1. PTYS 214 – Spring2011  Homework #3 DUE in class TODAY  Class website: http://www.lpl.arizona.edu/undergrad/classes/spring2011/Pierazzo_214/  Useful Reading: class website  “Reading Material” http://en.wikipedia.org/wiki/Sun http://www.solarviews.com/eng/sun.htm Announcements

2. Classification of living organisms by carbon and energy sources Plants are…Humans are… Nutritional TypeEnergy SourceCarbon Source Photo-autotrophsLightCO 2 Chemo-autotrophsInorganic Compounds (H 2, NH 3, NO 2, H 2 S) CO 2 Photo-heterotropsLightOrganic Compounds Chemo-heterotropsOrganic Compounds

3. Life needs energy Photosynthesis: 6CO 2 + 6H 2 O + h (Energy) → C 6 H 12 O 6 + 6O 2 99.9% of energy at the Earth’s surface is from Solar Radiation

4. The Sun  ~4.6 billion years old  G2 class star (~8% of stars are G class) based on photospheric temperature  In our galaxy >100 million stars are of the same class Sun in X-rays NASA/ESA SOHO

5. The Sun – Basic Facts Distance from Earth 1 AU = 1.5×10 8 km Mass 333,000 Earth Masses 99% mass of the Solar system Diameter 109 Earth Diameters Composition (by mass) 74% Hydrogen 24% Helium <2% other elements Average Density 1410 kg/m 3 Sun and Planets to scale

6. The size of the Sun is due to the overall balance between two main forces: Sun Size : Hydrostatic Equilibrium 1) Gravity: Tremendous weight of the mass of the Sun that presses inward under the force of gravity 2) Pressure: Enormous pressure inside the Sun (generated by nuclear fusion) that pushes outward The life of any star is a constant balancing of Gravity & Pressure

7. Solar Structure (7 Million K) (2 Million K) Nuclear Fusion

8. Fusion Reactions Combine atomic nuclei to form a heavier nucleus (a heavier element) 12 C + 1 H→ 13 N + γ (Energy) (C and H combine to form a new element, N) Very different from Chemical Reactions : Deal with electrons binding atoms of certain elements into molecules, but the elements (nuclei) do not change: 6CO 2 + 6H 2 O + h (Energy) → C 6 H 12 O 6 + 6O 2 (number of C, H and O atoms does not change)

9.  Nuclear fusion reactions can happen only under very high temperatures and pressures Energy released in nuclear fusion reactions is ~1,000,000 times larger than in chemical reactions Hydrogen bomb

10. The Sun’s Energy Source is Nuclear Fusion in its Core  Nuclear fusion occurs only at the very high temperatures and pressures at the Sun’s core  Proton-proton chain Four hydrogen nuclei “fuse” to form a single helium nucleus  It will continue to heat the Sun for another 5 billion years

11. Proton-Proton Chain One He nucleus has 99.3% of the weight of four H nuclei  Excess 0.7% mass is converted into energy: E=mc 2

12. Energy Transfer in the Solar Interior  The convection zone is a region right below the visible surface of the Sun  Here, turbulent convective motions occur, similar to a pot of boiling water  These bubbling motions are responsible for the granulation pattern seen on the Sun’s surface (photosphere) Core: Nuclear Fusion 1.57  10 7 K ~28,000°F Convection zone: 2.2  10 6 K Solar surface: 5,800 K

13. (in the photosphere) They are 100s to1000s of km wide Solar Granulation

14. Photosphere: Visible surface of the Sun Mean surface temperature 5,800K (~10,000 o F) The most obvious features on the surface of the Sun, sunspots have been observded since the 17 th century (Galileo)

15. Sunspots Sunspots vary greatly in size; typical ones measure a few tens of thousands of kilometers A Sunspot's life can be as short as an hour or two or as long as several months They clearly show the Sun’s 27- day rotation! Regions of low temperature and intense magnetic fields

