Let $M$ be a compact real analytic Riemann surface. Is it true to say that:

There are at most a finite number of disjoint simple closed geodesics on $M$.

If the answer is yes put $m$= the sup of the number of such disjoint closed geodesics.

what is a geometric interpretation for this geometric invariant $m$?

For a given $n\in \mathbb{N}$ ,is there a real analytic riemannian metric on $S^{2}$ for which $m=n$