advertisement

Week 2 - Lecture notes Chapter two contains the following fundamental topics (along with more general descriptive material that you can best read about there): 1. The source of energy for stars and the origin of the elements - nuclear energy generation and nucleosynthesis. 2. The blackbody function. Using the formulae from these topics, let me illustrate the use of proportionality and ratios: A. Nuclear energy generation by fusion works because when two or more light nuclei are combined, the result has slightly less mass than the original nuclei. Thus we might abstractly say: Mass per nucleon in atomic mass units: Ingredients A B Product C 1+a 1+b 2 + x with x < a + b then Mass of A plus mass of B = 2 + a+b Mass of C = 2 + x Mass difference = (a + b) - x ((a+b)-x) / (2+(a+b)) = fraction of the original mass that disappears. This ratio is independent of the units involved, so it can be (amu/amu) or (kg/kg). Thus the amount of energy released by converting a kg of (A + B) into (nearly) a kg of C is (a+b-x)/(2+a+b) x c 2 where c is the speed of light, 3x108 m/s. B. The luminosity of a star is related to its effective temperature (roughly the same as its surface temperature) by L = 4πr2 σ T4 To find L given r and T one can plug in the numbers and go. However, particularly if r is given in units of the radius of the Sun, there is an easier way: L/LSun = (r/rSun )2 (T/TSun )4 Similarly, λ max T = 2900 microns => λ max is proportional to 1/T => λ max, A / λ max, B = TB / TA