Mass of Jupiter using as Many moons as Possible

[walkera]

To calculate the mass of a binary system, one can use keplers law. P^2= (4*(pi)^2*a^3)/(G*(m1+m2)) To get a more accurate mass I must take into account as many moons as possibe for jupiter. Is it possible to change kepler's law alittle to make it accommodate more than a binary system?

ty

 

[Nereid]

Welcome to Physics Forums walkera!

First, I'm not sure why you'd want to tinker with Kepler's law for Jupiter (or the solar system, or anything in the solar system except Pluto/Charon and Earth/Moon ... the deviation caused by the other moons will be extremely small.

Second, if you do want to get greater accuracy, there are many different methods. From your post it seems you are interested in analytic methods (different formulae) rather than digital ones (e.g. a digital orrery, or a simulation on a PC); there are whole shelves in libraries devoted to various approximations and methods (look up 'celestial mechanics').

Perhaps you could consider the level of accuracy you want? Or the number of pages of formulae you could tolerate?

 

[tony873004]

Using any 1 moon is going to get you a very good answer. But if you want to venture further to the right of the decimal point, you have to consider that Io, Europa and Ganymede are locked in resonance with each other. I believe it's 1:2:3 or 1:2:4. And Callisto, spiraling outward will eventually get locked into resonance as well.

If all were instantly converted to massless particles, they'd continue to orbit as-is for a little while but soon would diverge from their real paths as the resonant forces would cease to exist. With the resonance, when anyone of them moves too fast or too slow to keep the resonance, subtle forces from the other 2 shepard them back into place which will have a small effect when trying to compute Jupiter's mass from their periods.

At least I think that's what's going on :shy: