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40. (a) When
θ
is measured in radians, it is equal to the arclength
s
divided by the radius
R
.F
o
ra
very large radius circle and small value of
θ
,sucha
sw
edea
lw
i
thinF
ig
.1
9
,thea
rcmaybe
approximated as the straight linesegment of length 1 AU. First, we convert
θ
= 1 arcsecond to
radians:
(1 arcsecond)
µ
1arcminute
60 arcsecond
¶µ
1
◦
60 arcminute
¶µ
2
π
radian
360
◦
¶
which yields
θ
=4
.
85
×
10
−
6
rad. Therefore, one parsec is
R
o
=
s
θ
=
1AU
4
.
85
×
10
−
6
=2
.
06
×
10
5
AU
.
Now we use this to convert
R
= 1 AU to parsecs:
R
=(1AU)
µ
1pc
2
.
06
×
10
5
AU
¶
=4
.
9
×
10
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 Spring '08
 FURLAN

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