UNIT 7: Kilo Hoku - Astronomy & Navigation
Teacher’s Notes for Part C: Comparing Planets
Mass, Density & Gravity
1. How much would a can of soda weigh on Pluto?
Weigh pennies and place them in soda cans to get the approximate weight of a can on
each planetary object or use a material such as quickcrete instead. (More advanced students
can calculate the number of pennies needed for each can.)
It is helpful to use a different type of soda can for each or paint each can a different
color. This allows the students to say, for example, the Coke can represents what a can of
soda would weigh on Jupiter and the Pepsi can represents what a can of soda would weigh
on Neptune. Tape the tops of each soda can so that the pennies will not fall out.
The amount of gravity a planet possesses depends on its mass and volume (density)
and radius. Function of mass and radius: g = (GM/R2) where:
G = 6.67x10-11 m3kg-1s-1; M =mass of object; R = radius of object
A person's weight depends on the mass of the person, mass of the planet and the
planet’s radius.
Therefore a person will weigh less on a planet that has less mass and similar radius
than the Earth and weigh more on a planet that has a larger mass than the Earth and similar
radius. This is illustrated by using a simple can of soda pop. On Earth a 16-ounce can weighs
386 grams. Take several other empty soda cans and fill them with material (lead pellets,
marbles, rock, etc.) until they weigh the amounts for each planet shown on the table below
(this lists how much a full can of soda would weigh on various planetary objects as well as
other statistics about the planetary objects).
Pennies
Mass (kg)
Radius
(km)
Density *Gravity **Relative
kg/m3
(GM/R2) Gravity
~4139
1.99E+30
69,595
1,409
274.03
27.9
Mercury 145
57
3.42E+23
2,440
5,427
3.83
0.4
Venus
349
135
4.97E+24
6,052
5,204
9.05
0.9
Earth
386
149
6.1E+24
6,371
5,515
9.82
1.0
Moon
64
24
7.32E+22
1,738
3,340
1.62
.2
Mars
145
54
6.52E+23
3,390
3,934
3.79
0.4
Jupiter
910
348
1.93E+27
71,492
1,326
25.20
2.6
Saturn
352
133
5.8E+26
60,268
687
10.44
1.1
Uranus
342
129
8.9E+25
24,973
1,290
9.52
1.0
Neptune 433
166
1.04E+26
24,764
1,638
11.10
1.1
Pluto
10
1.09E+22
1,151
2,030
0.5
0.1
Body
grams
Sun
10,808
25
2
-11
3
-1 -1;
* g = (GM/R ) where G = 6.67x10 m kg s M =mass of object; R = radius of object
** Object of interest/Earth’s Gravity, e.g., for the Sun 274.03/9.82 = 27.9
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Activity: Ask students try to put the cans in order from lightest to heaviest. Then show the
students which can correlates to which planet so they can see how heavy or light a can of
soda would be on the different planetary objects.
The goal here is for the students to make the connection that in general, the more
massive the planet the larger the gravitational pull, and therefore the can will “weigh” more on
larger planets. However, some planets which are larger than Earth, such as Saturn and
Uranus, have lower gravity. This is because Saturn and Uranus have a lower average
density and much greater radius than Earth. Note, the heaviest soda can goes with the
largest planet. If further guidance is needed, the correlation with size and mass can be
pointed out to them. It will be necessary to explain that Saturn and Uranus have similar
gravities to Earth. Here is a good place to talk about the difference between mass and
density.
Graphing Exercise: Have the students plot of grams of a can of soda on the planet versus:
1. mass of the planets; 2. radius of the planets; 3. gravity on each planet; and 4. density of
the planets (see graphs below). None of the graphs show any correlation except for the
graph of grams of a can of soda versus gravity. Ask students to interpret each graph in one
or two sentences.
ANSWER KEY for Exercise:
A
Graph A is a plot of how much a can of soda would weigh on a planetary body versus
the mass of the planet. The y-axis in graph A is written in scientific notation (Scientific
notation, or exponential notation, is a way of writing numbers that accommodates
values too large or small to be conveniently written in standard decimal notation, e.g.,
5,720,000,000 = 5.72 x 109)
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B
Graph B is a plot of how much a can of soda would weigh on a planetary body versus
the radius of the planet (data is listed in the above table). Diamond symbols represent
terrestrial planets; Mercury is blue/gray diamond, Venus is a royal blue diamond, Earth
is a green diamond, and Mars is a red diamond. Circles represent gas giants; Jupiter is
shown as an orange filled circle, Saturn is a pale yellow filled circle, Uranus is a cyan
filled circle, and Neptune is a dark blue filled circle, Pluto is shown as a white square
and the Earth’s Moon is a gray triangle.
On the next page, Graph A is a plot of how much a can of soda would weigh on a
planetary body versus the gravity of the planet and Graph B is a plot of how much a can
of soda would weigh on a planetary body versus the density of the planet (data is listed
in the above table). Diamond symbols represent terrestrial planets; Mercury is
blue/gray, Venus is a royal blue diamond, Earth is a green diamond, and Mars is a red
diamond. (Note that in graph A, Mars and Mercury plot on top of one another;
Mercury’s symbol is the inner, smaller diamond.) Circles represent gas giants; Jupiter is
shown as an orange filled circle, Saturn is a pale yellow filled circle, Uranus is a cyan
filled circle, and Neptune is a dark blue filled circle, Pluto is shown as a white square
and the Earth’s Moon is a gray triangle.
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A
B
Agood website that allows students to compare masses of planets is at:
http://btc.montana.edu/messenger/Interactives/ANIMATIONS/Planet_Mass_Compariso
n/planet_mass_comp_full.htm
A Bonus Assignment is to have the student select an object and determine what it
would weigh on each of the planets. This object can be themselves or anything else
that they know the weight of. It may be necessary to do an example on the board, as
well as give them a worksheet to fill out
Two websites to check the answers to the bonus assignment are:
 http://www.exploratorium.edu/ronh/weight/
 http://www.solarviews.com/eng/edu/weight.htm
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2. Calculating Weight on Different Planetary Objects – Answer Key
Student handout is printed in Part C of Unit 7 of the curriculum.
Source: http://www.exploratorium.edu/ronh/weight/ “Your Weight on Other Worlds”
Answers are according to what a person who weighed 100 lbs on Earth would weigh on
the other planets (and Pluto).
1. On what planet would you weigh the closest to what you weigh on Earth?
Saturn, 106.4
2. On what planet would you weigh the least?
Mars, 37.7
3. On which planet would you weigh the next least?
Mercury, 37.8
4. On what planet would you weigh the most?
Jupiter, 236.4
5. On which planet would you weigh the next most on? How does this compare
with what you weigh on Earth?
Neptune, 112.5 and Fairly close
6. On which 2 pairs of planets would you weigh almost the same? (your answer
should list 4 planets)
Mercury – Mars
and Venus – Uranus
37.8 - 37.7 (0.1) and 90.7 - 88.9 (1.8)
Individually, calculate how much would you weigh on the other 7 planets plus Pluto if
you weighed a 100 lbs on Earth.
Location
Mass on Earth
Gravity
Calculated Weight
Mercury
100 X
.378
= 37.8
Venus
X
.907
= 90.7
The Moon
X
.166
= 16.6
Mars
X
.377
= 37.7
Jupiter
X
2.364
= 236.4
Saturn
X
1.064
= 106.4
Uranus
X
.889
= 88.9
Neptune
X
1.125
= 112.5
Pluto
X
.067
= 6.7
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