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