Astronomy Lab

 
Department of Physics, University of Colorado at Denver
Physics 1052 (General Astronomy)
Card Ruler Card

Experiment #2 —Determining the Size of the Moon
The purpose of this experiment is to have you perf
orm a measurement of angular size in the sky,
and to confirm or discredit a folk – tale about
the apparent size of obj
ects are high in the sky
compared to when they are low on the horizon. A
ngular size is the apparent size of an object
measured in degrees, with no information on the obj
ect’s actual size (in kilo
meters or miles) or
distance.
First measure the angular diameter of the Moon to
the nearest 0.1
o
(tenth of a degree). The best
method for making this measurement is to take a
ruler (with divisions
at least
as small as 1 mm)
and hold it at arm’s length so th
at it is in front of the Moon. Us
e your thumb – nails (or two index
cards) to mark the edges of the
Moon cross the ruler as shown in
Fig above. At the same time,
have a friend measure the distance from your eye to
the ruler. Make sure
you are measuring the
size at the widest point of the Moon. There might be more accurate ways to do this measurement
say, taping a dime to the inside of the window a
nd step back until the dime just covers the moon
or other variations on this theme. You are encour
aged to be inventive. Now use the small angle
approximation
206265
D
d
?
??
?
method to estimate the Moon’s angular diameter. Th
e distance between your
thumb – nails is the
short side of the skinny triangle,
D
; the distance from your eye to
the ruler is the long side,
d
and
the angle of the triangle is the angular diameter of the Moon. Recall that above equation gives
You will want to comment on the possible sources
of error in the measurement will make on the
final outcome of the experiment. For example, how
will the distance from your eye to the ruler,
or the measured size of the Moon affect your outcome? If you find a more accurate method for
making the measurement, include
that in your report, too.
Also test the conjecture that th
e size of the Moon in th
e sky is larger when
it is near the horizon.
How do your results compare? What do you think of the folk – tale now?
Finally, estimate the actual diameter of the Moon in
km. Now the diameter is
the short side of a
triangle and the long side is the average
distance from the Earth to the Moon, about
5
3.8 10 km,
?
center to center. Give both th
e angular size and actual diamet
er you measured in your report.

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