Name
Period
Date
The Law of Universal Gravitation Activity
Purpose:
To create graphical and mathematical representations of the relationship between
the force of gravity Fg , the mass of a planet m p  , the mass of its moon mm  , and
their separation distance r  .
Procedure/Analysis:

Navigate to the Gravitation simulation page on the Physics Classroom website.
1. A planet and its moon are shown in the simulation window. Click and drag the
moon to various positions about the planet and observe the gravitational force
vector. In the diagram below, draw a force vector (arrow with arrowhead) to depict
the direction and relative magnitude of the force acting upon the moon at the
designated locations. Note: the size of the arrow should be representative of the
strength of the force.
2. Is the relationship between gravitational force and distance of separation (between
the moon and the planet) an inverse or direct relationship? Explain the evidence for
your conclusion.
3. Note that the simulation allows you to also display the force of the smaller moon
pulling upon the larger planet. Click / tap the button to show the force acting upon
the planet. Which force is largest: the force ON the smaller moon or the force ON
the larger planet? Justify your answer.
The Law of Universal Gravitation Activity
page 2
While using the simulation in #4-10, consider the planet's surface to be a distance of
one planet-radius 1R planet .


4. Now investigate the effect of varying the mass of the moon upon the gravitational
force between the moon and the planet with constant separation distance and
planet mass.
Mass of
Force of
 Use the sliders to alter the mass of the moon and
the moon
gravity
record the force of gravity.
(kg)
(N)
 Graph the force of gravity vs. the mass of the moon.
 Sketch the graph and state the relationship
0
0
between the variables
5 x 1022
10 x 1022
20 x 1022
30 x 1022
40 x 1022
50 x 1022
Mass of the planet = 402 x 1024 kg
Separation Distance = 3R planet
5. Use your observations to answer the following statements:
If the mass of the moon is ...
a. ... increased by a factor of 2, then the force of gravity is (increased, decreased) by a
factor of _______.
b. ... increased by a factor of 3, then the force of gravity is (increased, decreased) by a
factor of _______.
c. ... decreased by a factor of ¼, then the force of gravity is (increased, decreased) by
a factor of _______.
d. ... decreased by a factor of ½, then the force of gravity is (increased, decreased) by
a factor of _______.
The Law of Universal Gravitation Activity
page 3
6. Now investigate the effect of varying the mass of the planet upon the gravitational
force between the moon and the planet with constant separation distance and
planet mass.
Mass of
Force of
 Use the sliders to alter the mass of the planet and
the planet
gravity
record the force of gravity.
(kg)
(N)
 Graph the Force of gravity vs. the mass of the
planet.
0
0
 Sketch the graph and state the relationship
between the variables
200 x 1024
302 x 1024
402 x 1024
502 x 1024
600 x 1024
Mass of the moon = 25 x 1022 kg
Separation Distance = 3R planet
7. Use your observations to answer the following statements:
If the mass of the planet is ...
a. ... increased by a factor of 2, then the force of gravity is (increased, decreased) by a
factor of _______.
b. ... increased by a factor of 3, then the force of gravity is (increased, decreased) by a
factor of _______.
c. ... decreased by a factor of ¼, then the force of gravity is (increased, decreased) by
a factor of _______.
d. ... decreased by a factor of ½, then the force of gravity is (increased, decreased) by
a factor of _______.
The Law of Universal Gravitation Activity
page 4
8. Drag the moon to various locations in order to determine the quantitative effect of
separation distance upon the gravitational force. Examine the effect of doubling,
tripling and quadrupling the distance of separation (as measured from the planet's
center). Consider the planet's surface to be a distance of one planet-radius
1R planet .
Separation
Force of
 Use the table at the right to record the force of
Distance
gravity
gravity for whole-number multiples of R planet .
(m)
(N)
 Graph the Force of gravity vs. the separation
2 R planet
distance.
 Linearize the graph. You will have to do two
3R planet
different modifications to the separation distance
to linearize the graph!
4 R planet
 Sketch all three graphs (original, first attempt to
5 R planet
linearize, final linearized graph) and state the
relationship between the variables
6R


planet
7 R planet
8 R planet
9 R planet
10 R planet
11R planet
12 R planet
Mass of the moon = 25 x 1022 kg
Mass of the planet = 402 x 1024 kg
9. Use your data to complete the following sentences.
If the separation distance between the moon and the planet is ...
a. ... increased by a factor of 2, then the force of gravity is (increased, decreased) by a
factor of _______.
b. ... increased by a factor of 3, then the force of gravity is (increased, decreased) by a
factor of _______.
c. ... increased by a factor of 4, then the force of gravity is (increased, decreased) by a
factor of _______.
d. ... decreased by a factor of ¼, then the force of gravity is (increased, decreased) by
a factor of _______.
Conclusion:

Watch the video Law of Universal Gravitation to see how we can put together
all three relationships into one math model relating the Force of Gravity, the
masses of the objects and their separation distance!