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

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

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

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

Calculating Earth’s Orbit: If you know the Earth-Mars distance, Kepler’s law R E 3 = R M 3 T E 2 T M 2 now lets you figure out the radius of Earth’s orbit. (not too accurate – transits) 1.5 x 10 8 km

Concept -1: The Astronomical Unit - The Earth-Sun distance. Courtesy of Kepler, heresy, and Galileo 1 A.U. is 1.496 x 10 8 km  1.5 x 10 8 km

Neptune is 4500 million kilometers from the sun. How far is this in AUs? 4500x10 6 km/(1.5x10 8 km/AU) = 30AU 30AU

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

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) = 8.3x10 14 km or simply 1 pc = 3.08568025×10 13 km so 27 pc x (3.08568025×10 13 km/pc) = 8.3x10 14 km

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

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

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

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”

Light Year - The distance traveled by light in a year 1 ly = (2.998x10 8 m/s)(365.242199d/y)(24h/d)(3600s/h) 1 ly = 9.46x10 15 m =  10 16 m 1 ly = 9.46 x10 12 km  10 13 km 1 parsec = 1.496 x 10 8 /Tan(1/3600) = 3.086 x 10 13 km = (3.086 x 10 13 km)/(9.46x10 12 km/ly) = 3.26 ly

A star is 6.14 x 10 14 km away. How many parsecs is it away? What is its parallax in arc seconds? pc = (6.14 x 10 14 km) /(3.086 x 10 13 km/pc) = 19.9 pc parallax = 1/pc =.050” 19.9 pc,.050”

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 10 13 km/pc) = 2.1 x 10 15 km 67 pc, 2.1x10 15 km

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

Our Galaxy is 100,000 ly wide. How many meters wide is it? (100,000ly)(9.46x10 12 km/ly)(1000m/km) = 9.46x10 20 m

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