So how fast do things have to be moving past each other to produce an orbit? While I know darn near nothing about orbital mechanics, essentially you have to be doing fast enough for the inertial energy of your forward movement (i.e. centrifugal force) to balance out the force of gravity. The same thing works whether you're talking about the Shuttle around the earth, the earth around the sun, or a fat lady around a doughnut. (No, wait, that's something else...)
Also, the farther apart the two objects are, the less effect gravity has on them, and the slower they need to be going (relative to each other) to produce a stable orbit. This is why LEO (Low Earth Orbit) objects like spy satellites, the Space Shuttle and the ISS (International Space Station) have orbital periods of 2 hours or so, telecommunication satellites much higher up in geosynchronous orbits have orbital periods of 24 hours, and the moon, although huge in comparison, is distant enough to orbit once every 28 days or so.