Can a Planet's Gravitational Force Prevent a Comet or Asteroid Collision?

[MathematicalPhysicist]

my question is for example if we have a commet,asteroid in an impact collision with a planet, can the planet gravitational force can stop it from colliding, and bound it so the commet,asteroid will orbit the planet?

i think the answer is yes, but what minimal velocity should the the commet, asteroid have in order to be bound by the planet's gravitational force and not collide it?
(i guess if it can happen it depends on its velocity, because we have already seen that there are commets which collided on planets (our own for thesake of the argument)).

 

[tony873004]

The comet or asteroid would need to be slowed down relative to the planet as it passed on its hyperbolic trajectory. Otherwise, it would continue to sail past the planet.

It could enter the planet's Hill Sphere through the L1 or L2 points ("The Interplanetary Super Highway"). Comet Shoemaker-Levy 9 orbited Jupiter for several decades before it collided. Many of Jupiter's outer moons are captured asteriods.

 

[MathematicalPhysicist]

when you say L1 L2 are you referring to lagrange points?

 

[selfAdjoint]

when you say L1 L2 are you referring to lagrange points?

Yes. See this wiki discussion: http://en.wikipedia.org/wiki/Lagrange_points#L1