We study the dynamics of an idealized model of a planetary ring. We start
with the
n
+ 1 ring problem in a rotating coordinate system where an infinitesimal mass
is attracted by
n
small masses
m
located in a regular
n
-gon around a central mass
m
0
.
Assuming the mass ratio
m
0
/m
of order
n
3
, we construct a limiting problem as
n
tends to
infinity. This limit process is similar to Hill ´s problem. The central mass is pushed towards
the infinity while the distances between two consecutive ring...
We study the dynamics of an idealized model of a planetary ring. We start
with the
n
+ 1 ring problem in a rotating coordinate system where an infinitesimal mass
is attracted by
n
small masses
m
located in a regular
n
-gon around a central mass
m
0
.
Assuming the mass ratio
m
0
/m
of order
n
3
, we construct a limiting problem as
n
tends to
infinity. This limit process is similar to Hill ´s problem. The central mass is pushed towards
the infinity while the distances between two consecutive ring bodies is kept equal 1. We
study the dynamics of the problem including equilibria, periodic orbits and stability.