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

[Kovac]

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:

, where P is the orbital period in Earth years, a= semi major axis in AU.
For Jupiter: Pj =

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

to find the position for a? Meaning I need to solve for a with the new P?

 

[vanhees71]

I'd think a bit about units/dimensions first! How can a time squared equal a length cubed?

 

[Tom.G]

Could you explain in words what this phrase means?

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