Finding the Universal Gravitational Constant
Name:
The simulations used for this activity can be accessed in the any of the following ways.
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Download and run the Java files from Moodle
Follow the links to the PHET website that is posted in Moodle
Use these links… http://phet.colorado.edu/sims/html/gravity-force-lab/latest/gravity-force-lab_en.html
http://phet.colorado.edu/sims/gravity-and-orbits/gravity-and-orbits_en.jnlp
Introduction
The gravitational attraction between any two objects can be found using Newton’s Universal Law of Gravitation:
This is a very simple, yet accurate, formula that demands a few minimal approximations.
 Both masses are treated as point masses (not too far off when compared to the distances involved)
 “r” is the distance between the centers of the object (doesn’t matter with point masses)
 “G” is not the same as “g”. It is not approximately 9.81 m/s2. “Big G” is called the universal gravitational
constant, while “small g” is the acceleration that gravity induces on a freely falling object at the surface of
a planet.
The purpose of this activity is to use a gravity and orbit simulation to calculate the value of G.
Part 1: Finding G with the Gravity Force Lab
Change the mass and distance values for a broad mixture of situations, completing the first 4 columns of the
chart below. Then use the formula to calculate the value of G for each trial. (Note: you can move the ruler to measure
the distances.)
Mass Object 1 (kg)
Mass Object 2 (kg)
Distance (m)
Force (N)
Gravitation Constant, G
38 kg
25 kg
4m
3.96 X 10^-9
6.67 x 10-11 G
48 kg
35 kg
4m
7.0 X 10-9
6.66 x 10-11 G
35 kg
72 kg
4m
1.051 x 10-8
6.67 x 10-11 G
81 kg
68 kg
4m
2.296 x 10-8
6.66 x 10-11
74 kg
74 kg
4m
2.283 x 10-8
6.67 x 10-11
84 kg
60 kg
4m
2.101 x 10-8
6.66x 10-11
Calculate the average value of G from the table………………………………………
Look up the accepted value for G and place it here (including units)
6.67 X 10^-11
6.673 x 10-11 NxM^2/kg^2
Now, use the simulation to answer the following questions. (Drag the circle over you answer and resize it.)
1. Gravitational force is always……..
attractive / repulsive.
2. IF a gravitational force exists between two objects, one very massive and one less massive, then the force
on the less massive object will be….
greater than / equal to / less than
……the force
on the more massive object.
3. As the distance between masses decreases, force…….
Increases / decreases.h
4. Doubling the mass of both objects would result in the change in force of ….
4x / 2x
/ no change / (1/2) x / (1/4) x
5. Doubling the distance between two objects will change the force of….
4x / 2x
/ no change / (1/2) x / (1/4) x
Part 2: Gravity and Orbits Simulation
This part of the activity uses a different simulation. Be certain you switch to the new simulation or the questions
will not make sense.
Run several orbit simulations, changing the settings as needed, to answer the following questions.
6. In what direction is the gravitational force of the orbiting object oriented?
Towards the center of the sun
7. In what direction is the velocity of the orbiting object oriented?
Tangent to the direction of where the orbit is going, more towards to outer
8. If you turn gravity off, what happens? Why does this happen?
The orbit just floats off the direction of where you turned gravity off at. There is
nothing holding it in its orbital path
9. If you increase the mass of the Sun, what happens to the Earth?
Earth stays the same size.
10. If you decrease the mass of the Sun, what happens to the Earth?
Stays the same size.
11. Click on the Earth/satellite button. Increase the speed of the satellite. What happens? Explain.
(You can move the satellite or change its velocity by dragging each with the mouse – pause first)
The orbit of the satellite gets bigger and changes the shape
12. Decrease the speed of the satellite. What happens? Explain.
The velocity eventually runs into the earth.
13. Move the satellite. Describe what happens. Can you create a stable orbit further from the Earth? How
did you do it?
You can create a stable orbit further from the earth, I started with the satellite
further from earth and the orbit is way bigger
14. Change the mass of the satellite only. Will this change the orbit of the satellite? Why or Why not?
Explain what happens. (Use the slider at the bottom right.)
Nothing happens, it will not change the orbit of the satellite.
15. The mass of the moon is 7.35x1022kg and the mass of the earth is 5.97x1024kg. The moon’s orbit distance
is 3.84x108m. What is the gravitational force on the moon by the earth? What is the gravitational force
of the earth on the moon? (Calculate it)
The gravitational force is 1.986 X 10^20
16. What is the centripetal acceleration of the moon around the earth, realizing that the gravitational force is
the centripetal force? (Assume the orbit is circular and calculate it)
The acceleration I calculated is .003 m/s^2
17. What is the speed of the moon as it travels around the Earth? (Calculate it)
1020 m/s