Applying Newton's Universal Law of Gravitation

In summary, starting with Newton's Law of Gravitation, the height h needed for a person's weight to be reduced to one-third of their weight at the surface of the Earth is 4,685,125.17m. The radius of the Earth is 6.4X106m and the acceleration due to gravity at the surface is 9.8m/s2. The acceleration due to gravity at the point where the weight is reduced to 1/3rd is 9.37 X 10-3m/s2.
  • #1
science_rules
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Homework Statement


This problem only requires to find h, but I want to make sure that I also found Me and g correctly.
Starting with Newton's Law of Gravitation, determine the height h one person has to go from the surface of the Earth in order for that person's weight to be reduced to one-third of his/her weight at the surface of the earth. The only information you have is that the radius of the Earth is 6.4X106m. Knowing that the acceleration due to gravity at the surface of the Earth is 9.8m/s2, determine the acceleration due to gravity at the point were the weight of the person is reduced to 1/3rd.

Homework Equations


GMem/r2 = 1/3GMem/Re2
r2 = 3Re2
r = √3(6,400,000)
h = r - Re = 11,085,125.17m - 6,400,000m = 4,685,125.17m
Me = gRe2/G
g = G9.0 X 10-9/6.4 X 106

The Attempt at a Solution


GMem/r2 = 1/3GMem/Re2 Cross out the GMem, leaving: r2 = 3Re2
r = √3(6,400,000) = 11,085,125.17m
h = r - Re = 11,085,125.17m - 6,400,000m = 4,685,125.17m
6400km X 1000m/1km = 6.4 X 106m
h = 4,685,125.17m,
Me = gRe2/G = 9.8m/s2 X (6.4 X 106)2/6.67 X 10-11 = 9.0 X 10-9
Acceleration due to gravity at the point were the weight of the person is reduced to 1/3rd = g = G9.0 X 10-9/6.4 X 106 = 9.37 X 10-3m/s2
 
Last edited:
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  • #2
science_rules said:

Homework Statement


This problem only requires to find h, but I want to make sure that I also found Me and g correctly.
Starting with Newton's Law of Gravitation, determine the height h one person has to go from the surface of the Earth in order for that person's weight to be reduced to one-third of his/her weight at the surface of the earth. The only information you have is that the radius of the Earth is 6.4X106m.

Homework Equations


GMem/r2 = 1/3GMem/Re2
r2 = 3Re2
r = √3(6,400,000)
h = r - Re = 11,085,125.17m - 6,400,000m = 4,685,125.17m
Me = gRe2/G
g = G9.0 X 10-9/6.4 X 106

The Attempt at a Solution


GMem/r2 = 1/3GMem/Re2 Cross out the GMem, leaving: r2 = 3Re2
r = √3(6,400,000) = 11,085,125.17m
h = r - Re = 11,085,125.17m - 6,400,000m = 4,685,125.17m
6400km X 1000m/1km = 6.4 X 106m
h = 4,685,125.17m,
Me = gRe2/G = 9.8m/s2 X (6.4 X 106)2/6.67 X 10-11 = 9.0 X 10-9
g = G9.0 X 10-9/6.4 X 106 = 9.37 X 10-3m/s2
 
Last edited:

1. What is Newton's Universal Law of Gravitation?

Newton's Universal Law of Gravitation is a physical law that describes the force of gravity between two objects. It states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

2. How is Newton's Universal Law of Gravitation applied?

To apply Newton's Universal Law of Gravitation, you need to know the masses of the two objects and the distance between them. Then, you can use the formula F = G(m1m2)/d^2, where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.

3. What is the gravitational constant?

The gravitational constant, denoted by G, is a constant value that is used in the formula for calculating the force of gravity between two objects. It has a numerical value of approximately 6.67 x 10^-11 N(m/kg)^2 and is a fundamental constant in physics.

4. How does distance affect the force of gravity?

According to Newton's Universal Law of Gravitation, the force of gravity between two objects is inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the force of gravity between them decreases.

5. What are some real-world applications of Newton's Universal Law of Gravitation?

Newton's Universal Law of Gravitation is used in many real-world applications, including predicting the motion of planets and satellites in orbit, calculating the force of gravity between celestial bodies, and understanding the behavior of objects on Earth's surface.

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