The reason we do not hear about satellites
bumping into each other is because they each have their own
protected orbit, kind of like a one lane highway. Orbits aren't
patented, but “useful systems which incorporate particular orbits,
such as technological solutions for providing telecommunications
which utilize equipment in those orbits, are patent-eligible.”
So while a company couldn't attempt to patent a specific set of
gravitational dynamics, it could exert control over an orbit by
patenting the specific set of innovations needed to keep a satellite
in that orbit.
US Patent No. 5,410,728, was issued to Motorola, and outlines how a
formation of several satellites can optimize cellular coverage. The
satellite orbit is not subject to this patent, but the process of
deploying them into those orbits for some use as telecommunications
is patented.
Incidentally, Sci-Fi author Arthur C. Clarke wrote about
patenting orbits way back in 1945. The geostationary orbit he
proposed that year is now home to hundreds of satellites, and has
been officially designated the Clarke orbit by the International
Astronomical Union.