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# Development and Implementation of Student Activity to Find Mass of Black Hole by Naoki Matsumoto

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Presented at the GHOU 2018 conference in Vienna, Austria from 13-15 August. http://handsonuniverse.org/ghou2018/program/

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### Development and Implementation of Student Activity to Find Mass of Black Hole by Naoki Matsumoto

1. 1. DEVELOPMENT AND IMPLEMENTATION OF STUDENT ACTIVITY TO FIND MASS OF BLACK HOLE Naoki Matsumoto Keio Senior High School : JAPAN
2. 2. SURPRISING AT MICHELLE'S PRACTICE Almost same (^o^) I'm happy to meet teachers who make new teaching materials using new result of observations. There are some differences, so please listen. m(_ _)m
3. 3. BACKGROUND 1 In the high school curriculum of Japan, astronomy is learned by a part of earth science. Earth science includes geophysics, earth history, weather, ocean, contents are diverse. The earth science teacher does not spend too much time on astronomy. However, many students like cosmos, astronomy and black holes.
4. 4. Survey of interest in science terms for university first graders. (M.Kato, et al. 2004) Humanities students(#409) Science students(#415)Black Hole
5. 5. BACKGROUND 2 FINDING MASS PRACTICE USING M106 NGC4258（M106） Determine the velocity of the gas cloud from radio observation using H2O maser(22GHz) . The mass of the black hole is derived from the velocity v and the distance from the center of this galaxy r. (H.Shinohara, et al. 2015)
6. 6. BACKGROUND 2 FINDING MASS PRACTICE USING M106 NGC4258（M106） This student practice designed for physic class. Difficult (little bit). I thought that to develop a more simple practice using our galaxy for earth science class.
7. 7. KEPLER’S LAW The Japanese national curriculum of earth science contains Kepler 's law. Using Kepler's third law, we can find the mass of a celestial body. Object used in this practice is S2 star which was observed with infrared at European Southern Observatory. (Gillessen, et al.2009)
8. 8. Revolution period Ｐ Orbit radius ａ KEPLER'S 3RD LAW a 一定2 3 P a
9. 9. 2018/9/6 軌道半径 （天文単位） 公転周期 （年） 水星 0.39 0.24 金星 0.72 0.62 地球 1.00 1.00 火星 1.52 1.88 木星 5.20 11.86 土星 9.55 29.46 天王星 19.22 84.02 海王星 30.11 164.77 冥王星 39.54 247.80 a^3/P^2 0.9995 0.9998 1.0000 0.9999 1.0008 1.0052 1.0055 1.0055 1.0068 天文単位(Astronomical Unit：au ) 地球･太陽距離を １ とする
10. 10. CONSTANT ORBIT → GRAVITATION AND CENTRIFUGAL FORCE ARE BALANCED Gravitation force Centrifugal force a Mm 万有引力 F 2 a Mm GF  遠心力 F’ 2 22 P ma4 a mv 'F   Planet mass m Solar mass M Gravity constant G Revolution speed v=2πa／P
11. 11. WORKSHEET PRACTICE Word files of this worksheet can be downloaded from this QR code ⇗. Lower part of the first page 2πa P 𝑚∙4π2 𝑎2 𝑎𝑃2 = 4π2 𝑚𝑎 𝑃2
12. 12. NEWTON'S KEPLER'S THIRD LAW EVOLVED FORM 2 2 2 P ma4 a Mm G   22 P a4 a M G   Gravity = Centrifugal force 2 32 P a4 GM   22 3 4 GM P a   a : Orbital radius P : Revolution Period G: Gravity constant M: Mass of central object =Const.
13. 13. 2 32 GP a4 M  22 3 4 GM P a   Planet's movement → mass of the sun Satellite movement → mass of the planet Stellar motion around BH → mass of BH
14. 14. WORKSHEET PRACTICE Lower part of the first page 2πa P 𝑚∙4π2 𝑎2 𝑎𝑃2 = 4π2 𝑚𝑎 𝑃2 4𝜋2 𝑎3 𝐺𝑃2
15. 15. PRACTICE -- MASS OF THE SUN FROM EARTH’S ORBIT 2018/9/6 2 32 GP a4 M   Second page Earth’s A≒1.5×1011(m) P≒3×107(sec) G≒7×10-11 π2≒9 𝑀 = 4 ∙ 9 ∙ 3 2 3 × 1033 7 × 10−11 ∙ 9 × 10143 30 = 4 ∙ 33 × 1030 23 ∙ 7 = 27 14 × 1030 ≒ 2 × 1030 (kg)
16. 16. BLACK HOLE IN THE CENTER OF THE OUR GALAXY Sgr A* Stars revolve. 2018/9/6
17. 17. BLACK HOLE IN THE CENTER OF THE GALAXY Attention to the star S2. Revolution period + Orbit radius →Celestial mass Let's find it. 2018/9/6
18. 18. IMAGE CORRECTION Orbital inclination angle as viewed from the Earth of S2 is 45°. This image has the orbital inclination angle corrected to 90°. Therefore, it is determined only by measuring the orbital radius with a ruler.
19. 19. FIND ORBITAL RADIUS Just measure it with a ruler. scale 8.9 0.195×1014m→1.2cm 1.45×1014
20. 20. FIND REVORUTION PERIOD The rule of thumb OK! Apastoron → Periastron is half period. Periastron of BH Apastron of BH About 1:2(2002.33-2002.25)/3*2 =0.05 A: 2002.25+0.05 2002.30 About 1:3 1994.62 15.4 4.8×108 A B
21. 21. FIND MASS OF THE BLACK HOLE 2018/9/6 2 32 GP a4 M   S2’s a≒1.45×1014(m) P≒4.8×108(sec) G≒7×10-11 π2≒9 𝑀 = 4 ∙ 9 ∙ 1.453 × 1014×3 7 × 10−11 ∙ 4.82 × 108×2 = 0.68 × 1037 = 6.8 × 1036 (kg) = 4 ∙ 9 ∙ 1.453 7 ∙ 4.82 × 1037
22. 22. Literature value : 4.1× 106M☉ Same order → Very good! in astronomy. BH mass led with easy task and simple calculation without science calculator. FIND MASS OF THE BLACK HOLE 6.8 × 1036 3.4 × 106
23. 23. EDUCATIONAL IMPLEMENTATION At Yokohama Science Frontier High School. Teacher: Mitsuhiro Ishida. July 20, 2016; 29students, 12th grade, physics class. September 12, 2016; 18students, 12th grade, physics class. Using 1 school hour. YSF