How Large is the Moon?
Name__________________________________
Hour_____
Astronomers sometimes use the Moon to measure the sizes and distances of other objects in the sky. In order
to use the Moon as a measuring tool, we must first know the Moon’s distance, orbital speed, and diameter. By using
basic mathematics and geometry, astronomers were able to calculate the distance from Earth to the Moon to be
385,323 Km. Using the same basic math and geometry, you will calculate the size of the Moon. The method you will
use makes use of the geometry of similar triangles.
D/R = d/r
D = calculated diameter of the Moon
R = 385,323 Km (average distance from Earth to Moon)
d = width of slot in card in cm
r = distance from your eye to the card in cm
When the width of the Moon fits into the width of a notch in an index card, then the triangle between your eye
and the Moon has the same angles as the triangle between your eye and the notch in the card. You know the distance
to the Moon and you can measure the width of the notch in the card and the distance from the card to your eye. With
these measurements, you use like triangles to set up a comparison of each triangle’s height (D and d) to each
triangle’s diameter (R and r). Using the formula, D/R = d/r, you are able to solve for the unknown D,
the diameter of the Moon.
Directions
1.
Use a paper punch to make a hole about 1 cm from one edge
of a note card. With scissors, carefully make parallel cuts
from the edge of the card to the edges of the hole, as shown.
Be careful that the two cuts are no wider or narrower than
the punched circle. Punch a small hole in the center of the
card and fasten a 1 m length of string in the hole with a knot
behind the card.
2.
To measure the Moon, take your cardboard instrument to a
place where you can see the Moon. Hold the card
horizontally so that the diameter of the Moon fits into the
slot in the card. Move the card away from your face until
the width of the Moon just fills the slot that you cut in the
card. Stretch the string tightly from the card to your
cheekbone, just beneath your eye. Measure the length of the
string from the card to your eye. Do three trials one after
the next. Record all three lengths onto the back of this
sheet. Measure the width of the notch in the card and record
onto the back of this sheet.
3.
Use the measurements you have made to
calculate the diameter of the Moon and
answer the completion questions.
Data Sheet
R
r
d
D
=
=
=
=
Name_________________________ Hour_____
385,323 km (the average distance from the earth to the moon)
the distance from your eye to the card (cm)
the width of the slot in the card (cm)
the calculated width of the moon (km)
Please show all your work!
Trial #1:
R
r
d
D
=
=
=
=
385,323 km
__________ cm
__________ cm
__________ km
D = R x d = 385,323 km x d
r
r
385,323 km
__________ cm
__________ cm
__________ km
D = R x d = 385,323 km x d
r
r
385,323 km
__________ cm
__________ cm
__________ km
D = R x d = 385,323 km x d
r
r
Trial #2:
R
r
d
D
=
=
=
=
Trial #3:
R
r
d
D
=
=
=
=
Completion Questions: Show all your work
1. Calculated average Moon Diameter = __________ km
(Show your work)
2. Use a reference source (internet, encyclopedia, book, magazine) and find the actual measured diameter
of the Moon. Diameter = __________km.
3. Calculate the percentage your measurement was off from the actual diameter of the Moon?
(Your measurement - actual diameter) x 100%
Actual diameter
4. PARENT VERIFICATION: I verify that ________________________________________ has
completed the “How Large Is The Moon” exercise.
Student’s Name
______________________________________________
Parent Signature
____________________
Date