Earth/Moon Scale: Sizes, Distances and Ratios
Tony Leavitt, NASA AESP
Introduction: Students see pictures and models of the solar system
throughout their education. Often these images perpetuate
misconceptions about size, scale and positions of solar system objects.
(Approx. Time: 1 hour class period)
Purpose: Student will explore their concepts and misconceptions about
object sizes, distances and positions in the solar system.
Objectives:
1. Students will examine the meaning of “scale” as it relates to
measurement and models.
2. Students will construct several scale models of the Earth and moon
(and Mars).
3. Students will determine the proportional relationship of the moon
to the Earth (and Mars).
4. Students will explore the distance from Earth to the moon using
their scale models.
Materials:
*Earth models - different sizes (these may be globes, inflatable
globes,
balls of different sizes, or blue balloons) 1 per student
group
*12” balloons blue? = Earth (1) , white = Moon (2) per student group
*String Spool plus (1 length to each group- enough to measure Earth
circumference)
*Rulers with cm/mm.
*Calculators (phones have these)
*Solar System litho sets (optional)
*NASA Earth/Mars poster (optional)
Procedure:
Part 1: Scale Sizes of Earth - Moon - Mars (balloons)
(Student groups of 3-4)
1) Write “Scale” on the board. Ask students for any meaning they
attribute to the word. List these. (Examples: size, measurement,
weight, proportion, comparison, fish or reptile scales, music, to
climb…)
2) Bring out Earth globe model. What definition(s) of scale
applies to maps and models? (size, comparison, proportion - The
relationship of an “actual” distance or size, to a “scale” distance
(on a map) or a “scale” size of a model) (Models may be larger or
smaller than the actual)
3) Give each student group a different size Earth model (globe or
ball or blue balloon to inflate), a length of string long enough to go
around the model and a white balloon = non-inflated (moon).
4) Each group discusses the size relationship of the moon to their
Earth model. Inflate their white balloon to the appropriate size
to represent the moon to scale.
5) Using the string and ruler groups measure the circumferences
of their Earth model and their moon model to the 1/10th cm. (Ex:
30.2 cm)
6) Each group calculates ratio of the moon circumference to the
Earth circumference. Moon cir. / Earth cir. = ? (decimal)
7) Each group holds up their Earth and moon models and state
their size ratios. Discuss which group might be the closest to
correct ratio.
8) Explain that relating circumference, diameter and radius of two
spherical objects will result in the same ratio.
9) Have students look up the diameter of the moon and the Earth
on solar system litho or computer. Next, calculate the proper
ratio.
Moon cir. / Earth cir = 3,476 km / 12,756 km =
? (Answer may vary slightly – discuss this) Compare to group’s
answer.
10) (Optional) Repeat steps 4 -9 with the red Mars balloon.
11) Now show NASA Earth/Mars Poster to compare Mars balloon
size to actual scale on poster. Ask class what ratio of the Mars’
diameter to Earth’s. (approx.= .5) 6792 km / 12,756 km = ?
Part 2: Earth – Moon: Scale Distance
1) Groups now have scale Earth and moon models. (Moon
diameter ¼ that of the Earth globe.)
2) Each group should discuss, estimate and create an Earth to
moon scale distance model. Groups share models with class.
3) Groups now check their model by calculating the scale
distance to the moon. (Students could look up the data below,
again using solar System litho or computer)
Earth- Moon distance / Earth circumference
~380,000 km / ~40,000 km
9.5
E-MDistance= 380,000 km = 380,000 km = 38 = 9 2/4 = 9 ½ =
Earthcircum= 40,000 km
40,000 km
4
4) Groups wrap the string nine and a half times around the globe
to reach the moon. Extend the string and compare to their
estimate model.
Part 3: Earth – Moon Scale: “Nickel”
Materials:
*Nickels (one per group)
*Index card
*Paper hole punch (punch circle for each group)
Procedure:
1) Pass out nickels to groups. Have groups discuss with the Earth
the size of a nickel, what is appropriate for a scale model for the
moon.
2) Pass out hole punches (1 per group), ruler. Measure the Earth
(nickel) diameter (approx. 2 cm) and ‘moon’ diameter (.5 cm)
3) We will use Earth diameters to measure out to the moon. Groups
divide Earth-moon distance by Earth’s diameter.
( 384,000 km / 12,756 km = ?) approx. = 30 times
4) Groups calculate Earth-moon distance in ‘nickel’ scale. Create a
model on their desktops. (2 cm X 30 = 60 cm distance)