1. Astronomical Units of distance
Astronomical units (a.u.)
Parsecs (pc)
Light Years (ly)

2. The Astronomical Unit - The Earth - Sun distance.
First, we knew Kepler’s Period/Radius relationship for the orbit of Mars and Earth around the Sun:
RE3 = RM3
TE2 TM2
Second, we knew the distance to Mars:

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

5. The Astronomical Unit - The Earth - Sun
distance.
Using Kepler’s Period/Radius relationship for the
Orbit of Mars and Earth around the Sun:
RE3 = RM3
TE2 TM2
And a triangulation of Mars to find how far Earth was
from Mars (RM - RE) since the periods were well
known, they now had two equations, and two
unknowns.
RE is of course, 1 A.U.
1 A.U. is x 108 km = 1.5 x 108 km

6. An astronomical unit (AU) is 1.5 x 108 km
Concept -1:
An astronomical unit (AU) is 1.5 x 108 km
3.2*3600=11520

7. Neptune is 4500 million kilometers from the sun. How far is this in AUs?
4500x106 km/(1.5x108km/AU) = 30AU
4500E6/1.5E8 = 30
30AU

8. Parsecs - Parallax Seconds
The distance in parsecs is defined as 1/Ø where Ø is
the parallax angle in seconds
(1 second - 1/3600 of a degree)
From Douglas Giancoli’s Physics

9. Which star is the closest?
Toggle between images
Which star is the closest?
3.2*3600=11520

10. Concept 0:
There are 3600 seconds to a degree. (Parallax angles are really small, and measured in seconds)
3.2*3600=11520

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

12. 45 arc seconds is how many degrees? 45”/3600”/o=.0125o .0125o

13. The distance in parsecs is defined as 1/Ø where Ø is
Concept 1:
The distance in parsecs is defined as 1/Ø where Ø is
the parallax angle in seconds
3.2*3600=11520

14. If a star has a parallax of .12”, what is its distance in parsecs?
Parsecs = 1/arcseconds =
1/.12 = 8.3 pc
Parsecs = 1/arcseconds = 1/.12 = 8.3 pc
8.3 pc

15. 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”
Parsecs = 1/arcseconds so 89 = 1/arseconds, arseconds = 1/89 = .0112”
.0112”

16. the kilometers to the star.
Suppose Ø = 1” so parsecs
= 1/1 = 1 pc
Since d is 1 AU, if we
know Ø – the parallax
Angle we can find D –
the kilometers to the star.
You know that Tan(Ø ) = d/D, so
D = 1.5 x 108 km/Tan(1/3600o) = 3.1 x 1013 km So
1 pc = 3.1 x 1013 km
From Douglas Giancoli’s Physics

17. Light Year - The distance traveled by light in a year
1 ly = (2.998x108m/s)( d/y)(24h/d)(3600s/h)
1 ly = 9.46x1012 km = 1013 km
1 parsec = x 108/Tan(1/3600) = x 1013 km
= (3.086 x 1013 km)/(9.46x1012 km/ly) = 3.26 ly

18. All together: 1 ly = 9.46x1012 km 1 parsec = 3.26 ly = 3.086 x 1013 km
1 A.U. is 1.5 x 108 km
1 ly = 9.46x1012 km
1 parsec = 3.26 ly = x 1013 km

19. How many meters wide is it?
Our Galaxy is 100,000 ly wide.
How many meters wide is it?
(100,000ly)(9.46x1012*km/ly)(1000m/km) =
9.46x1020m
100,000x9.46E12*1000 = 9.46E20m
9.46x1020m

20. A star is 4.3 light years from Earth. How many parsecs is this?
= 4.3 ly/(3.26 ly/pc) = 1.3 pc
= ly/3.26 = 1.3 pc
1.3 pc