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

  • Thread starter Thread starter Kovac
  • Start date Start date
  • Tags Tags
    Resonance
AI Thread Summary
To find the location of celestial bodies in a 4:1 or 3:1 mean motion resonance with Jupiter using Kepler's third law, the orbital period (P) of the resonant body should be calculated as a fraction of Jupiter's orbital period. For a 4:1 resonance, P would be set to 1/4 of Jupiter's period, and the semi-major axis (a) can then be determined using the formula a^3 = P^2. The discussion also raises a question about the dimensional analysis of the formula, specifically how time squared relates to length cubed. Understanding the variables involved in these resonances and their directional implications is crucial for accurate calculations. The conversation emphasizes the importance of careful unit consideration when applying Kepler's laws.
Kovac
Messages
13
Reaction score
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?
 
Physics news on Phys.org
I'd think a bit about units/dimensions first! How can a time squared equal a length cubed?
 
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
 
Thread 'Collision of a bullet on a rod-string system: query'
In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...

Similar threads

Back
Top