# Universal Gravitation

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Universal Gravitation
Purpose and Objectives
Gravity is a universal phenomenon. Regardless of the frame of reference, gravity is an all-present
consequence of matter and it’s existence in space. An understanding of the nature of gravity and its
influence on objects at the Earth’s surface can demystify this universal phenomenon. It is often
implied that Newton simply perceived that gravity was a universal force. While historically
inaccurate, it was rather that he reasoned the connection between the force holding the moon in its
orbit around the Earth and the force that causes an apple to fall toward the ground from a tree at
the Earth’s surface. Newton concluded that these forces were the same force.
In part one of this lab, you will have an opportunity to address many misconceptions by conducting
a relatively simple lab designed to quantify the relationship between masses suspended on a spring
scale and the force of gravity on those masses.
In part two of this lab, you will have an opportunity to relate the distance that objects are separated
by to the force of gravity between them. You will utilize data from several bodies in the solar system
to infer this relationship. Combining the two parts of this lab will provide you with a greater context
of the relationships that govern gravity throughout the universe.
These procedures will greatly assist in understanding some of the most basic physical principles.
After performing the experiment and analyzing the data, you should be able to do the following:
1. To determine the graphical and mathematical relationship between the mass of an object
suspended on a spring scale and the force of the Earth acting on that mass.
2. To determine the graphical and mathematical relationship between the distance that objects
are separated and the force of gravity acting on that object.
Equipment
5 masses of known value
LabQuest Mini
Stand
Dual Range Force Sensor
Data Tables of Solar System bodies
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String
Clamps
Procedure
Part A.
1.
2.
3.
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5.
Connect the Vernier Dual Force Sensor to the LabQuest interface and open LoggerPro.
Connect a string to the hook of the Force Sensor and zero out the sensor.
Hang an object of known mass and record the force of gravity.
Repeat for four other known masses.
Graph the Gravitational force vs. the Mass to determine the relationship between the
two.
Part B.
1. Choose a parent body (ex: Earth, Sun, Saturn, etc….)
2. Choose 5 satellites (or moons) of the parent body. (If they choose the Sun, only take
data for the first 4 planets, so that the range of data is not too large to graph).
3. Find the radius for each satellite (making sure to measure from the center of the satellite
to the center of the parent body) and record in data table. Make sure the numbers have
the units of meters.
4. Find the orbital period for each satellite and record in data table. Make sure the numbers
have the units of seconds
5. Calculate the velocity of each satellite by using v = 2πr/T. Be sure that the units are m/s.
Record these values in a new data table.
6. Calculate the acceleration of each satellite by using a = v2/r. Be sure that the units are in
m/s2.
7. Graph Acceleration vs. Orbital Radius to determine the relationship between the two.
Data
Part A
Part B
Questions
Part A
1. What does the graph of the data suggest about the relationship between mass and
gravitational force?
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2. What would the force of gravity be on 10 Kg mass at the surface of the Earth? How do we
know?
3. What does the slope of the graph represent? Explain the slope in words.
4. What would you expect a similar graph to look like if data were collected on the moon?
Why?
5. Draw a force diagram for the situation. What is the source of the force acting on the
suspended mass?
6. How many objects must be present for a gravitational force to exist? In the interaction
between the Earth and the suspended mass, which object exerts the greater force? Why?
7. What is the weight of a 5 Kg bowling ball at the surface of the Earth?
8. What is the weight of the Earth on the surface of a 5 Kg bowling ball?
9. What can we conclude about the influence of mass on gravitational force?
Part B
10. What is the general shape that the graph of Acceleration vs. Radius produces? Express this
in a verbal form and a general mathematical form.
11. What is a way to linearize the graph that you produced in Part B?
12. Construct test plots of different relationships until you construct a linear version of the
information. Do not use the curve-fitting feature of Logger Pro but instead create new data
columns that calculate these values. Be careful of the units and size of the values.
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13. When you obtain the linear relationship, choose Linear Fit and record the slope and yintercept of this relationship. Express this in a verbal form and a mathematical form.
14. Explain your data in terms of Forces and not accelerations.
15. Using the data and the relationships, those given and those that were experimentally
determined, determine whether a satellite’s speed will increase or decrease as it gets farther
from the object it orbits. Show a mathematical proof of your answer.
Conclusion
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