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1 Introduction: Tools of the Trade |
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1 | (20) |
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1 | (3) |
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4 | (6) |
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1.2.1 Fundamental Dimensions |
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5 | (1) |
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1.2.2 Constants of Nature |
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6 | (1) |
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1.2.3 Astrophysical Units |
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7 | (1) |
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1.2.4 Dimensional Analysis |
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8 | (2) |
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10 | (6) |
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1.3.1 Phases of an Electron Gas |
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11 | (3) |
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1.3.2 Stars, Familiar and Exotic |
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14 | (2) |
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16 | (1) |
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17 | (4) |
Part I Using Gravity and Motion to Measure Mass |
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21 | (14) |
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21 | (4) |
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25 | (3) |
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28 | (5) |
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33 | (1) |
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34 | (1) |
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3 Gravitational One-Body Problem |
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35 | (18) |
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3.1 Deriving Kepler's Laws |
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35 | (5) |
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3.2 Using Kepler III: Motion —> Mass |
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40 | (7) |
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3.2.1 The Black Hole at the Center of the Milky Way |
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40 | (2) |
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3.2.2 Supermassive Black Holes in Other Galaxies |
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42 | (4) |
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3.2.3 Active Galactic Nuclei |
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46 | (1) |
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47 | (3) |
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3.3.1 Sphere of Influence |
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47 | (2) |
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3.3.2 Stellar Dynamical Evaporation |
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49 | (1) |
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50 | (1) |
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51 | (2) |
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4 Gravitational Two-Body Problem |
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53 | (26) |
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4.1 Equivalent One-Body Problem |
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53 | (9) |
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53 | (1) |
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54 | (2) |
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4.1.3 Energy and Angular Momentum |
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56 | (1) |
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57 | (2) |
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4.1.5 Application to the Solar System |
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59 | (2) |
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4.1.6 Kepler III Revisited |
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61 | (1) |
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62 | (5) |
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4.2.1 Background: Inclination |
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62 | (2) |
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64 | (1) |
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4.2.3 Spectroscopic Binary |
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65 | (2) |
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67 | (1) |
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67 | (8) |
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68 | (2) |
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70 | (3) |
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4.3.3 Status of Exoplanet Research |
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73 | (2) |
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75 | (2) |
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77 | (2) |
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79 | (10) |
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5.1 Derivation of the Tidal Force |
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79 | (3) |
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5.2 Effects of Tidal Forces |
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82 | (3) |
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82 | (2) |
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84 | (1) |
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85 | (1) |
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85 | (1) |
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86 | (2) |
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88 | (1) |
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6 Gravitational Three-Body Problem |
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89 | (10) |
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6.1 Two "Stars" and One "Planet" |
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89 | (4) |
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6.1.1 Theory: Lagrange Points |
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89 | (3) |
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92 | (1) |
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6.2 One "Planet" and Two "Moons" |
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93 | (3) |
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94 | (1) |
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95 | (1) |
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96 | (2) |
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98 | (1) |
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7 Extended Mass Distributions: Spiral Galaxies |
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99 | (28) |
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99 | (5) |
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7.1.1 Luminosity Profiles |
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101 | (1) |
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102 | (2) |
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104 | (1) |
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104 | (1) |
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105 | (1) |
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105 | (9) |
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106 | (1) |
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7.3.2 Observations and Interpretation |
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107 | (3) |
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110 | (3) |
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7.3.4 Is Dark Matter Real? |
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113 | (1) |
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114 | (10) |
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114 | (1) |
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115 | (2) |
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117 | (2) |
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7.4.4 Application to Spiral Arms |
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119 | (5) |
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124 | (2) |
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126 | (1) |
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8 N-Body Problem: Elliptical Galaxies |
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127 | (16) |
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8.1 Gravitational N-Body Problem |
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127 | (6) |
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8.1.1 Equations of Motion |
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127 | (1) |
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8.1.2 Conservation of Energy |
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128 | (2) |
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130 | (1) |
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8.1.4 A Simple Application: N = 2 |
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131 | (2) |
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133 | (4) |
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133 | (2) |
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135 | (1) |
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136 | (1) |
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137 | (3) |
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137 | (2) |
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139 | (1) |
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8.4 Other N-Body Problems |
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140 | (1) |
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140 | (2) |
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142 | (1) |
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9 Bending of Light by Gravity |
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143 | (34) |
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9.1 Principles of Gravitational Lensing |
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143 | (11) |
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9.1.1 Gravitational Deflection |
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143 | (3) |
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146 | (2) |
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9.1.3 Lensing by a Point Mass |
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148 | (1) |
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9.1.4 Distortion and Magnification |
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149 | (5) |
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154 | (1) |
