Lec02-Jan22

Lec02-Jan22 - 1/22/10 Discussion Ques@on Astro 109...

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Unformatted text preview: 1/22/10 Discussion Ques@on Astro 109 Lecture 2: Tools of the Trade Jan. 22 The spacecra; that landed on the Moon in the 1960s and 1970s are s@ll there. Can we see them from Earth? A.  B.  C.  D.  E.  Yes, with the naked eye. Yes, with a telescope. No, not at all. There is no way to tell without actually looking. I don’t know how to answer this ques@on. Jan. 22 Science as a way of knowing Key Concepts •  science as a way of knowing Science is a way of thinking much more than it is a body of knowledge. – Carl Sagan •  Science: •  angles •  angular vs. actual size •  units •  power ­of ­10 nota@on Jan. 22 •  Focus on specific ideas that can be tested with reproducible experiments/observa@ons. •  Not science: –  astrology –  invoking a supernatural event or divine interven2on Jan. 22 Science and scien@sts •  Scien@sts are people, who are trying to generate knowledge. –  I was like a boy playing on the sea ­shore, and diver2ng myself now and then finding a smoother pebble or a preFer shell than ordinary…. – Isaac Newton –  We are driven by the usual insa2able curiosity of the scien2st, and our work is a delighHul game. – Murray Gell ­Mann •  Science is an ins@tu@on, which provides a framework for evalua@ng knowledge. –  There are many hypotheses in science which are wrong. That’s perfectly alright; they’re the aperture to finding out what’s right. Science is a self ­ correc2ng process. To be accepted, new ideas must survive the most rigorous standards of evidence and scru2ny. – Carl Sagan Jan. 22 (Webster’s New World Dic2onary, 2ed) –  “systema@zed knowledge derived from observa@on, study, and experimenta@on carried out in order to determine the nature or principles of what is being studied” Falsifiability No amount of experimenta2on can ever prove me right; a single experiment can prove me wrong. – Albert Einstein •  Scien@fic theories cannot be proved – only disproved –  can only work “to the best of our knowledge” –  our understanding is never complete •  Untenable ideas must be discarded –  no person is too “great” to be challenged –  no idea is sacrosanct if it conflicts with solid experimental evidence •  The “Scien@fic Method” –  experiments/observa@ons, evidence, hypotheses, theories, laws Jan. 22 1 1/22/10 Predic@on Cornerstones It doesn’t maQer how beau2ful your theory is. It doesn’t maQer how smart you are. If it doesn’t agree with experiment, it’s wrong. – Richard Feynman The most incomprehensible thing about the world is that it is comprehensible. – Albert Einstein •  A theory should explain what is already known, and predict something that is not yet known. •  Causality •  Start with simple systems. •  Universality –  everything that happens has a cause –  the laws we have discovered on Earth hold everywhere and everywhen –  astronomy puts this to the test! •  Not everything is predictable. –  weather, climate, stock market, personal rela2onships, … –  just too many factors Jan. 22 Jan. 22 Scien@sts need… Coordinates on Earth The most exci2ng phrase to hear in science, the one that heralds new discoveries, is not “Eureka!” but “ That’s funny…”. – Isaac Asimov •  Technical skills –  facts, experiments, calcula2ons, … •  la@tude and longitude •  Cri@cal thinking skills –  judgment, logic, reading, wri2ng, … –  to evaluate scien2fic evidence and arguments •  angular coordinates •  Crea@vity –  to see connec2ons (e.g., falling apple < ­ ­> planets) –  to develop hypotheses and explana2ons •  Perseverance –  to explore ideas, discard those proved wrong Jan. 22 Jan. 22 Figure 1V ­ertical 11a Coordinates on the Sky Moon 90° la@tude  ­ ­> Declina@on 1/2° Horizontal The angular diameter of the full moon in the sky is about 1/2°. longitude  ­ ­> Right ascension Jan. 22 Complete circle = 360° (a) Measuring angles in the sky angular coordinates Jan. 22 2 1/22/10 Figure 1 ­11b,c 6° 5° (b) Angular distances in the northern