            1. First Law (Elliptical Orbits)
            2. Second Law (Equal Areas)
            3. Third Law (Harmonic Law)
            4. Derivation from Newtonian Mechanics
            5. Modifications for Binary Systems
         4. Orbital Mechanics
            1. Two-Body Problem
            2. Types of Orbits
               1. Circular Orbits
               2. Elliptical Orbits
               3. Parabolic Orbits
               4. Hyperbolic Orbits
            3. Conservation Laws
               1. Conservation of Energy
               2. Conservation of Angular Momentum
            4. Orbital Elements
            5. Escape Velocity
            6. Perturbations and N-body Problem
      2. Electromagnetism
         1. Maxwell's Equations
            1. Gauss's Law for Electricity
            2. Gauss's Law for Magnetism
            3. Faraday's Law of Induction
            4. Ampère's Law with Maxwell's Addition
            5. Wave Solutions
         2. Electromagnetic Radiation
            1. Nature of Light
            2. Wave-Particle Duality
            3. Electromagnetic Spectrum
               1. Radio Waves
               2. Microwaves
               3. Infrared Radiation
               4. Visible Light
               5. Ultraviolet Radiation
               6. X-rays
               7. Gamma Rays
            4. Photon Energy and Frequency
            5. Polarization
         3. Blackbody Radiation
            1. Planck's Law
            2. Wien's Displacement Law
            3. Stefan-Boltzmann Law
            4. Rayleigh-Jeans Law
            5. Applications in Stellar Astrophysics
         4. Synchrotron Radiation
            1. Mechanism of Emission
            2. Spectral Properties
            3. Astrophysical Sources
            4. Polarization Characteristics
         5. Bremsstrahlung Radiation
            1. Free-Free Emission
            2. Thermal Bremsstrahlung
            3. Applications in Hot Plasmas
      3. Thermodynamics and Statistical Mechanics
         1. Laws of Thermodynamics
            1. Zeroth Law (Thermal Equilibrium)
            2. First Law (Conservation of Energy)
            3. Second Law (Entropy)
            4. Third Law (Absolute Zero)
         2. Kinetic Theory of Gases
            1. Maxwell-Boltzmann Distribution
            2. Mean Free Path
            3. Collision Rates
         3. Equation of State
            1. Ideal Gas Law
            2. Van der Waals Equation
            3. Degenerate Gas Equations
            4. Polytropic Equations
         4. Phase Transitions
            1. Ionization Equilibrium
            2. Saha Equation
            3. Recombination Processes
         5. Virial Theorem
            1. Statement and Derivation
            2. Applications to Star Clusters
            3. Applications to Galaxies
            4. Applications to Stellar Structure
      4. Quantum Mechanics
         1. Fundamental Principles
            1. Wave-Particle Duality
            2. Uncertainty Principle
            3. Schrödinger Equation
            4. Quantum States and Wavefunctions
         2. Atomic Structure and Spectra
            1. Bohr Model
            2. Quantum Numbers
            3. Electron Orbitals
            4. Emission and Absorption Lines
            5. Selection Rules
            6. Fine Structure
            7. Hyperfine Structure
         3. Quantum Tunneling
            1. Barrier Penetration
            2. Tunneling in Nuclear Fusion
            3. Astrophysical Implications
         4. Degeneracy Pressure
            1. Fermi-Dirac Statistics
            2. Electron Degeneracy
            3. Neutron Degeneracy
            4. Role in Stellar Remnants
         5. Pauli Exclusion Principle
            1. Applications to Stellar Structure
            2. White Dwarf Support
            3. Neutron Star Support
      5. Special and General Relativity
         1. Special Relativity
            1. Postulates of Special Relativity
            2. Lorentz Transformations
            3. Time Dilation
            4. Length Contraction
            5. Relativistic Velocity Addition
            6. Relativistic Energy and Momentum
            7. Mass-Energy Equivalence
         2. General Relativity
            1. Equivalence Principle
            2. Spacetime Curvature
            3. Einstein Field Equations
            4. Geodesics
            5. Schwarzschild Solution
            6. Kerr Solution
         3. Gravitational Effects
            1. Gravitational Time Dilation
            2. Gravitational Redshift
            3. Gravitational Lensing
               1. Deflection of Light
               2. Strong Lensing
               3. Weak Lensing
               4. Microlensing
            4. Frame Dragging
         4. Gravitational Waves
            1. Generation Mechanisms
            2. Propagation Properties
            3. Quadrupole Formula
            4. Detection Methods
            5. Astrophysical Sources
   2. Mathematical Tools and Methods
      1. Vector Calculus
         1. Gradient
         2. Divergence
         3. Curl
         4. Vector Identities
      2. Differential Equations
         1. Ordinary Differential Equations
         2. Partial Differential Equations
         3. Boundary Value Problems
      3. Fourier Analysis
         1. Fourier Series
         2. Fourier Transforms
         3. Power Spectra
      4. Statistical Methods
         1. Error Analysis
         2. Probability Distributions
         3. Hypothesis Testing
         4. Bayesian Statistics
   3. Observational Astrophysics
      1. The Electromagnetic Spectrum
         1. Radio Astronomy
            1. Radio Telescopes
            2. Interferometry
            3. Radio Sources
               1. Pulsars
               2. Quasars
               3. Radio Galaxies
            4. 21-cm Hydrogen Line
         2. Microwave Astronomy
            1. Cosmic Microwave Background Studies
            2. Atmospheric Effects
