Find the location knowing the resonance using Kepler's third law

  • #1
Kovac
13
2
Thread moved from the technical forums to the schoolwork forums
TL;DR Summary: .

I need to find the location of following bodies MMR with Jupiter: 4:1, 3:1, with the help of Keplers third law.Keplers third law:
1697974988128.png
, where P is the orbital period in Earth years, a= semi major axis in AU.
For Jupiter: Pj =
1697975054421.png
years.

Now my question is, to find the location of 4:1, should I simply take 1/4 * Pj as the new P? (Since 4 orbits are made with each Jupiter orbit)
And then use the formula again with
1697974988128.png
to find the position for a? Meaning I need to solve for a with the new P?
 
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  • #2
I'd think a bit about units/dimensions first! How can a time squared equal a length cubed?
 
  • #3
Could you explain in words what this phrase means?
Kovac said:
MMR with Jupiter: 4:1, 3:1,
Such as: to what variables do the 4:1 and 3:1 apply, and in which direction?

Cheers,
Tom
 

1. What is Kepler's third law?

Kepler's third law, also known as the law of harmonies, states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. In simpler terms, it relates the time it takes for a planet to orbit the sun to its distance from the sun.

2. How does Kepler's third law help us find the location of resonance?

Kepler's third law allows us to calculate the orbital period of a planet based on its distance from the sun. When two planets have a ratio of orbital periods that is a simple fraction, such as 2:1 or 3:2, they are said to be in resonance. This helps us locate the position of these planets in their orbits.

3. What is resonance in terms of planetary orbits?

Resonance occurs when two planets have orbital periods that are related by a simple fraction and their orbits intersect at specific points. This can cause gravitational interactions between the planets, affecting their orbits and potentially leading to changes in their positions.

4. How do we use Kepler's third law to determine the resonance of planets?

To determine the resonance of planets, we first need to know their orbital periods. Using Kepler's third law, we can calculate the orbital period of each planet based on its distance from the sun. Then, we can compare the two orbital periods to see if they have a simple fraction ratio, indicating resonance.

5. Can Kepler's third law be applied to all planetary systems?

Kepler's third law is a fundamental law of planetary motion and can be applied to all planetary systems. However, it is important to note that this law assumes that planets have circular orbits, which is not always the case. In some cases, the law may need to be modified to account for elliptical orbits.

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