hemisphere (c) Angular distances in the southern hemisphere Jan. 22 Jan. 22 Angular units •  full circle = 360 degrees Example •  The diameter of the Moon is about half a degree. How many arcseconds is that? •  1 deg = 60 arcmin •  1 arcmin = 60 arcsec •   ­ ­> 1 deg = ? arcsec Jan. 22 0.5 deg × 60 arcmin 60 arcsec × = 1800 arcsec 1 deg 1 arcmin Note how we can convert units. Always keep track of units! Jan. 22 Angular vs. actual size: Small ­angle formula angular size D= distance αd 206265 arcsec actual size; a.k.a. physical or linear size Jan. 22 Jan. 22 3 1/22/10 Example Example •  The angular diameter of the Moon is about half a degree. The Moon is about 384,000 km away. What is its physical diameter? •  The angular diameter of the Moon is about half a degree. The Moon is about 384,000 km away. What is its physical diameter? •  •  •  •  Situa@on: relate angular to actual size Tools: small ­angle formula Answer: … Review: does our answer make sense? Jan. 22 D αd 206265 arcsec 60 arcmin 60 arcsec 384000 km = 0.5 deg × × × 1 deg 1 arcmin 206265 arcsec = 3350 km = Jan. 22 Units Discussion Ques@on Jupiter’s diameter is about 143,000 km. On Dec. 11, 2006, it was 944 million km from Earth. What was its angular diameter? A.  B.  C.  D.  E.  3 arcsec 30 arcsec D 3 arcmin 30 arcmin α 3 deg αd 206265 arcsec D = × 206265 arcsec d 143, 000 km = × 206265 arcsec 944, 000, 000 km = 31.2 arcsec •  SI units (metric system) –  length: meter or kilometer –  mass: kilogram –  @me: second or year –  angle: degree, arcmin, or arcsec = Jan. 22 •  Units are as important as numbers! Always keep track of units! •  Convert units by mul@plying by 1. Jan. 22 Power ­of ­10 nota@on •  A convenient way to express very large and very small numbers, and to compute with them. =1 10 101 = 10 10−1 = 102 = 100 103 = 1000 10−2 = 10−3 = 10 Jan. 22 0 0 944 million km = 944 × 106 km = 9.44 × 100 × 106 km =1 = 9.44 × 102 × 106 km 1 = 0.1 101 1 = 0.01 102 1 = 0.001 103 = 9.44 × 102+6 km = 9.44 × 108 km Jan. 22 4 1/22/10 The Jupiter example 1.43 × 105 km × 2.06265 × 105 arcsec 9.44 × 108 km 1.43 × 2.06265 = × 105+5−8 arcsec 9.44 = 0.312 × 102 arcsec = α = 3.12 × 101 arcsec = 31.2 arcsec Jan. 22 Jan. 22 Astronomers’ units Discussion Ques@on The Sun’s mass is 1.99×1030 kg, three ­quarters of which is hydrogen. The mass of a hydrogen atom is 1.67×10 ­27 kg. About how many hydrogen atoms are there in the Sun? A.  B.  C.  D.  E.  42 2.5×103 1.5×1030 1057 a gazillion Length •  Astronomical Unit (AU) = average distance between Earth and Sun 1 AU = 1.496 × 108 km N 3 1.99 × 1030 kg × 4 1.67 × 10−27 kg 3 × 1.99 = × 1030+27 4 × 1.67 = 0.9 × 1057 = Jan. 22 •  light ­year (ly) = distance light travels in 1 year ￿ ￿ ￿ ￿ 365 d 86400 s 1 ly = 3 × 105 km s−1 × 1 yr × × = 9.46 × 1012 km 1 yr 1d •  parsec (pc) 1 pc = 206265 AU = 3.09 × 1013 km = 3.26 ly Jan. 22 1 AU Astronomers’ units Sun Mass Earth’s orbit •  Sun M⊙ = 1.99 × 1030 kg •  Jupiter MJ = 1.90 × 1027 kg •  Earth M⊕ = 5.97 × 1024 kg Figure 1 ­14 Distance: 1 pc (3.26 ly) Angle: 1 arcsec At a distance of 1 parsec, a length of 1 AU subtends an angle of 1 arcsec. Jan. 22 Observer Jan. 22 5 1/22/10 Discussion Ques@on Recap •  science as a way of knowing •  angles •  angular vs. actual size •  units The spacecra; that landed on the Moon in the 1960s and 1970s are s@ll there. Can we see them from Earth? A.  B.  C.  D.  E.  Yes, with the naked eye. Yes, with a telescope. No, not at all. There is no way to tell without actually looking. I don’t know how to answer this ques@on. •  power ­of ­10 nota@on Jan. 22 Jan. 22 Discussion Ques@on The Moon is approximately 384,000 km away from Earth. Our telescopes can resolve objects as small as 1 arcsec in diameter. The smallest object we can resolve on the Moon is A.  B.  C.  D.  E.  an astronaut’s footprint an Apollo Lunar Module a crater 20 m in diameter a crater 2 km in diameter a crater 200 km in diameter D= 1 arcsec × 384000 km = 1.9 km 206265 arcsec Jan. 22 6 ...
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