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Explanation of Applications of Universal Gravitation Equation - Succeed in Understanding Physics. Also refer to attraction, force, mass, distance, Earth, Moon, tides, centrifugal, physical science, astronomy, Ron Kurtus, School for Champions. Copyright © Restrictions
Applications of Universal Gravitation Equation
by Ron Kurtus (29 June 2009)
You can apply the Universal Gravitation Equation to show the force of attraction between two objects, provided you know the mass of each object and their distance apart. The equation is: F = GMm/R2, where G = 6.67*10−11 N-m2/kg2.
With this equation, you can make calculations to determine such things as the force between the Earth and the Moon, between a boy and a girl and between the Moon and a girl.
Questions you may have include:
- What is the force of attraction between the Earth and the Moon?
- What is the force of attraction between a boy and a girl?
- What is the force of attraction between the Moon and a girl?
This lesson will answer those questions. There is a mini-quiz near the end of the lesson.
Useful tools: Metric-English Conversion | Scientific Calculator.
Force attracting Earth and Moon
To calculate the gravitational force pulling the Earth and Moon together, you need to know their separation and the mass of each object.
Attraction between Earth and Moon
Distance
The Earth and Moon are approximately 3.84*105 kilometers apart, center to center. Since the units of G are in meters, you need to change the units of distance to meters.
R = 3.84*108 m
Mass of each object
Let M be the mass of the Earth and m the mass of the Moon.
M = 5.98*1024 kg
m = 7.35*1022 kg
Force of attraction
Thus, the force of attraction between the Earth and Moon is:
F = GMm/R2 =
(6.67*10−11 N-m2/kg2)(5.98*1024 kg)(7.35*1022 kg)/(3.84*108 m)2
F = (293.2*1035 N-m2)/(14.75*1016 m2)
F = 1.99*1020 N
Note: Notice how all the units, except N, cancelled out.
Result of force
This considerable force is what holds the Moon in orbit around the Earth and prevents it from flying off into space. Inward force of gravitation equals the outward centrifugal force from the motion of the Moon.
Also, the gravitational force from the Moon pulls the oceans toward it, causing the rising and falling tides, according to the Moon's position.
Force attracting boy and girl
If a 50 kg (110 lb) girl sat 0.5 m (19.7 in) from a boy who was 75 kg (165 lb), what would be the gravitational attraction between them?
Note: The distance between the boy and girl is measured from the center of the first person to the center of the other.
Substituting the values into the equation, you get:
F = GMm/R2
F = (6.67*10−11 N-m2/kg2)(50 kg)(75 kg)/(0.5 m)2
F = (6.67*10−11 N-m2/kg2)(50 kg)(75 kg)/(0.5 m)2
F = (25012.5*10−11 N-m2)/(0.25 m2)
F = 100050*10−11 N
F = 10−6 N or one-millionth of a Newton
That is a very small gravitational attraction, but it can be measured on a sensitive instrument.
Force attracting girl and Moon
What is the gravitational pull from the Moon on the 50 kg (110 pound) girl?
The distance between them center to center is the distance from the center of the Moon to the center of the Earth, 3.84*108 m, minus the radius of the Earth, 6400 km).
6400 km = 6,400,000 m = 0.064*108 m
R = 3.84*108 m − 0.064*108 m = 3.716*108 m
Thus, the force between the girl and the Moon is:
F = GMm/R2
F = (6.67*10−11 N-m2/kg2)*(50 kg)*(7.35*1022 kg)/(3.716*108 m)2
F = (2451*1011 N-m2)/(13.8*1016 m2)
F = 177.6*10−5 N
F = 1.77*10−3 N = 0.00177 N
The girl would not notice the pull from the Moon, since the gravitation pull on her toward the Earth is 490 N. But still, she is attracted more toward the moon than the boy who was sitting next to her.
Summary
You can apply the Universal Gravitation Equation to show the force of attraction between two objects. With this equation, you can show the force between the Earth and the Moon is F = 1.99*1020 N, between a boy and a girl is F = 10−6 N and between the Moon and a girl is F = 1.77*10−3 N.
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Resources
The following resources provide information on this subject:
Websites
Acceleration due to Gravity Calculations - from Western Washington University
Gravitation and Gravity Resources
Books
Top-rated
books on Simple Gravity Science
Top-rated
books on Advanced Gravity Physics
Mini-quiz to check your understanding
If you got all three correct, you are on your way to becoming a Champion in Physics. If you had problems, you had better look over the material again.
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Applications of Universal Gravitation Equation