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154 | (7) |
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155 | (1) |
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156 | (1) |
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157 | (2) |
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159 | (2) |
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161 | (7) |
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9.3.1 Extended Mass Distribution |
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161 | (1) |
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9.3.2 Circular Mass Distribution |
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162 | (1) |
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9.3.3 Singular Isothermal Sphere |
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163 | (1) |
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9.3.4 Singular Isothermal Ellipsoid |
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164 | (1) |
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9.3.5 Spherical Galaxy with External Shear |
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165 | (1) |
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9.3.6 Science with Galaxy Strong Lensing |
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166 | (2) |
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168 | (3) |
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171 | (4) |
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175 | (2) |
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177 | (44) |
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10.1 Space and Time: Classical View |
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177 | (1) |
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10.2 Special Theory of Relativity |
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178 | (6) |
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10.2.1 Lorentz Transformation |
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179 | (2) |
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10.2.2 Loss of Simultaneity |
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181 | (1) |
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182 | (1) |
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183 | (1) |
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10.2.5 Length Contraction |
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184 | (1) |
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10.3 General Theory of Relativity |
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184 | (7) |
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10.3.1 Concepts of General Relativity |
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185 | (1) |
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10.3.2 Principle of Equivalence |
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185 | (1) |
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10.3.3 Curvature of Spacetime |
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186 | (3) |
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10.3.4 Gravitational Redshift and Time Dilation |
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189 | (2) |
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10.4 Applications of General Relativity |
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191 | (8) |
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10.4.1 Mercury's Perihelion Shift (1916) |
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191 | (2) |
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10.4.2 Bending of Light (1919) |
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193 | (1) |
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10.4.3 Gravitational Redshift on Earth (1960) |
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193 | (1) |
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10.4.4 Gravitational Redshift from a White Dwarf (1971) |
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194 | (1) |
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10.4.5 Flying Clocks (1971) |
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195 | (3) |
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10.4.6 Global Positioning System (1989) |
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198 | (1) |
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10.5 Mathematics of Relativity |
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199 | (5) |
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10.5.1 Spacetime Interval |
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199 | (2) |
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201 | (2) |
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10.5.3 Relativistic Momentum and Energy |
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203 | (1) |
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204 | (12) |
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10.6.1 Schwarzschi Id Metric |
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204 | (2) |
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10.6.2 Spacetime Geometry |
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206 | (1) |
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10.6.3 Particle in a Circular Orbit |
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207 | (2) |
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10.6.4 General Motion Around a Black Hole |
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209 | (4) |
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10.6.5 Gravitational Deflection |
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213 | (3) |
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216 | (1) |
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217 | (2) |
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219 | (2) |
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11 Cosmology: Expanding Universe |
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221 | (22) |
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11.1 Hubble's Law and the Expanding Universe |
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221 | (1) |
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11.2 Relativistic Cosmology |
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222 | (7) |
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11.2.1 Robertson-Walker Metric |
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223 | (1) |
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11.2.2 The Friedmann Equation |
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224 | (3) |
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11.2.3 Einstein's Greatest Blunder |
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227 | (1) |
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228 | (1) |
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11.3 Observational Cosmology |
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229 | (8) |
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11.3.1 Cosmological Redshift |
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230 | (1) |
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11.3.2 Cosmological Distances |
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231 | (2) |
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233 | (4) |
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237 | (2) |
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239 | (4) |
Part II Using Stellar Physics to Explore the Cosmos |
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243 | (20) |
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12.1 Kinetic Theory of Gases |
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243 | (8) |
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12.1.1 Temperature and the Boltzmann Distribution |
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243 | (1) |
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12.1.2 Maxwell-Boltzmann Distribution of Particle Speeds |
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244 | (3) |
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12.1.3 Pressure and the Ideal Gas Law |
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247 | (2) |
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12.1.4 Assumptions in the Ideal Gas Law |
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249 | (2) |
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12.2 Hydrostatic Equilibrium |
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251 | (1) |
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12.3 Planetary Atmospheres |
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252 | (7) |
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252 | (2) |
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254 | (1) |
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255 | (4) |
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259 | (2) |
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261 | (2) |
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13 Planetary Temperatures |
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263 | (22) |
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263 | (6) |
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263 | (1) |
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264 | (3) |
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267 | (1) |
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268 | (1) |
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13.2 Predicting Planet Temperatures |
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269 | (1) |
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270 | (4) |
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271 | (1) |
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272 | (2) |
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274 | (1) |
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13.4 Interaction of Light with Matter |
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274 | (5) |
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275 | (1) |
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13.4.2 Electron Excitation |
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276 | (1) |
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13.4.3 Molecular Vibration |
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276 | (2) |
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13.4.4 Molecular Rotation |
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278 | (1) |
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279 | (1) |
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13.5 Greenhouse Effect and Climate Change |
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279 | (3) |
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279 | (2) |
