There are a number of nodes around that offer possible solutions to orbital strikes against a planet. Most of these tend to rely upon either railguns, mass drivers or some form of far-future technology such as ionised plasma cannons or particle beam weapons. And most of these nodes conclude that the technology's infeasible, at least for the most part.
Now the far-future technology is definitely infeasible for at least the next 50 to 100 years or so (at least), however the main problem for the mass driver/railgun technology seems to be that it's rather hard to get enough energy to do a decent amount of damage to your target while also stopping your weapons platform (typically a satellite) from going very quickly in the opposite direction.
It's very possible that there's a solution to this problem. However, it does not use any form of railgun, mass driver or linear accelerator. It relies on tried-and-true technology - primarily that of rockets and/or missiles.
The problem with firing something out of a mass driver (we'll use this term to refer to all forms of mass drivers, railguns and linear accelerators for the rest of this writeup - it's much simpler that way) is that when you give it a force to go in one direction - towards your target - the thing giving the projectile the force - the mass driver - also experiences a force of equal magnitude in the opposite direction (Newton's Third Law of Motion). So unless you expend an awful lot of energy using engines or some other form of propulsion, your weapons platform is going to be leaving orbit in a hurry.
The solution to this problem is to change what is giving the projectile its force. For the purposes of discussion, we'll be using a 100kg mass in the form of a tungsten cylinder (assumed to be a particle for simplicity of calculation). If this were to be fired out of a mass driver of length 100m, we can do some calculations to find the force required:
First, we need to know the final speed of the projectile once it leaves the mass driver. For simplicity's sake, let's assume we're firing on a small rabbit warren, so we only need the projectile to be travelling at about 500m/s.
Assuming the projectile starts at rest, and is accelerated constantly, we can work out the acceleration thus:
v2 = u2 + 2as
5002 = 02 + 2 * a * 100
250,000 = 200a
a = 250,000 / 200
a = 1,250m/s2
As you can see, we need to give our mass quite a hefty kick to get it up to speed. The size of this kick - the force required - is quite easy to work out:
F = ma (From Newton's Second Law of Motion)
F = 100 * 1,250
F = 125,000 Newtons
As you can see, this is quite a large force. And since our weapons platform is exerting this force on our projectile, the projectile is exerting the same force on the weapons platform in the opposite direction. Assuming our weapons platform has a mass of 10,000kg (10 tonnes), it's going to end up moving in the opposite direction at a decent speed:
F = ma
125,000 = 10,000a
a = 12.5m/s2
v = at + u
v = 12.5 * 0.4 + 0
v = 5m/s
OK, so while this isn't going to break any speed records, it's enough to play merry hell with the orbit of our weapons platform, and will require correction after every shot (this would probably be done by some form of thruster or rocket engine).
There is, however, a somewhat better solution to the problem of annihilating immobile objects from orbit using nothing more than a big lump of metal (and some extra bits).
We firstly need to throw away our mass driver, or alternatively we can sell it to raise some much-needed capital to embark upon our new planetary assault strategy.
In order to attack our target now, we're going to use missiles. Albeit missiles with no warheads, but when you're firing a big hunk of metal at a fair lick towards your target, you don't exactly need a warhead - the kinetic energy of your hunk of metal will do the job just fine.
To create our projectile, we need to take our 100kg tungsten cylinder and stick a rocket engine on the back. Also add various guidance equipment (additional maneuvering thrusters or whatever), a targetting computer (to figure out where the projectile needs to be at launch to hit our rabbit warren quite a few miles away and at least a couple of minutes later) and a mounting for our initial launch mechanism.
For our initial launch mechanism, we'll be using springs. Yes, you read correctly - springs. Those little coiled bits of metal. We use these springs to launch the projectile away from our weapons platform at a leisurely 1m/s. The force needed to do this is drastically less than that needed to hurl our projectile originally, and as a result it's hardly going to affect our platform at all - an almost negligible amount of energy will need to be expended to correct for this launch.
You may be asking how we expect to blow anything up moving at 1m/s. Simple: we don't. Instead, we wait a while - 20 seconds or so - for the projectile to clear the weapons platform. During this time the targetting computer can be doing its maths to figure out where it needs to point the projectile. Now comes the part that gets the projectile really moving - we ignite the rocket engine on the back of the tungsten cylinder. This gets the thing moving at a decent warren-obliterating speed. We use the guidance equipment to make sure that we hit our target, and then as we enter the atmosphere, the rocket engine and guidance equipment is rendered useless and most likely is vapourised by the insane heat. All that's left is a rather large chunk of metal travelling at a tremendous speed towards our target.
The end result is the same as using a mass driver - instead of a rabbit warren we're left with a rather large hole in the ground and the lingering smell of barbecue. However, by using a very small force to get the projectile clear of the platform, then pelting it towards the target independently, we prevent the problem of our platform drifting off into space, and us losing a rather expensive piece of mass-destruction-inducing hardware.
Note: no actual rabbits were hurt during the production of this writeup. If you feel for the rabbits, please feel free to mentally replace any references to them with your target of choice - small and fluffy or otherwise.
The numbers used as initial values in this writeup are pulled completely off the top of my head, and as such are massively unlikely to actually do anything remotely useful - they're simply there to illustrate the point. If you want to build one of these yourself and have it work, doing the maths yourself with more sensible numbers would be advisable. Additionally, air resistance and that is partially neglected, however I'm told that tungsten ought to survive the re-entry process sufficiently to leave large holes in the ground.
Thanks to rootbeer277 for informing me of some typographical errors.