16. The Corona  Outermost layer of the solar atmosphere, made of very high- temperature gases at extremely low density  It is extremely hot: temperatures reach up to about 2 million K  What heats the corona remains an open question!  Material (charged particles) from the corona is continuously blown away from the Sun towards space: Solar wind Visible light X-rays

17. Energy from the Sun Once energy reaches the Sun’s surface, it is radiated outward, into space Solar Luminosity: Total energy emitted by the Sun per second L = 3.84 x 10 26 W = 3.84 x 10 26 J/s

18. Energy Conversion The biggest hydrogen bomb ever exploded (Tsar Bomba) was ~50 Megatons of TNT (>3000 times Hiroshima)  1 ton TNT = 4.184 ×10 9 J How many Tsar bombs would be necessary to explode per sec to obtain Solar Luminosity? 1 Tsar bomb = 2.1×10 17 J ~ 1.8 billion Tsar bombs per sec!

19. Solar Flux - Luminosity divided by the area over which it is distributed (energy per sec per unit area) The area over which solar luminosity is distributed increases with distance from the Sun How? How does the solar flux change with distance from the Sun? Why is Earth not destroyed by the energy coming from the Sun?

20. As energy moves away from the Sun, it is spread over a greater area  Inverse Square Law Solar constant:

21. The Solar Constant 1. Determine the area of distribution at the Earth’s orbit A=4πd E 2 1 AU = 1.496×10 11 m 2. Divide L by A

22. Each planet has its own solar constant… …depending on its distance from the Sun

23. S E ~ 1370 W/m 2 d E = 1 AU We can relate the inverse square law to the Earth’s solar constant: SESE S dEdE d A more convenient form of the inverse square law:

24. S Mars = ? S Venus = ? S Jupiter = ? d Mars orbit =1.52 AU d Venus orbit = 0.72 AU d Jupiter orbit = 5.2 AU S Earth = 1370 W/m 2

25. 2642 1370593 51 D= 0.72 1 1.52 5.2 AU Planetary Solar Constant, W/m 2

26. The Sun is not really constant Solar luminosity varies, e.g. sunspots  Solar flares can release hundreds of millions megaton of energy in a few minutes  Prominences/coronal loops eject large amounts of charged particles into space in a few minutes What causes this variability is an active area of research

27. Solar Activity Any type of variation in the appearance or energy output of the sun Sunspots Flares Prominences Can solar activity affect the Earth?

29. Solar Activity and Earth Aurora from Space Shuttle  Solar activity releases large amounts of plasma, charged particles (gases) and electromagnetic radiation moving at up to 3 million miles per hour, making up the Solar Wind  Variation in solar activity results in variation of solar wind intensity  This can affect Earth’s atmosphere and climate, and disrupt telecommunications on Earth  Earth’s magnetic field deflects most incoming charged particles toward Earth's north and south poles Solar wind Earth’s magnetic field

30. Polar Auroras Aurora over Circle, Alaska  Charged particles deflected toward Earth's poles collide with atmospheric molecules causing them to give off light  Each atmospheric gas emit light of a particular wavelength that depend on its electrical state and on the energy of the particle that hits it  The light emitted by atmospheric gases appears as the northern and southern lights, a.k.a. auroras

31. How does the Sun Influence Earth?  Provides energy for life, warms the planet, drives the dynamic atmosphere and oceans  UV light can cause mutations in living organisms  Geomagnetic storms (high solar activity) –Aurora –Power-grid failures (Canada, 1989); Telecommunications failures  High-energy solar particles (solar wind) –can destroy ozone –dangerous radiation dosages to astronauts and passengers/pilots on polar air-travel routes

32. Solar Luminosity Varies in Time Faint Young Sun  The sun was probably 20-25% cooler about 3.5 Gyr ago  Yet, there is no evidence of a cold (freezing) Earth surface The “Faint Young Sun” is important for climate - not so critical for photosynthesis 3.84  10 26 W/m 2

33. Why the Sun gets brighter with time  H fuses to form He in the core  Core slowly loses mass  Core contracts and heats up  Fusion reactions proceed faster  More energy is produced  more energy needs to be emitted warmer!