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