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.