[jacquesm]

Like the moon is moving slowly? About 1 km/second for an object that weighs ~10^18 tons at a distance of 300,000 km?

Now think of what that kind of force would do on a much lighter object that moves faster.

[MauranKilom]

I'm not sure I understand your point... The object mass does not impact its trajectory (unless it either touches our atmosphere or is so massive as to measurably change earth's orbit). The gravitational force earth exerts on the moon and some asteroid is also very different, because the force is proportional to both object masses.

[jacquesm]

Think 'gravitational slingshot' but without missing the planet. The object will change direction and accelerate into us. It could end up grazing the atmosphere or it could go from grazing the atmosphere or even non-impact to impact.