Lesson 1: The Sun. Reading Assignment. Summary of Fundamental Forces

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1 Lesson 1: The Sun Reading Assignment Chapter 16.1: Physical Properties of the Sun Chapter 16.2: The Solar Interior Discovery 16-1: SOHO: Eavesdropping on the Sun Chapter 16.3: The Sun s Atmosphere Chapter 16.4: Solar Magnetism Chapter 16.5: The Active Sun Discovery 16-2: Solar-Terrestrial Relations Chapter 16.6: The Heart of the Sun More Precisely 16-1: Fundamental Forces More Precisely 16-2: Energy Generation in the Proton-Proton Chain Chapter 16.7: Observations of Solar Neutrinos Summary of Fundamental Forces Read More Precisely 16-1 Gravitational Force Attractive between all particles Range: infinite Strength: The weakest force by far. We only notice it because Earth consists of so many massive particles ( protons and neutrons). Example: This is the force that keeps you and the atmosphere from floating off into space. Not that Earth (or any other massive object) would have formed in the first place without it. Electromagnetic Force Attractive between oppositely charged particles Repulsive between particles of the same charge Range: infinite Strength: Technically times stronger than gravity, but since most objects have approximately as many positively charged particles as negatively charged particles, the electromagnetic force almost always cancels out on large scales, leaving the gravitational force to dominate the universe. Example: This is the force that binds electrons to atomic nuclei, making atoms, and atoms to other atoms, making molecules, and molecules to other molecules, making, among other things, you. Weak Nuclear Force Can change particles from one type to another (yes, alchemy). Range: m (smaller than an atomic nucleus).

2 Example: This is the force that causes fusion (which powers the sun and heats Earth) and fission (which powers our nuclear power plants, which we will be forced to rely on more over the next decade or two as oil becomes more expensive). Strong Nuclear Force Attractive between quarks and particles made of quarks, such as protons and neutrons. Range: m when holding neutral particles together, but only m when working against the electromagnetic force to hold particles of the same charge together. Strength: The strongest force. Example: This is the force that binds protons and neutrons to other protons and neutrons, making atomic nuclei. Without it, our atomic nuclei would fly apart because the protons are all positively charged. Ouch! Summary of the Proton-Proton Chain Reaction Read Chapter proton: p or 1 H deuterium (proton + neutron): D or 2 H tritium (proton + 2 neutrons): 3 H helium (2 protons + 2 neutrons): 4 He electron: e - positron (antimatter electron): e + electron neutrino: ν e photon (energy): γ The first step of the proton-proton chain reaction is usually written in either of two, equivalent, ways: 1. p + p D + e + + ν e 1. 1 H + 1 H 2 H + e + + ν e The positron almost immediately runs into an electron and annihilates, producing energy: e + + e - 2γ The electron neutrino, which is highly non-interactive, escapes the sun without running into anything. The second and third steps are usually written: 2. 2 H + 1 H 3 He + γ 3. 3 He + 3 He 4 He + 2( 1 H) Since the third step requires two tritium nuclei, the first and second steps have to occur twice. So overall: 6( 1 H) 4 He + 2( 1 H) + 2e + + 2ν e + 2γ Ignoring the two protons that act as catalysts: 4( 1 H) 4 He + 2e + + 2ν e + 2γ Including the two electrons that annihilate the two positrons:

3 4( 1 H) + 2e - 4 He + 2ν e + 6γ Hence there should be two electron neutrinos produced for every six photons produced. And we know how many photons are produced because all of this energy eventually leaves the sun in the form of light, which we can measure very accurately. If you work the numbers, you then find that about two trillion neutrinos are passing through your skull every second. Fortunately for us, neutrinos are extremely non-reactive! Summary of the CNO Cycle proton: 1 H helium (2 protons + 2 neutrons): 4 He carbon-12 (6 protons + 6 neutrons): 12 C carbon-13 (6 protons + 7 neutrons): 13 C nitrogen-13 (7 protons + 6 neutrons): 13 N nitrogen-14 (7 protons + 7 neutrons): 14 N nitrogen-15 (7 protons + 8 neutrons): 15 N oxygen-15 (8 protons + 7 neutrons): 15 O electron: e - positron (antimatter electron): e + electron neutrino: ν e photon (energy): γ C + 1 H 13 N + γ 13 N has too many protons to be stable and radioactively decays: N 13 C + e + + ν e The positron runs into an electron and annihilates: e + + e - 2γ The electron neutrino escapes C + 1 H 14 N + γ N + 1 H 15 O + γ 15 O has too many protons to be stable and radioactively decays: O 15 N + e + + ν e The positron runs into an electron and annihilates: e + + e - 2γ The electron neutrino escapes N + 1 H 12 C + 4 He So overall: 12 C + 4( 1 H) 12 C + 4 He + 2e + + 2ν e + 3γ Ignoring the carbon nucleus that act as catalysts: 4( 1 H) 4 He + 2e + + 2ν e + 3γ Including the two electrons that annihilate the two positrons: 4( 1 H) + 2e - 4 He + 2ν e + 7γ The CNO cycle accounts for only about 10% of the energy output of the sun, but most of the energy output of higher-mass stars:

