the asteroid would be accelerating.In which case it could be accelerating for a long long time as its pulled toward the attracting body or bodies.But in this situation, chances are pretty good that the asteroid will slam into whatever is pulling on it; so it wont reach any other maximum it might have gotten to.And of course asteroids do get caught into orbit, where they are doomed to a maximum that comes and goes as they go from aphelion to perihelion and back again.......
Unimpeded by space dust and debris, asteroids can still be limited by the sum of all gravity forces acting on it. If the net force is a braking one, the asteroid will be slowing down rather than speeding up. In the other direction, the asteroid would be accelerating. In which case it could be accelerating for a long long time as it's pulled toward the attracting body or bodies. But in this situation, chances are pretty good that the asteroid will slam into whatever is pulling on it; so it won't reach any other maximum it might have gotten to. And of course asteroids do get caught into orbit, where they are doomed to a maximum that comes and goes as they go from aphelion to perihelion and back again.
And thus we reach the ultimate maximum, the speed of light. Even if the pull of gravity causes the asteroid to continue accelerating, there will come a point where its inertia will be so great, from relativistic effects, that the asteroid cannot accelerate one more iota. So that unlikely maximum will fall short of the speed of light.
Acceleration is a change of velocity, that is of speed or direction since velocity is speed in a given direction.
Any orbiting body is accelerating even if it's speed is constant since it's direction is constantly changing... It will gain speed if the orbit is decaying, meaning the body is falling toward the body it's orbiting and that gain is determined by the normal laws of motion.
If it is very far from the central body it might not gain much speed in one revolution but as the orbit decays the gain in speed for each revolution becomes greater.
The speed of a body and it's distance from the body it's orbiting are related. See Kepler's Laws of planetary motion, which apply to all orbiting bodies.
http://www.physicsclassroom.com/class/ci…
Well, all objects with mass they are limited to below the speed of light.
But they will continue to accelerate as they are attracted by gravitation by a second body.
They must have a maximum speed because they can't go faster than light, so they must stop accelerating at some point, at least thats what my logic would be. Hope I helped :) Have a nice day xx