The Search for Earth-like Worlds - How a Little Bit of Math Goes a Long Way!

Transcription

1 LIVE INTERACTIVE YOUR DESKTOP The Search for Earth-like Worlds - How a Little Bit of Math Goes a Long Way! Presented by: Dr. Sten Odenwald March 31, 2011

2 Exoplanet Exploration Dr. Sten Odenwald NASA March 30, 2011 Space NASA

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9 Let s pause for questions from the audience

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13 Bizarro solar system with cubical star and planet!

14 Bizarro solar system with cubical star and planet! From Earth, the transiting planet dims the starlight during its transit. The fraction of starlight dimming is just given by the ratio of their projected crosssections:

15 Bizarro solar system with cubical star and planet! From Earth, the transiting planet dims the starlight during its transit. The fraction of starlight dimming is just given by the ratio of their projected crosssections: Star = 16 Planet = 4 Ap = A* 16

16 A star dimmed its brightness by 4%. How big is the planet compared to the star? A) 0.4 B) 0.2 C) 0.02

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19 The star HAT-P-7 Distance 320 parsecs Mass 1.5 suns Temperature 6350 K Radius 1.2 million km The graph shows that the star dimmed to from an initial brightness of What is the radius of the transiting planet?

20 Initial brightness Final brightness Dimming = Rs = 1.2 million km

21 Our answer = 100,000 km. Jupiter R = 71,000 km So we got : 1.4 times Jupiter.

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24 Let s pause for questions from the audience

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31 Kepler 10b has a mass of 4 times Earth and a radius 1.4 times Earth. What is its surface gravity if its acceleration is approximately given by: M G = m / s 2 R 2 A) 20 C) B) 5 D) 9.8

32 Water or Ice? Planet surface temperature range Water boils 212 F Water freezes 32 F Or in other words 273 < T < 373

33 Venus D = 0.7 AU T = 750 K D = 0.8 AU Earth D = 1.0 AU T = 184 K to 331 K D = 1.8 AU Europa D = 5.2 AU T = 50 K to 110 K

34 Venus D = 0.7 AU T = 750 K D = 0.8 AU Goldilocks Zone (Habitable Zone) D = 1.8 AU Europa D = 5.2 AU T = 50 K to 110 K

35 Planet surface temperature determined by: Luminosity of star L Distance from star D Reflectivity A

36 To melt ice, you must first raise it to a temperature of 32 F (0 C or 273 K) The energy input is called the Specific Heat = 2,000 Joules/kg/C Then you must actually melt the ice at 0C Called the Latent Heat of Fusion 333,000 Joules/kg Example. I have a 2 kg block of ice, T = 250 K, and I want to melt it. How much thermal energy do I need?

37 To melt ice, you must first raise it to a temperature of 32 F (0 C or 273 K) The energy input is called the Specific Heat = 2,000 Joules/kg/C Then you must actually melt the ice at 0C Called the Latent Heat of Fusion 333,000 Joules/kg Example. I have a 2 kg block of ice, T = 250 K, and I want to melt it. How much thermal energy do I need? E = 2,000 J/kgC x ( ) x ( 2.0 kg) + 330,000 J/kg x 2 kg E = 92,000 J + 660,000 J so E = 752,000 Joules

38 Reflectivity A Also called the Albedo (0.0 < A < 1.0) The more light a body reflects, The less it absorbs, So the cooler it will be.

39 Reflectivity A Also called the Albedo (0.0 < A < 1.0) The more light a body reflects, A becomes larger The less it absorbs, ( 1 A) becomes smaller So the cooler it will be. Asphalt is hot to the touch A = 0.1 White clothing is cold to the touch A = 0.9

40 Distance from star D The farther you are from a star, the less energy will be deposited to a given surface to heat it. Ye Old Inverse Square Law Delivered energy per square meter Total energy from the star = π D 2

41 Stefan-Boltzmann Law For any body that emits like a black body The temperature of a black body, T Is related to the emission of light energy per square meter, F F = σ T 4 where σ = 5.67x10-8 Watts meter -2 K -4 Example. On a hot day, a square-meter of asphalt emits 460 watts about what is its black body temperature?

42 Let s pause for questions from the audience

43 Now lets put it all together!

44 Now lets put it all together! The temperature of a planetary surface depends on σ T 4 =

45 Now lets put it all together! The temperature of a planetary surface depends on The light energy emitted by the star it orbits L σ T 4 =

46 Now lets put it all together! The temperature of a planetary surface depends on The light energy emitted by the star it orbits The distance of the planet from the star L σ T 4 = π D 2

47 Now lets put it all together! The temperature of a planetary surface depends on The light energy emitted by the star it orbits The distance of the planet from the star And the amount of light the surface can absorb L ( 1 A ) σ T 4 = π D 2

48 Now lets put it all together! The temperature of a planetary surface depends on The light energy emitted by the star it orbits The distance of the planet from the star And the amount of light the surface can absorb Oh there is also a factor of 4, to account for the planet absorbing light from π r 2 but emitting over 4 π r 2 L ( 1 A ) σ T 4 = π D

49 Now lets put it all together! The temperature of a planetary surface depends on The light energy emitted by the star it orbits The distance of the planet from the star And the amount of light the surface can absorb There is also a factor of 4, to account for the planet absorbing light from π r 2 but emitting over 4 π r 2 So the final, fundamental, formula for planetary equilibrium temperatures is:

50 Example for Earth: D = 150 million kilometers L = 3.8 x watts A = 0.30 So T = 254 K

51 Habitable Zones The Habitable Zone of every star is defined, mathematically, by determining the range for D where: Water is liquid: 273 < T < 373 For a star of a given luminosity L

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55 Kepler search after 1 year: Total searched.. 156,453 Transit candidates Earth-sized. 68 In Habitable Zone.. 5

56 If 5 Goldilocks Earth-sized planets were detected by Kepler in a search of 156,435 stars, how many are there in the entire Milky Way with 300 billion stars? A) Significantly more than 9,600,000 B) About 9,600,000 C) Much less than 9,600,000

57 By next fall, Space NASA Will produce a resource guide with other math problems related to the search for life in the universe Space NASA

58 Please use your cell phone to give me feed-back on this talk.. Question: Did the content serve your students needs? Set your cell phone up to send a text message. In the TO field enter the number In the TEXT WINDOW enter ONE of the following codes to vote..vote only once please! Too advanced for my students enter Challenging, but would work well enter Just right for my students enter Too elementary for my students enter

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62 National Science Teachers Association Dr. Francis Q. Eberle, Executive Director Zipporah Miller, Associate Executive Director Conferences and Programs Al Byers, Assistant Executive Director e-learning NSTA Web Seminars Paul Tingler, Director Jeff Layman, Technical Coordinator LIVE INTERACTIVE YOUR DESKTOP