What is the Correct Way to Calculate the Period of Io?

In summary, the problem involves finding the gravitational force and period of Jupiter's closest moon, Io. The mass and mean radius of Jupiter, along with the center-to-center distance to Io, are given. After solving for the gravitational force, the equation for the period is set up, with a reminder to use the center-to-center distance instead of the distance minus the radius of Jupiter.
  • #1
Sheneron
360
0
[SOLVED] Universal Gravitation

Homework Statement



Jupiter's closest moon, Io has a mass of 8.90 x 10^22 kg. The mean radius of Jupiter is 6.99 x 10^7m, the mean distance from the center of Jupiter to the center of Io is 4.22 x 10^8m, and the mass of Jupiter is 1.90 x 10^27.

A) Determine the gravitational froce
B)Find the period of Io

The Attempt at a Solution



I solved for F_G and got = 6.334 x 10^22

Then I set up my equation like so:

[tex] F_G = \frac{m_{Io}4\pi^2(R)}{T^2} [/tex]

My question is, for R in the above equation would I just use the distance between the center of masses, or the distance between the center of mass minus the radius of Jupiter? I am sure it is the center of masses, but why is Jupiter's radius in the problem then...
 
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  • #2
Probably to tempt you to make the mistake of NOT using the center to center distance. Resist that temptation.
 
  • #3
Tricky indeed. Thanks
 

What is Universal Gravitation?

Universal Gravitation is a scientific law that explains the force of gravity between any two objects in the universe. It states that the force of attraction between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them.

Who discovered Universal Gravitation?

Sir Isaac Newton is credited with discovering and formulating the law of Universal Gravitation in the late 17th century. He published his findings in his famous work, Principia Mathematica, which revolutionized the field of physics and laid the groundwork for modern theories of gravity.

How does Universal Gravitation affect objects on Earth?

Universal Gravitation is responsible for the force of gravity that keeps objects on Earth and the other planets in orbit around the sun. It also affects the tides on Earth's oceans and the motion of celestial bodies in the universe.

What is the difference between Universal Gravitation and General Relativity?

Universal Gravitation is a classical theory that describes the force of gravity between two objects. General Relativity, on the other hand, is a modern theory that explains gravity as the curvature of space and time caused by the presence of massive objects. It is a more accurate and comprehensive theory that can explain phenomena that Universal Gravitation cannot, such as the bending of light around massive objects.

Is Universal Gravitation a proven theory?

Yes, Universal Gravitation is a well-established and proven theory that has been supported by numerous experiments and observations. It accurately predicts the motion of objects in our solar system and has been confirmed by modern technologies such as satellite tracking. However, it is important to note that scientists are constantly refining and expanding our understanding of gravity through ongoing research and discoveries.

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