Astronomical Units of distance Size of the Earth (Geometry!!!!!)Size of the Earth (Geometry!!!!!)...
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Transcript of Astronomical Units of distance Size of the Earth (Geometry!!!!!)Size of the Earth (Geometry!!!!!)...
Astronomical Units of distanceAstronomical 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/rTwo wells E-WMeasure sTime 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 lawRE
3 = RM
3
TE2 TM
2
now lets you figure out the radius of Earth’s orbit.(not too accurate – transits)
1.5 x 108 km
Concept -1:
The Astronomical Unit - The Earth-Sun distance.Courtesy of Kepler, heresy, and Galileo
1 A.U. is 1.496 x 108 km 1.5 x 108 km
Neptune is 4500 million kilometers from the sun. How far is this in AUs?
4500x106 km/(1.5x108km/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 degreesopp = 1.496E8 kmdistance = (1.496E8 km)/Tan(1.02777 E-5 degrees) = 8.3x1014 km
or simply
1 pc = 3.08568025×1013 kmso 27 pc x (3.08568025×1013 km/pc) = 8.3x1014 km
How many arc seconds are there in 3.2 degrees?
3.2o*3600”/o=11520”
11520”
45 arc seconds is how many degrees?
45”/3600”/o=.0125o
.0125o
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 arcseconds?
Parsecs = 1/arcseconds so 89 = 1/arseconds, arseconds = 1/89 = .0112”
.0112”
Light Year - The distance traveled by light in a year
1 ly = (2.998x108m/s)(365.242199d/y)(24h/d)(3600s/h)1 ly = 9.46x1015 m = 1016 m1 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
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 pcparallax = 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 1013 km/pc) = 2.1 x 1015 km
67 pc, 2.1x1015 km
A star is 4.3 light years fromEarth. How many parsecs isthis?
= 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)(9.46x1012 km/ly)(1000m/km) = 9.46x1020m
9.46x1020m