            3. Microwave Telescopes
         3. Infrared Astronomy
            1. Infrared Detectors
            2. Atmospheric Windows
            3. Dust Penetration
            4. Star Formation Studies
            5. Cool Object Detection
         4. Optical Astronomy
            1. Optical Telescopes
            2. CCD Detectors
            3. Photometric Techniques
            4. Spectroscopic Techniques
            5. Adaptive Optics
         5. Ultraviolet Astronomy
            1. UV Detectors
            2. Atmospheric Absorption
            3. Hot Stars
            4. Interstellar Medium Studies
         6. X-ray Astronomy
            1. X-ray Telescopes
            2. Focusing Systems
            3. High-Energy Sources
            4. Accretion Processes
         7. Gamma-ray Astronomy
            1. Gamma-ray Detectors
            2. Pair Production
            3. Compton Scattering
            4. Gamma-ray Bursts
            5. Active Galactic Nuclei
      2. Telescopes and Instrumentation
         1. Ground-Based Telescopes
            1. Reflecting Telescopes
               1. Newtonian Design
               2. Cassegrain Design
               3. Ritchey-Chrétien Design
            2. Refracting Telescopes
            3. Radio Telescopes
               1. Single Dish
               2. Arrays
            4. Atmospheric Effects
               1. Seeing
               2. Scintillation
               3. Absorption
            5. Adaptive Optics
               1. Wavefront Sensing
               2. Deformable Mirrors
               3. Laser Guide Stars
         2. Space-Based Telescopes
            1. Advantages over Ground-Based
            2. Orbital Considerations
            3. Thermal Management
            4. Major Space Telescopes
         3. Detectors and Sensors
            1. Photomultiplier Tubes
            2. Charge-Coupled Devices (CCDs)
            3. Complementary Metal-Oxide Semiconductors (CMOS)
            4. Infrared Arrays
            5. X-ray Detectors
         4. Spectrographs and Spectroscopy
            1. Principles of Spectroscopy
            2. Dispersive Elements
               1. Prisms
               2. Gratings
            3. Spectral Resolution
            4. Echelle Spectrographs
            5. Fiber Optics
            6. Applications in Astrophysics
         5. Photometry
            1. Photometric Systems
               1. Johnson-Cousins System
               2. Sloan Digital Sky Survey System
            2. Magnitude Systems
            3. Color Indices
            4. Light Curves
            5. Variability Studies
         6. Interferometry
            1. Principles of Interferometry
            2. Baseline and Resolution
            3. Very Long Baseline Interferometry (VLBI)
            4. Optical Interferometry
            5. Applications in High-Resolution Imaging
      3. Multi-Messenger Astronomy
         1. Neutrino Astronomy
            1. Neutrino Properties
            2. Detection Methods
            3. Neutrino Telescopes
            4. Astrophysical Neutrino Sources
               1. Solar Neutrinos
               2. Supernova Neutrinos
               3. High-Energy Neutrinos
         2. Gravitational Wave Astronomy
            1. Gravitational Wave Observatories
               1. LIGO
               2. Virgo
               3. KAGRA
            2. Detection Principles
            3. Data Analysis
            4. Multi-messenger Events
            5. Future Detectors
         3. Cosmic Ray Detection
            1. Primary Cosmic Rays
            2. Secondary Cosmic Rays
            3. Air Shower Detection
            4. Ground-Based Arrays
            5. Space-Based Detectors
            6. Ultra-High-Energy Cosmic Rays
   4. Positional Astronomy and Celestial Coordinates
      1. The Celestial Sphere
         1. Apparent Motion of Stars
         2. Diurnal Motion
         3. Annual Motion
         4. Celestial Poles and Equator
         5. Ecliptic and Zodiac
         6. Great Circles
      2. Coordinate Systems
         1. Equatorial Coordinate System
            1. Right Ascension
            2. Declination
            3. Hour Angle
            4. Sidereal Time
         2. Horizontal Coordinate System
            1. Azimuth
            2. Altitude
            3. Zenith and Nadir
         3. Ecliptic Coordinate System
            1. Ecliptic Longitude
            2. Ecliptic Latitude
         4. Galactic Coordinate System
            1. Galactic Longitude
            2. Galactic Latitude
         5. Transformations Between Systems
      3. Time Systems
         1. Solar Time
            1. Apparent Solar Time
            2. Mean Solar Time
         2. Sidereal Time
            1. Local Sidereal Time
            2. Greenwich Sidereal Time
         3. Universal Time
         4. Atomic Time
         5. Dynamical Time
      4. Precession and Nutation
         1. Precession of the Equinoxes
         2. Nutation
         3. Proper Motion
         4. Aberration
      5. Measuring Astronomical Distances
         1. Parallax
            1. Trigonometric Parallax
            2. Annual Parallax
            3. Secular Parallax
            4. Statistical Parallax
            5. Limitations and Applications
         2. Standard Candles
            1. Cepheid Variables
               1. Period-Luminosity Relation
               2. Classical Cepheids
               3. Type II Cepheids
            2. RR Lyrae Stars
            3. Type Ia Supernovae
            4. Red Giant Branch Tip
            5. Surface Brightness Fluctuations
            6. Calibration of Distance Ladder
         3. Standard Rulers
            1. Baryon Acoustic Oscillations
            2. Angular Diameter Distance
         4. Redshift Methods
            1. Doppler Effect
            2. Cosmological Redshift
            3. Hubble's Law
            4. Distance-Redshift Relation
            5. Peculiar Velocities