The Sun and the Properties of Stars
The unit takes the Sun apart layer by layer, explains its energy source, its magnetic cycle and the sound waves that reveal its interior, and then turns to the other stars. Students learn how distance, luminosity, temperature, radius and mass are measured, and how the Hertzsprung-Russell diagram and the mass-luminosity relation bring order to the results.
1 The Sun as a star
The Sun is an ordinary star at an unusual distance, about 270,000 times closer than the next nearest one. That is why its mass, radius, luminosity and surface temperature are known to four digits, and why every other star is described in units of them.
The mass follows from the orbit of the Earth and Kepler’s third law (Unit 2): \(\Msun = 1.989\times10^{30}\unit{kg}\), or 333,000 Earth masses. The radius follows from the angular diameter of \(0.533^\circ\) at a distance of 1 au: \(\Rsun = 6.957\times10^{8}\unit{m}\), which is 109 Earth radii. The mean density is \(1410\unit{kg\,m^{-3}}\), only 1.4 times that of water, yet the Sun is gas all the way down (plasma, to be exact), because its interior is far too hot for atoms to bind into a liquid or a solid. By mass, the surface layers are 74% hydrogen, 25% helium and a little over 1% everything else, which astronomers lump together as “metals”. Radioactive dating of meteorites (Unit 5) gives an age of 4.57 billion years.
The luminosity \(L\) is the total power radiated. Satellites measure the solar constant, the flux of sunlight at 1 au, as \(S = 1361\unit{W\,m^{-2}}\), and the inverse square law of Unit 3 converts it into a luminosity. A ball of gas has no surface to put a thermometer on, so the effective temperature \(T_{\mathrm{eff}}\) of a star is defined as the temperature of a black body of the same radius and the same total power.
1.1 The energy source in outline
Fossils show that the Sun has shone at close to its present power for billions of years. Slow contraction, the nineteenth-century proposal of Kelvin and Helmholtz, releases gravitational energy of order \(G\Msun^2/\Rsun = 3.8\times10^{41}\unit{J}\), where \(G\) is the gravitational constant. That pays for 30 million years, far too little for the geologists. The answer came in 1920, when Francis Aston measured that a helium nucleus is 0.7% lighter than the four hydrogen nuclei needed to build it, and Arthur Eddington pointed out that fusing hydrogen into helium would release the difference as energy, \(E = mc^2\). Unit 9 treats the reactions and the neutrinos they emit; the energy budget needs no nuclear physics.