
Abstract
We study the problem in which $N$ bodies, called primaries, of
equal masses $m$ are describing circular keplerian solutions in
the $xy$ plane and a body $\mu$, of zero mass, moves on a line
perpendicular to the plane of motion of the primaries and passing
through their center of mass. We show that such a problem is
equivalent to the Classical Circular Sitnikov Problem, in which
$N=2$ and $m=\frac{1}{2}$. We also show that the main parameter in
searching for periodic solutions is $M=mN$, the total mass of all
the primaries. We add an analytic study of the period, $T(h)$, as
a function of the negative energy $h$. We generalize some results
of [2] and we show the dependence of $T(h)$ on the mass
parameter $M$. Finally, we confirm, the expected result that the
case of the Newtonian potential for a homogeneous circular ring of
mass $M$ is just the limit case of the problem we have studied, in
which we let $N$ go to infinity, while keeping the product $mN$
finite.
Mathematics Subject Classification: Primary: 70F10, 34C25.
\begin{equation} \\ \end{equation}

Access History