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281 | (1) |
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282 | (1) |
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283 | (2) |
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285 | (14) |
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14.1 Atomic Excitation and Ionization |
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285 | (8) |
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14.1.1 Energy Level Occupation |
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287 | (1) |
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287 | (2) |
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14.1.3 Application to Hydrogen |
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289 | (4) |
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14.2 Stellar Spectral Classification |
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293 | (2) |
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295 | (2) |
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297 | (2) |
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299 | (26) |
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15.1 What Powers the Sun? |
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299 | (2) |
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301 | (9) |
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15.2.1 Mass and Energy Scales |
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301 | (1) |
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15.2.2 Requirements for Fusion |
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302 | (3) |
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305 | (2) |
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307 | (3) |
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15.3 Nuclear Reactions in Stars |
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310 | (5) |
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15.3.1 Cast of Characters |
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310 | (1) |
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15.3.2 Masses and Binding Energies |
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311 | (1) |
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15.3.3 Burning Hydrogen Into Helium |
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312 | (3) |
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315 | (6) |
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15.4.1 Neutrino Production in the Sun |
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315 | (1) |
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15.4.2 Neutrino Detection (I) |
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316 | (1) |
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15.4.3 Neutrino Oscillations |
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317 | (1) |
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15.4.4 Neutrino Detection (II) |
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318 | (3) |
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321 | (2) |
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323 | (2) |
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16 Stellar Structure and Evolution |
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325 | (26) |
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325 | (6) |
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325 | (4) |
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329 | (2) |
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331 | (7) |
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16.2.1 Equations of Stellar Structure |
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332 | (2) |
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334 | (1) |
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335 | (3) |
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16.3 Evolution of Low-Mass Stars (M < or ~ to 8 M) |
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338 | (3) |
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16.3.1 Hydrogen, Helium, and Beyond |
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338 | (2) |
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340 | (1) |
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16.4 Evolution of High-Mass Stars (M > or ~ to 8 M) |
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341 | (6) |
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16.4.1 Beyond Carbon and Oxygen |
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342 | (1) |
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16.4.2 Explosion: Supernova |
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343 | (3) |
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346 | (1) |
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347 | (2) |
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349 | (2) |
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351 | (14) |
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17.1 Cold, Degenerate Gas |
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351 | (2) |
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353 | (8) |
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354 | (1) |
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354 | (4) |
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17.2.3 Testing the Theory |
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358 | (3) |
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17.3 Neutron Stars and Pulsars |
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361 | (1) |
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362 | (2) |
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364 | (1) |
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18 Charting the Universe with Stars |
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365 | (12) |
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365 | (5) |
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365 | (2) |
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367 | (3) |
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370 | (4) |
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374 | (1) |
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375 | (2) |
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19 Star and Planet Formation |
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377 | (18) |
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19.1 Gravitational Collapse |
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377 | (5) |
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19.1.1 Equilibrium: Virial Temperature |
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377 | (2) |
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19.1.2 Conditions for Collapse |
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379 | (1) |
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380 | (2) |
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19.1.4 Collapse Time Scale |
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382 | (1) |
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382 | (2) |
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19.3 Halting the Collapse |
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384 | (4) |
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19.3.1 Cessation of Cooling |
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385 | (1) |
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19.3.2 Radiation Pressure |
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385 | (2) |
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387 | (1) |
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19.4 Protoplanetary Disks |
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388 | (3) |
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19.4.1 Temperature Structure |
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388 | (1) |
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19.4.2 Picture of Planet Formation |
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389 | (2) |
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391 | (2) |
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393 | (2) |
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20 Cosmology: Early Universe |
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395 | (18) |
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20.1 Cosmic Microwave Background Radiation |
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395 | (6) |
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396 | (1) |
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20.1.2 Theory: Recombination Temperature |
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397 | (1) |
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398 | (2) |
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400 | (1) |
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20.2 Big Bang Nucleosynthesis |
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401 | (7) |
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20.2.1 Theory: "The First Three Minutes" |
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401 | (4) |
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20.2.2 Observations: Primordial Abundances |
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405 | (3) |
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20.3 How Did We Get Here? |
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408 | (1) |
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408 | (1) |
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409 | (4) |
Part III Appendices |
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413 | (10) |
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A.1 Cartesian and Polar Coordinates |
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413 | (2) |
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A.2 Cylindrical and Spherical Coordinates |
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415 | (1) |
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A.3 Rotating Reference Frame |
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416 | (2) |
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418 | (1) |
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A.5 Taylor Series Approximation |
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419 | (1) |
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A.6 Numerical Solution of Differential Equations |
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420 | (1) |
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421 | (1) |
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422 | (1) |
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423 | (6) |
Index |
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429 | |