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
Measuring Earth-Mars:
In 1672:
Paris
Ø
Cayenne (in French Guiana)
This angle was measured simultaneously
Calculating Earth’s Orbit:
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)
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 =
Adj
(1 A.U)
(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
How many arc seconds are
there in 3.2 degrees?
3.2o*3600”/o=11520”
11520”
45 arc seconds is how many
degrees?
o
45”/3600”/o=.0125
.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 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 = (2.998x108m/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
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”
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 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)(9.46x1012 km/ly)(1000m/km) =
9.46x1020m
9.46x1020m