Astronomy 114. Lecture 2: Measurement, astronomical distance. Martin D. Weinberg. UMass/Astronomy Department

Transcription

1 Astronomy 114 Lecture 2: Measurement, astronomical distance Martin D. Weinberg UMass/Astronomy Department A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 1/18

2 Announcements Show and tell Constellations are random... Human brains detect patterns (even when they are not there!) A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 2/18

3 Announcements Show and tell Constellations are random... Human brains detect patterns (even when they are not there!) Problem Set #1 available on line Practice with scientific notation and units Due next Friday Score vs letter grades correct on web site A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 2/18

4 Announcements Show and tell Constellations are random... Human brains detect patterns (even when they are not there!) Problem Set #1 available on line Practice with scientific notation and units Due next Friday Score vs letter grades correct on web site Please read Chapters 1 & 2 Note: In class, I will not cover all material in the reading! A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 2/18

5 Announcements Last class: Distance in meters (m) over 40 orders of magnitude A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 2/18

6 Powers of ten Concept of powers of ten or orders of mangitude is related to the??????? A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 3/18

7 Powers of ten Concept of powers of ten or orders of mangitude is related to the logarithm: A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 3/18

8 Powers of ten Concept of powers of ten or orders of mangitude is related to the logarithm: y = 10 x x = log 10 (y) A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 3/18

9 Powers of ten Concept of powers of ten or orders of mangitude is related to the logarithm: y = 10 x x = log 10 (y) Examples: log 10 (1000) = 3 or log 10 (10 3 ) = 3 A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 3/18

10 Powers of ten Concept of powers of ten or orders of mangitude is related to the logarithm: y = 10 x x = log 10 (y) Examples: log 10 (1000) = 3 or log 10 (10 3 ) = 3 log 10 (3000) = 3.48 = = = A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 3/18

11 Powers of ten Concept of powers of ten or orders of mangitude is related to the logarithm: y = 10 x x = log 10 (y) Examples: log 10 (1000) = 3 or log 10 (10 3 ) = 3 log 10 (3000) = 3.48 = = = log 10 (y 3 ) = log 10 (10 3x ) = 3x log 10 (y n ) = n log 10 (y) A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 3/18

12 Sample data Standard notation Scientific notation Logarithmic Mass Luminosity Mass Luminosity Mass Luminosity A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 4/18

13 Plots (1/2) Direct plot of data A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 5/18

14 Plots (2/2) Logarithmic plot A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 6/18

15 Plots (2/2) Logarithmic plot Logarithmic axes A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 6/18

16 Location of points in space A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 7/18

17 Location of points in space One dimensional A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 7/18

18 Location of points in space One dimensional Number line Mile markers on a highway A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 7/18

19 Location of points in space One dimensional Number line Mile markers on a highway Two dimensional A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 7/18

20 Location of points in space One dimensional Number line Mile markers on a highway Two dimensional Battleship game Longitude and latitude A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 7/18

21 Location of points in space One dimensional Number line Mile markers on a highway Two dimensional Battleship game Longitude and latitude N-dimensional... A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 7/18

22 Location of points in space One dimensional Number line Mile markers on a highway Two dimensional Battleship game Longitude and latitude N-dimensional... N = 3, cubic grid, spherical grid N = 4, time and space N = 10, 11, 26, string theory A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 7/18

23 Two-dimensional coordinate systems (1/2) Rectangular grid Polar grid A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 8/18

24 Two-dimensional coordinate systems (2/2) Projection of sphere onto paper A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy 114 9/18

25 Astronomical measurement Measuring distance directly is hard A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

26 Astronomical measurement Measuring distance directly is hard Measuring angles on the sky is easy A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

27 Astronomical measurement Measuring distance directly is hard Measuring angles on the sky is easy Strategy: measure angles and infer distance A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

28 Geometry of distance (1/4) θ/2 θ/2 d d D/2 D/2 A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

29 Geometry of distance (1/4) θ/2 θ/2 d d D/2 D/2 D/2 = d sin(θ/2) A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

30 Geometry of distance (1/4) θ/2 θ/2 d d D/2 D/2 D/2 = d sin(θ/2) D = 2d sin(θ/2) A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

31 Geometry of distance (2/4) θ/2 θ/2 d d D/2 D/2 When the angle is very small: sin(θ) θ where the angle θ must be expressed in radians D = 2d sin(θ/2) D = dθ A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

32 Geometry of distance (3/4) Surveyor s transit: Used to measure terrestrial angles for surveying A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

33 Examples: size of Moon, distance to Sun d θ D d A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

34 Examples: size of Moon, distance to Sun d θ D d D = dθ d = D/θ A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

35 Geometry of distance (4/4) Small angle formula: D = dθ where θ is in radians. A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

36 Geometry of distance (4/4) Small angle formula: D = dθ where θ is in radians. 2π radians is 360 degrees so: D = d360 2π θ where θ is in degrees. A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

37 Geometry of distance (4/4) Small angle formula: D = dθ where θ is in radians. 2π radians is 360 degrees so: D = d360 2π θ where θ is in degrees. Adegree is often too large a unit Divide one degree into 60 minutes Divide one minute into 60 seconds D = d 2π θ and doing the arithmetic: D = where θ is in seconds of arc. dθ 206,265 A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

38 The Parsec Earth moves around Sun in nearly a circle A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

39 The Parsec Earth moves around Sun in nearly a circle Diameter of orbit is 1 astronomical unit (1 AU = m) A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

40 The Parsec Earth moves around Sun in nearly a circle Diameter of orbit is 1 astronomical unit (1 AU = m) Define a parsec as the distance of an object if angle on the sky changes by one second of arc for a baseline of 1 AU A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

41 More distance units Lightyear: distance light travels in a year, km Parsec(pc): km = 1.3 ly Kiloparsec(kpc): 1,000 = 10 3 pc Megaparsec(Mpc): 1,000,000 = 10 6 pc A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

42 More distance units Lightyear: distance light travels in a year, km Parsec(pc): km = 1.3 ly Kiloparsec(kpc): 1,000 = 10 3 pc Megaparsec(Mpc): 1,000,000 = 10 6 pc Solarsystem: 100 AU = 100/206,265 pc = pc MilkyWaygalaxy: 40,000 pc = 40 kpc Local group of galaxies: few Mpc Great wall: 100 Mpc Observable Universe: 3,000-6,000 Mpc A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

43 Location of Galaxies A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18

44 Location of Galaxies A114: Lecture 2 31 Jan 2007 Read: Ch. 1-2 Astronomy /18