# Jupiter as a Circular Mass Ring

I am trying to model the planet Jupiter as a uniform circular ring of matter and calculate the central force inside of it. This ring has the Sun as its center and defined by its linear mass density λ = M/2πR where M is the mass of Jupiter and R the radius of its orbit. With that in mind, i'd like to put Mercury as a third body and calculate its resultant orbit from the force applied by said ring.

I first tried doing a simple Torus plot, with

ParametricPlot3D[{Cos[t](64 + Cosu[u]), Sin[u]}, {t,0,2 Pi}, {u,0,2 Pi}]


But then i don't know how to add mass to that ring, then i tried SolidData with

SolidData["SolidTorus","ImplicitRegion"];
DiscretizeRegion[%[.08,0.45]]


which gave an circle but not uniform solid ring, first of all i am having trouble into giving said circle a variable mass and then compute its force as a central force inside of it.

• – David G. Stork Oct 23 '18 at 4:08
• I would question the physics behind this endeavor (though it's a perfectly reasonable math problem). Funny though, the reverse might make physical sense (modeling Mercury as a ring for purposes of analyzing the effect exerted on Jupiter). – Daniel Lichtblau Oct 23 '18 at 19:57