The rotation curves of spiral galaxies usually display near-constant velocities in their outer regions. This is contrary to an expected continuing decline in the velocities moving away from the galaxies’ centers. The behavior prompted astrophysicists to declare that dark matter must exist and enclose these galaxies to hold the velocities constant. The centrifugal accelerations that the velocities would produce if the bodies were in orbit are small. They imply that the gravitational accelerations toward the centers of the galaxies on the bodies are also small relative to other orbital systems (e.g., the solar system). The accelerations may not be strong enough to hold the bodies in orbits about the galactic center. Consequently, the bodies may not be in orbit around the galactic centers, but moving away from them. That would allow explanations of flat rotation curves without introducing dark matter or altering gravity. However, due to the radii of the orbits (kilo-parsecs) and the assumed orbital velocities of the bodies (hundreds of km/s), the bodies would move only an infinitesimal distance of the length of their presumed orbital paths over many human generations. This makes verification that the bodies are actually in orbit virtually impossible.