Understanding Solar Rotation and Fusion in AST 1120 Lab 3

AST 1120: Stellar Astronomy Name: Lab 3 (40 points) The Sun & Fusion Learning Goals  Describe the Sun’s rotation rate and how it is measured  Describe how the Sun maintains hydrostatic equilibrium  Describe the steps of the proton-proton chain fusion reaction  Explain how energy is produced in the Sun Recall from lab 1: write very large and very small numbers in scientific notation. Keep only 3 significant figures unless told otherwise. Show work on math problems. In addition to the hyperlinks shared throughout, this lab also refers to content in Chapter 15 and Chapter 16 of OpenStax Astronomy. Part 1: Solar Rotation Images in Figure 1 are from the SOHO spacecraft taken in 2002. Blank boxes are days when no data was collected. Safely assume that the Sun still existed on those days. Figure 1 - SOHO data of the Sun from June 13 - June 30, 2002

1. Based on Figure 1, how many total days does it take for sunspot group 5 to move across the Sun’s disc as seen by SOHO? Include days when data was not taken if you can safely assume that sunspot group 5 was still present on that day. 13 days June 17 - June 29 2. Multiply your answer above by 2 to get the total number of days that it takes the Sun to rotate at sunspot group 5’s latitude. Units are days per rotation. 26 days 3. Based on Figure 1, how many total days does it take for sunspot group 1 to move across the Sun’s disc as seen by SOHO? Include days when data was not taken if you can safely assume that sunspot group 1 was still present on that day. 10 days 4. Multiply your answer above by 2 to get the total number of days that it takes the Sun to rotate at sunspot group 1’s latitude. Units are days per rotation. 20 days 5. How many total days does it take for sunspot group 8 to move across the Sun’s disc as seen by SOHO? Include days when data was not taken if you can safely assume that sunspot group 8 was still present on that day. 12 days 6. Multiply your answer above by 2 to get the total number of days that it takes the Sun to rotate at sunspot group 8’s latitude. Units are days per rotation. 24 days 7. Does your data above support differential rotation in the Sun? Use your data to justify your response. 8. Using your answers above determine the average number of days per rotation for the Sun’s rotation. 9. At the Sun’s equator, the known rotation rate is 25 days per rotation. Use your average as data and compare to the known value. % error = | ( ( data−known ) known ) | × 100 = ¿ 2

10.Explain why there is an issue with comparing your data to data from the Sun’s equator. Part 2: Fusion and Hydrostatic Equilibrium in the Sun This Animation describes the steps of the proton proton chain fusion process and this video describes the solar core . These topics are also covered in Chapter 16 . 11.Balance within our sun is called hydrostatic equilibrium. What two forces are working against each other to produce this balance? 12.Why do protons repel each other at low temperatures? 13.What force allows protons to combine at high temperatures? 14.What is the minimum temperature required for fusion to occur in the Sun? 3

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Figure 2 - Steps of Proton-Proton Chain fusion 15.What antimatter particle is produced during the proton-proton chain? 16.The equation E = mc 2 means that matter can be converted completely into energy. How is this achieved in the core of the sun? 17.Why are neutrinos important to our understanding of the fusion process? 18.How many total hydrogen atoms go into the proton-proton chain process? 19.How much mass is lost during a single instance of proton-proton chain fusion? Use the numbers given below. Take the starting hydrogen minus the resulting helium. Four hydrogen nuclei have a mass of 6.6904 × 10 − 27 kilograms. One helium nucleus has a mass of 6.6447 × 10 − 27 kilograms. 4

20.How much energy is produced from the mass lost during proton-proton chain fusion? Use E = mc 2 where m is the mass lost (found above) and c is the speed of light, 3 × 10 8 meters/second. Show your work. The units of energy are Joules (J). 21.How many fusion reactions would it take to power a 100 Watt light bulb for 1 second? (100 Watts = 100 Joules/sec). Divide 100 by your answer in Joules above (yes 100 divided by your previous answer). You should get a big number! 22.The total energy output of the Sun each second is 4 × 10 26 Joules . Rearrange E = mc 2 to solve for the total mass that the Sun must fuse each second, m = E c 2 . C is still the speed of light. For energy, use E = 4 × 10 26 Joules . Show your work. The mass lost has units of kg/sec. 23.Figure out how long the Sun would last if it converted its entire mass into energy through the proton-proton chain. The total mass of the Sun is 2 × 10 30 kg . Use the mass lost in kilograms per second that you found in the previous question. Show your work. Lifetime ( seconds ) = total mass ( kg ) masslost ( kg / second ) 5

24.For the Sun, convert the lifetime in seconds into lifetime in years. There are 3.16 × 10 7 seconds in one year. Show your work. Your answer in years should be smaller than the number in seconds. 25.Main Sequence stars such as our Sun obey a Mass-Luminosity relationship that can be written as: Luminosity ∝ Mass 3.5 . The symbol there means proportional to and luminosity is a measurement of energy output in Joules. How will the luminosity of a 10 solar mass star compare to the luminosity of our sun? 26.Thinking about hydrostatic equilibrium, why do more massive main sequence stars have to have higher luminosities? 27.The main sequence lifetime of a star like our Sun is 1 × 10 10 years. Explain why a low mass main sequence star can live much longer, for 5 × 10 11 years. 6

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Figure 3 - Size comparison of the stars Betelgeuse, Rigel and our Sun Check out the highly scientifically accurate image shown in Figure 3. Betelgeuse and Rigel are both supergiant stars in the constellation Orion. 28.Rigel and Betelgeuse are no longer in hydrostatic equilibrium. What force is winning in these stars? Explain how you can tell. 29.Which of the supergiants shown in Figure 3 has a colder surface temperature than our sun and which has a hotter surface temperature? 30.Can you determine the core temperature of a star from its outward appearance? Explain your answer. 7

Figure 4 - Cutaway image showing the layers of the Sun’s interior 31.In your own words, explain how energy travels outward from the sun’s core toward the photosphere. 32.Recall from earlier in the lab, which type of electromagnetic radiation is produced in the sun’s core during the proton-proton chain? 33.What type of electromagnetic radiation is emitted from the sun’s photosphere? 34.Why do photons of light lose so much energy in their journey from the core to the photosphere? 8

AST1120-lab3

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