First of a it is a difficult thing to "capture" something. If a stray asteroid starts at a large distance from a planet, it must have some velocity, and therefore some Kinetic energy with respect to the planet. Its distance from the planet is potential energy with respect to the planet. In the normal run of things the astroid will gain kinetic energy and lose potential energy as it approaches the planet, conservation of energy tells us that the total energy, that is the sum of the potential and kinetic energies must remain the same. One could essentially charaterize an orbit by its energy, that is the total of the kinetic and potential energy of the satilite in that orbit. At any point the energy will be shared between kinetic and potential but the total wil remain constant. If you think about this it means that a body is either in orbit or NOT in orbit. There is some threshold energy, below which a body is in orbit and above which it is not. So if some body, with to much energy approaches a planet it cannot be captured unless it LOSSES some energy. This can be done by collison or if the approach is just right, a reverse sling shot effect could happen.
You have all heard about the sling shot effect in refernece to the deep space satilites we have launched. They do a close approach to Jupiter or Saturn and gain huge amounts of velocity which is the same as energy in passing. In regards to my previous paragraph how is this possible?
Well as the satilite falls into the gravitational well of the large planet it is drug along with the planets ORBITAL velocity. This is all gained energy. The velocity gained due to the close approach is all lost as the satilite leaves the vacinity of the large planet, what is not lost is the velocity imbued to the satilite by the ORBITAL motion of the planet, thus the slingshot.
So now if an asteroid approachs on an exact reverse of the slingshot approach it, instead of gaining velocity, will lose velocity, and thus could be captured. You must realize that the chances of this happening are very slim.
Thus any captured satilite MUST have motion retrograde to the orbital motion of the planet. If its original motion is in the same direction as the orbital motion it will get the slingshot ride and be sent away at an even higher velocity then with which it approached.
The only other possible way to capture something is for it to collide with either the planet or an orbiting body, this case would be indicated by lots of rubble in the orbit.