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Astronomical Units of distance Size of the Earth (Geometry!!!!!) Astronomical units (a.u.)

Astronomical Units of distance Size of the Earth (Geometry!!!!!) Astronomical units (a.u.) Parsecs (pc) Light Years (ly). Measuring Earth - Geometry.  = s/r Two wells E-W Measure s Time sun /2 = t/24 hr. Paris. Ø. Cayenne (in French Guiana). This angle was measured simultaneously.

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Astronomical Units of distance Size of the Earth (Geometry!!!!!) Astronomical units (a.u.)

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  1. Astronomical Units of distance • Size of the Earth (Geometry!!!!!) • Astronomical units (a.u.) • Parsecs (pc) • Light Years (ly)

  2. Measuring Earth - Geometry  = s/r Two wells E-W Measure s Time sun /2 = t/24 hr

  3. Paris Ø Cayenne (in French Guiana) This angle was measured simultaneously Measuring Earth-Mars: In 1672:

  4. 1.5 x 108 km If you know the Earth-Mars distance, Kepler’s law RE3 =RM3 TE2 TM2 now lets you figure out the radius of Earth’s orbit. (not too accurate – transits) Calculating Earth’s Orbit:

  5. Concept -1: The Astronomical Unit - The Earth-Sun distance. Courtesy of Kepler, heresy, and Galileo 1 A.U. is 1.496 x 108km 1.5 x 108 km

  6. Neptune is 4500 million kilometers from the sun. How far is this in AUs? 4500x106 km/(1.5x108km/AU) = 30AU 30AU

  7. Parsecs - Parallax Seconds d (parsec) = 1 p (arc-second) p = parallax angle in seconds (1 second - 1/3600 of a degree) From Douglas Giancoli’s Physics

  8. Example: A star has an annual parallax of .037”. What is its distance in parsecs? How far away is it in km? pc = 1/.037 = 27 pc Tan(Ø) = Opp = (1 A.U) Adj (distance to the star) Ø = .037”/3600 = 1.02777 E-5 degrees opp = 1.496E8 km distance = (1.496E8 km)/Tan(1.02777 E-5 degrees) = 8.3x1014 km or simply 1 pc = 3.08568025×1013 km so 27 pc x (3.08568025×1013 km/pc) = 8.3x1014 km

  9. How many arc seconds are there in 3.2 degrees? 3.2o*3600”/o=11520” 11520”

  10. 45 arc seconds is how many degrees? 45”/3600”/o=.0125o .0125o

  11. If a star has a parallax of .12”, what is its distance in parsecs? Parsecs = 1/arcseconds = 1/.12 = 8.3 pc 8.3 pc

  12. If a star is 89 parsecs away, what is its parallax in arc seconds? Parsecs = 1/arcseconds so 89 = 1/arseconds, arseconds = 1/89 = .0112” .0112”

  13. Light Year - The distance traveled by light in a year 1 ly = (2.998x108m/s)(365.242199d/y)(24h/d)(3600s/h) 1 ly = 9.46x1015 m =  1016 m 1 ly = 9.46 x1012 km  1013 km 1 parsec = 1.496 x 108/Tan(1/3600) = 3.086 x 1013 km = (3.086 x 1013 km)/(9.46x1012 km/ly) = 3.26 ly

  14. A star is 6.14 x 1014 km away. How many parsecs is it away? What is its parallax in arc seconds? pc = (6.14 x 1014 km) /(3.086 x 1013 km/pc) = 19.9 pc parallax = 1/pc = .050” 19.9 pc, .050”

  15. A star has a parallax of .015” what is its distance in parsecs and km? Parsecs = 1/arcseconds = 1/.015 = 66.666 pc km = (66.666 pc) (3.086 x 1013 km/pc) = 2.1 x 1015 km 67 pc, 2.1x1015 km

  16. A star is 4.3 light years from Earth. How many parsecs is this? = 4.3 ly/(3.26 ly/pc) = 1.3 pc 1.3 pc

  17. Our Galaxy is 100,000 ly wide. How many meters wide is it? (100,000ly)(9.46x1012 km/ly)(1000m/km) = 9.46x1020m 9.46x1020m

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