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Astronomical Units of distance
•Astronomical units (a.u.)
•Parsecs (pc)
•Light Years (ly)
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 1.496 x 108 km = 1.5 x 108 km
Concept -1:
An astronomical unit (AU) is
8
1.5 x 10 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
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
Concept 0:
There are 3600 seconds to a
degree. (Parallax angles are
really small, and measured in
seconds)
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
Suppose Ø = 1.45 x 10-5o
x3600 = .0522” so parsecs
= 1/.0522 = 19.2 pc
Since d is 1 AU, if we
know Ø – the parallax
Angle we can find D –
The distance to the star.
You know that Tan(Ø ) = d/D, so
D = 1.5 x 108 km/Tan(1.45 x 10-5o) = 5.9 x 1014 km
From Douglas Giancoli’s Physics
Concept 1:
The distance in parsecs is
defined as 1/Ø where Ø is
the parallax angle in seconds
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”
Concept 2:
You know that Tan(Ø ) = d/D
(Where d = 1.5 x 108 km)
A star has a parallax of .015” what
is its distance in parsecs and km?
Parsecs = 1/arcseconds =
1/.015 = 66.666 pc
Tan(angle) = 1.5E8km/D,
so D = 1.5E8km/ Tan(angle) =
1.5E8/tan(.015/3600)
15
= 2.06x10 km
2.06x1015 km
A star is 6.14 x 1014 km away.
What is its parallax in arc seconds?
How many parsecs is it away?
-1
Angle = tan (d/D) =
tan-1(1.5E8/6.14E14) =
1.4E-5 degrees x 3600 =
.0504 arcseconds
Parsecs = 1/ = 1/.0504 = 19.8 pc
19.8 pc
Light Year - The distance traveled by light in a year
1 ly = (2.998x108m/s)(365.2499d/y)(24h/d)(3600s/h)
1 ly = 9.46x1012 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 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