4 Summary of Solar Neutrino Experiments Read Chapter Homestake (1960s) Chlorine detector 1 per day expected But only few per week detected But not sensitive to proton-proton chain electron neutrinos Gallium Detectors (1990s): Soviet-American Gallium Experiment (SAGE) Gallium Experiment (GALLEX) Sensitive to proto-proton chain electron neutrinos But about half still missing Super Kamiokande (1990s) Purified water detector Not sensitive to proto-proton chain electron neutrinos Again, about half missing Detects neutrino oscillations for non-solar neutrinos, proving that neutrinos have mass (1998) Sudbury Neutrino Observatory (2000s) Heavy water detector Detects neutrino oscillations for solar neutrinos, accounting for the missing neutrinos (2001) Math Notes Diameter Review from ASTR 101: Lesson 5 D = diameter of object θ = angular diameter of object d = distance to object D 2πd (θ / 360 ) Note: This equation is only valid if θ is much less than 360. Radius D = diameter of object R = D / 2 Mass Review from ASTR 101: Lesson 2, Lesson 5

5 m = mass of satellite P = orbital period of satellite a = orbital semi-major axis of satellite G = Newton s constant Newton s form of Kepler s Third Law tells us that: P 2 = [4π 2 / G(M + m)] a 3 If m is much less than M: P 2 (4π 2 / GM) a 3 Solving for M yields: M (4π 2 / G) a 3 / P 2 Ratio Astronomy: Average Density Review from ASTR 101: Lesson 5, Lesson 6 average density = constant M / R 3 Hence: Earth s average density = constant M Earth / R Earth 3 Division yields: average density / Earth s average density = (M / R 3 ) / (M Earth / R Earth 3 ) Simplification yields: average density / Earth s average density = (M / M Earth ) / (R / R Earth ) 3 Note: Earth s average density = 5520 kg/m 3 Example: The sun s mass is 333,000 Earth masses and the sun s radius is 109 Earth radii. Hence, the sun s average density is 333,000 / = times Earth s average density. Ratio Astronomy: Surface Gravity Review from ASTR 101: Lesson 6 surface gravity = constant M / R 2 Hence: Earth s surface gravity = constant M Earth / R Earth 2 Division yields: surface gravity / Earth s surface gravity = (M / R 2 ) / (M Earth / R Earth 2 ) Simplification yields: surface gravity / Earth s surface gravity = (M / M Earth ) / (R / R Earth ) 2 Ratio Astronomy: Escape Speed

6 Review from Review from ASTR 101: Lesson 2, Lesson 6 escape speed = constant (M / R) 1/2 Hence: Earth s escape speed = constant (M Earth / R Earth ) 1/2 Division yields: escape speed / Earth s escape speed = (M / R) 1/2 / (M Earth / R Earth ) 1/2 Simplification yields: escape speed / Earth s escape speed = [(M / M Earth ) / (R / R Earth )] 1/2 Note: Earth s escape speed = 11.2 m/s Luminosity L = luminosity (W) B = brightness (W/m 2 ) d = distance (m) L = B 4πd 2 Example: Earth s distance from the sun is 1 AU = m. The sun s brightness at this distance is 1360 W/m 2. Hence, the sun s luminosity is (1360 W/m 2 ) 4π( m) 2 = W. Nuclear Fusion Read Chapter Consider the overall proton-proton chain reaction: 4( 1 H) + 2e - 4 He + 2ν e + 4γ mass of four protons: kg mass of two electrons: kg Hence, the total initial mass is: kg mass of one helium nucleus: kg mass of two electron neutrinos: negligible mass of four photons: 0 kg Hence, the total final mass is: kg mass difference: total initial mass total final mass = kg kg = kg This mass does not disappear, but is instead converted into the energy that powers the sun, by Einstein s law of conservation of mass and energy: E = mc 2 = ( kg) ( m/s) 2 = (kg m 2 / s 2 ) = J 1 Joule (or J) = 1 kg m 2 / s 2 In the sun, about 600 Mtons of H are converted to He every second. But only the mass difference, corresponding to about 4 Mtons/s, of mass is converted into energy. Still, that s a lot of mass being converted into energy!

7 Homework 1 To put it in perspective, a mere paperclip s worth of mass, if it all could be converted into energy, would be enough to power the city of Chapel Hill for an entire month! Download Homework 1 from WebAssign. Feel free to work on these questions together. Then submit your answers to WebAssign individually. Please do not wait until the last minute to submit your answers and please confirm that WebAssign actually received all of your answers before logging off.

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