Yes, that's right. Kinetic energy equals mass times velocity squared. So something traveling at, say, a thousand times the velocity of the Chicxulub asteroid would only need one millionth of the mass to do an equal amount of damage. Heck, we have plenty of everyday experience with the principle. A bullet has extremely little mass -- maybe 10-12 grams, the mass of a couple of nickels. If someone just threw it at you, it wouldn't do any damage. But since a gun fires it at very, very high speed, that gives it enough kinetic energy to be deadly. By the same token, if your car bumps into a tree at 2 MPH, it won't do any real harm, but if your car bumps into the same tree at 80 MPH -- 40 times the velocity and thus 1600 times the kinetic energy -- that would destroy the car and severely damage the tree, not to mention possibly killing the driver. The speed is a more important factor than the mass. Yes. It's a matter of angles. The farther away you are when you change the asteroid's course, the smaller the angle you have to change it by to move it by the same amount when it crosses the planet's orbit. At a thousand times the distance, you'd only need to alter the angle by a thousandth as much to have the same effect. This is why NASA & JPL's planetary defense program is trying to identify all potentially hazardous asteroids ahead of time -- because we want to have plenty of advance warning in case we spot something on a collision course. This is the huge problem with "The Paradise Syndrome." Given that they started two months in advance, it should've been easy to divert the asteroid. They didn't need to try to do it all in one big push; they could've tugged on it with a tractor beam a little bit more each day and gradually nudged it off course. The only possible rationalization is to assume it was an exceptionally massive asteroid, with too much momentum to allow its course to be changed in time. This is also the case with the moon in "Deja Q" -- it was just too big (and they had a lot less time). But asteroids come in all sizes, and as I said, the faster you get it, the smaller it needs to be in order to devastate a planet. Think in terms of shooting someone with a sniper bullet vs. dropping a boulder on them from five stories up. The bullet is much easier to move into position, but it's just as effective.