lenoir (wml297) – homework 02 – Turner – (58220)
1
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001
(part 1 of 4) 10.0 points
The radius of the moon is 1
.
74
×
10
6
m
,
the
radius of the sun is 6
.
96
×
10
8
m, the average
moonearth distance is 3
.
84
×
10
8
m
,
and the
average sunearth distance is 1
.
496
×
10
11
m.
What is the apparent angle the diameter of
the moon subtends, as seen from the earth?
Correct answer: 0
.
0090625 rad.
Explanation:
If you have an angle
θ
that is very small
(
≈
1
◦
) in measure, then
θ
≈
tan
θ,
for
θ
measured in radians.
r
earth
−
moon
r
earth
−
moon
d
moon
θ
Since the distance from the earth to the
moon or the sun
≫
than the diameters in
volved, the angle can thus be approximated
by its tangent, and
θ
≈
tan
θ
=
diameter
distance
AlternateSolution:
The definition of an
gular displacement is the arc length divided
by the radius. The angular displacement us
ing this definition is labeled using rad (actu
ally a pure number).
For this problem, the “arc length” is ap
proximately the diameter
2
×
R
moon
=
D
moon
= 2 (1
.
74
×
10
6
m)
= 3
.
48
×
10
6
m
of the moon and the radius is the “distance”
R
earth
moon
= 3
.
84
×
10
8
m from the earth to the
moon.
Thus
θ
≡
arc length
radius
=
2
R
moon
d
EM
=
2 (1
.
74
×
10
6
m)
3
.
84
×
10
8
m
=
0
.
0090625 rad
.
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 Spring '10
 Turner
 Correct Answer

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