How do I Calculate GMm with Given a and T for Gravitation Problem?

  • Thread starter Clara Chung
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In summary, the conversation involves discussing a problem that requires the use of Kepler's laws and gravitational equations to find the mass of Jupiter and one of its moons. The participants discuss how to use Kepler's third law and the provided variables to solve for the mass, and ultimately come up with the answers for parts A and B of the problem.
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Clara Chung
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Homework Statement


The question is attached

Homework Equations


Kepler's laws and gravitational equations

The Attempt at a Solution


the question gave me a and T, I related it with Kepler's third law a^3/T^2, then I don't know what to do next. The answer of part a is 1.27 x10^17 /r^2 , part b = 1.9 x 10^27, How can I find GMm as the question only provided a and T?
 

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  • #2
What did you get out of Keplers third law ?
 
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  • #3
BvU said:
What did you get out of Keplers third law ?
If I assume a=r, I can get GM?
 
  • #4
I think you can ignore the excentricity, yes.
 
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  • #5
BvU said:
I think you can ignore the excentricity, yes.
How can I get m after that?
 
  • #6
Kepler's third law says a^3/T^2 is 'constant', namely ...
(They only ask for M of Jupiter and that's >> m of moons)
 
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  • #7
BvU said:
Kepler's third law says a^3/T^2 is 'constant', namely ...
(They only ask for M of Jupiter and that's >> m of moons)
Thanks I got part A and B
 
Last edited:

Related to How do I Calculate GMm with Given a and T for Gravitation Problem?

1. What is the force of gravity?

The force of gravity is a natural phenomenon by which all physical bodies attract each other. It is the weakest of the four fundamental forces of nature, but it is the most dominant force on a large scale, determining the motion of planets, stars, and galaxies.

2. What is the formula for calculating gravitational force?

The formula for calculating gravitational force is F = G * (m1 * m2) / r^2, where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of mass of the two objects.

3. How does the mass and distance between objects affect gravitational force?

The mass of an object directly affects the force of gravity, meaning that the greater the mass, the greater the gravitational force. However, the distance between objects has an inverse relationship with gravitational force, meaning that the farther apart the objects are, the weaker the force of gravity between them.

4. What is the difference between weight and gravitational force?

Weight is the measure of the force of gravity on an object, while gravitational force is the actual physical force of attraction between two objects. Weight can vary depending on the gravitational pull of the planet or celestial body, while gravitational force remains constant.

5. How does Einstein's theory of relativity relate to gravitation?

Einstein's theory of relativity explains that gravity is not a force between masses, but rather a curvature of space and time caused by the presence of mass. This theory has been proven correct through numerous experiments and observations, and it has greatly expanded our understanding of gravitation.

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