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