Introduction to Astrophysics
Edited by
Professor William H. Press
for Spring Term, 1997
Preface and Acknowledgments
1 Introduction
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- 1.1 Astronomy and Astrophysics 1
- 1.1.1 What distinguishes them? What are they? 1
- 1.1.2 Characteristics of astrophysics 1
- 1.2 Quick history of some pre-astrophysics discoveries 3
- 1.2.1 Copernicus gets Solar System geometry, but no scale 3
- 1.2.2 Parallax of Mars, transits of Venus determine scale 4
- 1.2.3 Newton's Law of Gravitation gives mass of Sun 6
- 1.2.4 Compare Sun to candle to get its "candlepower" 7
- 1.2.5 Stellar distances from Parallax across Earth's orbit 8
- 1.2.6 Luminosities in modern units (watts) 9
2 The Astronomical Context
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- 2.1 Angular and positional measurements 11
- 2.1.1 Angles between objects measured "on the sky" - i.e.,
in projection 11
- 2.1.2 Coordinate systems in the sky 12
- 2.1.3 Angular separations from coordinates in Sky 14
- 2.1.4 Solid angles 14
- 2.2 Brightness measurements 15
- 2.2.1 Flux and UBV system 15
- 2.2.2 Apparent magnitude 17
- 2.2.3 Absolute Magnitude 18
- 2.2.4 Spectra 19
- 2.3 Velocity measurements 20
- 2.4 Distance measurements 22
3 Radiation
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- 3.1 Photon description of light 26
- 3.1.1 Photons 26
- 3.1.2 Phase space density 26
- 3.1.3 Brightness 30
- 3.2 Wave description of light 31
- 3.2.1 Waves 31
- 3.2.2 Connection between particle and wave descriptions 32
- 3.3 Radiation units 33
- 3.3.1 Specific intensity I 33
- 3.3.2 Specific intensity I 34
- 3.3.3 Net flux 34
- 3.3.4 Energy density and radiation pressure 35
- 3.3.5 ExampleSphere of uniform brightness 38
- 3.4 Telescopes 39
- 3.4.1 Astronomical Telescopes 39
- 3.4.2 Telescopes you look through (e.g. binoculars) 41
- 3.5 Thermal ("Black Body") Radiation 43
- 3.5.1 Black Body radiation is universal 43
- 3.5.2 Derivation of the Planck spectrum 44
- 3.5.3 Asymptotics of the Planck spectrum 46
- 3.5.4 Integral of the Planck spectrumStephan-Boltzman law 50
- 3.5.5 Color temperature and brightness temperature 52
- 3.5.6 Radiative temperature balance of the Earth 53
- 3.5.7 The spectral sequence of stars 55
- 3.6 Radiation emission mechanisms briefly described 58
- 3.6.1 Synchrotron radiation 58
- 3.6.2 Thermal bremsstrahlung 59
- 3.6.3 Line emission from atoms 59
4 Classical Dynamics
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- 4.1 Newtonian gravity 61
- 4.1.1 Basic law of attraction 61
- 4.1.2 The little known codicil to Newton's 3rd law 62
- 4.1.3 Gravitational Potential 63
- 4.2 The 2-body problem 64
- 4.2.1 Conservation laws for 2-body orbits 64
- 4.2.2 Two-body orbits 68
- 4.2.3 Shapes of the orbits 73
- 4.2.4 Orbital elements 79
- 4.2.5 The mass of the Sun and the masses of binary stars 82
- 4.2.6 Supernovae in binary systems 88
- 4.3 Tides and Roche effects 91
- 4.3.1 Weak tides 93
- 4.3.2 Tidal drag and the lengthening of the day 97
- 4.3.3 Roche stability limit for satellites 100
- 4.3.4 Roche Lobe overflow 101
- 4.3.5 Effect of mass transfer on binary orbits 103
- 4.3.6 Accretion disks 104
- 4.3.7 The Lagrange points 105
- 4.4 The virial theorem 111
5 Stars and Stellar Structure
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- 5.1 Phenomenology of stars 114
- 5.1.1 Elemental abundances, populations I and II 114
- 5.1.2 Nuclear reactions 118
- 5.2 Stellar structure 120
- 5.2.1 Order-of-magnitude stellar structure 120
- 5.2.2 Quantities describing the stellar interior 124
- 5.2.3 Equations of stellar structure 126
- 5.2.4 PolytropesThe Lane-Emden equation 128
- 5.2.5 Boundary conditions and Lane-Emden functions 130
- 5.2.6 Physical properties of polytropes 131
- 5.3 Specific cases of polytropic models 134
- 5.3.1 Adiabatic indices for a perfect gas 134
- 5.3.2 Fully convective stars 136
- 5.3.3 Equation of state for degenerate matter 137
- 5.3.4 White dwarf stars 142
- 5.3.5 Stellar structure virial theorem 146
- 5.4 Beyond the Chandrasekhar mass 148
- 5.4.1 Inverse fi decay 149
- 5.4.2 Neutron stars and pulsars 149
- 5.4.3 Black holes 152
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