Size of the Earth Geometry Astronomical units au Parsecs pc Light Years ly Measuring Earth Geometry sr Two wells EW Measure s Time sun 2 t24 hr Measuring EarthMars ID: 360762
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Slide1
Astronomical Units of distance
Size of the Earth (Geometry!!!!!)
Astronomical units (a.u.)
Parsecs (pc)
Light Years (ly)Slide2
Measuring Earth - Geometry
= s/r
Two wells E-W
Measure s
Time sun
/2 = t/24 hrSlide3
Measuring Earth-Mars:
In 1672:
Paris
Cayenne (in French Guiana)
This angle was measured simultaneously
ØSlide4Slide5
Calculating Earth’s Orbit:
If you know the Earth-Mars distance, Kepler’s law
R
E
3
=
R
M
3
T
E
2 TM2
now lets you figure out the radius of Earth’s orbit.(not too accurate – transits)
1.5 x 10
8
kmSlide6
Concept -1:
The Astronomical Unit
- The Earth-Sun distance.Courtesy of Kepler, heresy, and Galileo1 A.U. is 1.496 x 108
km
1.5 x 10
8 kmSlide7
Neptune is 4500 million kilometers from the sun. How far is this in AUs?
4500x10
6
km/(1.5x10
8
km/AU) = 30AU
30AUSlide8
Parsecs -
Parallax Sec
onds
d (parsec) =
1
p (arc-second)
p = parallax angle in seconds (1 second - 1/3600 of a degree)
From Douglas Giancoli’s PhysicsSlide9Slide10
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 km
distance = (1.496E8 km)/Tan(1.02777 E-5 degrees) = 8.3x1014 kmor simply1 pc = 3.08568025×10
13 kmso 27 pc x (
3.08568025×1013 km/pc) = 8.3x10
14 kmSlide11
How many arc seconds are
there in 3.2 degrees?
3.2
o
*3600”/o=11520”
11520”Slide12
45 arc seconds is how many
degrees?
45”/3600”/o=.0125
o
.0125
oSlide13
If a star has a parallax of .12”,
what is its distance in parsecs?
Parsecs = 1/arcseconds =
1/.12 = 8.3 pc
8.3 pcSlide14
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”Slide15
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 =
10
16
m
1 ly = 9.46 x1012 km 10
13 km
1 parsec = 1.496 x 108/Tan(1/3600) = 3.086 x 1013 km= (3.086 x 10
13 km)/(9.46x1012 km/ly) = 3.26 lySlide16
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 pcparallax = 1/pc = .050”
19.9 pc, .050”Slide17
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, 2.1x1015
kmSlide18
A star is 4.3 light years from
Earth. How many parsecs isthis?
= 4.3 ly/(3.26 ly/pc) = 1.3 pc
1.3 pcSlide19
Our Galaxy is 100,000 ly wide.
How many meters wide is it?
(100,000ly)(9.46x10
12
km/ly)(1000m/km) =
9.46x10
20m
9.46x1020m