The astronomical unit (AU) is defined in terms of the distance from the earth to the sun, namely
1.46•1011 meters. A parsec is the radius of a circle for which a central angle of 1 s intercepts an arc of
length 1 AU. The light year is the distance that light travels in one year.
a) How many parsecs are in one AU?
b) How many meters are in a parsec?
c) How many meters are in a light year?
d) How many AU are in a light year?
e) How many light years are in a parsec?
a) So – start with the definition of an arc-second. 1 arc-second is defined as 4.848µrad. The
relationship between arclength, radius and angle (in radians) is given by S = Rθ . So, with S = 1AU
and theta as given, then the radius of the circle which is one
S
1AU
= 2.06 • 10 5 AU
parsec… R = =
−6
θ 4.848 • 10
b) Since we have parsecs and AU related to each other and meters related to AU then
1.46 • 1011 m
5
5
= 3.007 • 1016 m
… 1 parsec is 2.06•10 AU and so 2.06 • 10 AU
1AU
c) A light-year is a distance measurement, given by the speed of light, multiplied by the length of time
m
day
hour
min
sec
24
60
60
1year = 9.46 • 1015 m
in a year… 3 • 10 8 365
s
year
day
hour min
m
AU
AU
= 6.48 • 10 4
d) 9.46 • 1015
11
light − year 1.46 • 10 m
cy
e) Finally…1 parsec is known in meters. Light-years are known in meters.
m light − year
cy
3.007 • 1016
= 3.18
15
par sec 9.46 • 10 m
par sec