Announcements

1. Announcements • Homework: Chapter 14 # 47 & 48 + Supplemental Problems Solutions will be posted Monday afternoon. • Exam 2 is next time. Will cover parallax, brightness/luminosity/distance, luminosity/temperature/size, luminosity/mass, mass/lifetime and what is covered today.

2. The energy source of stars A young Albert Einstein proposed that mass and energy were two sides of the same coin and could be interchanged. His famous equation from special relativity was E = mc2

3. Fusion: the means of converting mass into energy The first person to propose that stars fused hydrogen into helium was Sir Arthur Eddington in the 1920’s. His critics said that stars were not hot enough. His retort: “I am aware that many critics consider the stars are not hot enough. The critics lay themselves open to an obvious retort; we tell them to go and find a hotter place.”

4. The Proton-Proton Cycle: The Mechanism of Solar Fusion Hans Bethe worked out the details of how the Sun fused hydrogen into helium in the 1930’s. He won the Nobel Prize in 1967 for his work

5. Example Determine the energy released (or required) in each step of the CNO Cycle The mass of the neutrino can be ignored but the mass of an electron or positron cannot. Gamma rays have no mass Masses can be found at www.freebase.com/view/en/carbon www.freebase.com/view/en/nitrogen www.freebase.com/view/en/oxygen

6. Example Solution Masses from freebase.com:

7. Example Solution 2 To find the energy from each step add up the masses of all the particles going into a step then subtract all the mass coming out of that step. Multiply the result by the speed of light squared to get the energy in Joules. Gamma rays have no mass and the mass of the neutrino can be ignored Step 1: 12C + 1H 13N

8. Example Solution 3 Step 2: 13N 13C + e+ Step 3: 13C + 1H 14N

9. Example Solution 4 Step 4: 14N + 1H 15O Step 5: 15O 15N + e+

10. Example Solution 4 Final Step: 15N + 1H 12C + 4He This final step actually consumes energy rather than releasing it! Overall Energy produced

11. Angular Momentum

12. Objects in orbit have orbital angular momentum For a point mass moving in a circular orbit of radius r and at a speed v, the orbital angular momentum is just L = mvr

13. Rotating objects have rotational angular momentum For solid objects we express the rotational angular momentum as the product of their moment of inertia (I) and the angular velocity they rotate at (w). L = Iw I will depend on the shape of the body and the axis of rotation.

14. Moments of Inertia The moment of inertia (I) depends on both the shape of the body and the axis of rotation. For a point mass m, moving in a circular orbit with a radius R, I = mR2

15. If gravity is the only force acting on a system, angular momentum is conserved Internal forces cannot change the total angular momentum

16. Example When a massive star explodes in a Type II supernova the core of the star collapses from an iron core with a diameter of 12,500 km to a neutron star with a diameter of 18.0 km. If the total mass of the core remains the same and the original rotational period before the collapse was 31.5 days, what is the rotational period of the resulting neutron star?

17. Example Solution A conserved quantity is simply one that stays the same so Lbefore = Lafter In this case, the object is a sphere before and after the supernova so I = 2/5MR2 and M remains the same