EDG said:
I'm trying to get my head around the numbers involved here in case they shed any light on the matter.
(SNIP energy calculations)
Summary:
Asteroid Mass: 500KTons
Volume: 37.4KTons
Orbital Velocity: 5km/s
So far so good... but I can't help but feel that we're overlooking something here. The problem is that asteroids aren't stationary objects - they're orbiting the star. This means that they have velocity to start with, which also means that they have momentum. Let's say that out in the Kuiper belt (call it about 40 AU from the star), the orbital velocity of a planetoid is about 5 km/s - similar to Pluto. Momentum is equal to (mass * velocity), so our 50m radius iceball, with its mass of 500,000,000 kg, and going at 5000 m/s (funny how this is all fives!) has a momentum of 2.5e12 Newton seconds.
Unfortunately, here's where my understanding breaks down because I can't recall how to figure out how its initial momentum affects any attempt to change the velocity of the asteroid. This is possibly complicated by the fact that thrusters are reactionless drives, and so conservation of momentum kinda gets thrown out of the window. But qualitatively speaking at least my gut instinct is that the asteroid's orbital momentum (or possibly its inertia) has to be overcome before its velocity and acceleration vector can be changed to point toward the centre of the system (where the habitable target planet is), and that is probably going to be hard to do for a body of this mass travelling at 5 km/s. But I'll have to leave that to someone with a better understanding of mechanics than I have...
Well, it's been about 10 years since my Orbital Mechanics classes, but I should be able to help:
Since we are using reactionless thrusters, you don't have conservation of momentum, so you don't need to worry about it. Also, momentum would be important here if we had to worry about reaction mass for thrust, which we don't.
BUT, since the object is most likely orbiting in the same direction as the target planet, you will have to overcome that 5kps orbital speed as part of your calculations. Since we are going Near-C, you can probably not worry about that though. Assume 0.5c (150,000 kps) and that 5kps is negligible.
So, figuring Kinetic Energy directly is probably just fine.
When the object (solid or ice or rubble or whatever) hits the atmosphere, it will convert all of it's KE to heat and deformation of the atmosphere (wind) and planetary surface (crater). Some of that will leak back in to space, but most would be absorbed by the planet and atmosphere.
While it is possible that a SMALL fission process might take place, I don't have the formulas to crunch the actual temperatures to see if fission is possible, so lets assume it isn't.
All of this will happen within a fraction of a second.
I don't think even a 500Kton rock will be enough to extinguish life on a planet (the Dinosaur killer was what 10 km in diameter?). BUT, it would sure ruin a cities day and have devastating weather changes all over the planet.
Compared to the size of a PLANET, a 50m rock isn't all that big, but the velocity is what gets you. You could probably get the same effect by accelerating a ship (5000tons or so) to the same velocity and aiming it at a planet.
At 1g, it would take 177 days (25.3 weeks) to get to 0.5c.
It would have to travel approximately 7,650 AU.
So, while it is POSSIBLE, surely a few well placed Nukes would be cheaper, easier and faster.