Let's say aliens were trying to drop rocks on the Earth to kill us all. What could we do so we don't die?
What can humanity do?
The best answer is to get higher up on the gravity well and blast their ships out of the sky.
Defending from KE bombardment from the ground is very difficult, since the incoming rounds are generally very small and moving very fast (typical studies like Project THOR were looking at tungsten rods about the size of broomsticks, so the cross section would be very small indeed). The rods would be best attacked by shooting down the carrying satellite or warship, with the second best option trying to hit them as they re enter and are still highly visible inside the plasma sheath. Remember, this is a "broomstick" sized object moving at Mach 25, so you'd better have good aim! Railguns firing clouds of pellets might be able to disrupt the incoming rounds enough to make them tumble and break up in flight, but you still have pieces of metal falling at random at high mach numbers, so you are not really that much ahead of the game.
Improbably powerful laser weapons are another means of fighting back. At the Atomic Rockets website, there is some discussion about massive FEL Xasers which can fire deadly coherent beams out to a light second (almost the distance from the Earth to the Moon), but since this uses X-ray frequencies, the atmosphere would absorb much of the energy, and you would have a bolt of plasma running back to the laser emitter... oops!
A massive laser weapon like this in orbit is another matter. The accelerator for the electron beam would be a racetrack over a kilometre in diameter, but with the amount of laser energy being deployed, you could vaporize the incoming rounds in space, plus damage the launching mechanism on the moon and even spacecraft out to the edge of the Hill sphere (while the laser is a Ravening Beam of Death (RBoD) out to a light second, it will still be dangerous out to a light minute. It just won't vaporize steel in microseconds like it does at one light second...) In a high enough orbit, the RBoD will be able to shoot "down" at enemy spacecraft and rounds, and also be able to cover a significant fraction of the Earth and orbital space. Three in orbit should cover the entire globe with some overlap, plus provide for mutual coverage (one shoots at incoming spacecraft to protect the other one shooting projectiles on the way to Earth). Having more is better, since even saturation attacks can be split between multiple battle stations carrying RBoDs.
Once you have the ability to build these sorts of weapons installations in orbit, it is a short step to turning them from battle stations to battlestars and being the ones going after the aliens instead.
Most of the answers seem to be focused on offensive methods against the aliens in orbit, which would be a great way to stop the orbital bombardment, but are not strictly defensive measures.
Some purely defensive measures to survive orbital bombardment:
Stay on the Move: Depending on the targeting and deployment methods the aliens are using it could easily take the aliens near a full orbit (90 minutes at LEO) to move an impactor into a decaying orbit and toward an intended target. So you just need to move fast enough that you won't be there when the bombardment hits, you would likely want to be several hundred miles away depending on the size of the explosion (quite easily on par with large nuclear weapons) so a speed of 100s of mph would be necessary mostly limited to airplanes, something like flying Air Force One and not landing for an extended period of time.
Hide: the Earth is big, so depending on the aliens agenda (are they here to exterminate all humans or only the troublesome ones opposing them) you may be able to hide. Large population centers are going to be pretty easy to see, but small bases located underground or with camouflage may work, or you could hide your operations around not target humans. This is potentially a lot easier if the aliens have limited numbers of ships or observation satellites, as this would limit the times they are overhead and able to observe. Another good hiding spot would be under the sea, submarines on the move would be hard to spot and depending on the depth and size of the aliens bombardment offers some shielding.
Dig Deep: The response by a number a number of Earth governments over the last century when faced with potential large nuclear explosions was to dig bunkers, this could likely work as a defense against orbital bombardment as well. This also has the potential benefit of the hide option above if your bunkers are in hidden locations and difficult to detect from orbit.
Spread Out: This is the internet style of survival, originally design to survive a nuclear war, have enough nodes that if one goes down the system survives. As noted above the Earth is big, and if the aliens have a limited number of impactors they want to deploy, having a dispersed population would allow some to survive even a large scale bombardment. Survival could be improved by not only disseminating the population, but also infrastructure to support the population as widely and redundantly as possible.
Ultimately if the aliens are intent on humanities extinction and don't want or care about the Earth as a place to live an orbital bombardment could go to the level of melting the crust into a molten cinder which I don't think has any effective defense, but if they are looking for a limited victory you could likely employ some of these defensive strategies to save some population of humans.
Best bet, put a few nuclear tipped missiles on the Falcon 9, SpaceShipOne, A soyuz spacecraft, or whatever and get into orbit.
Being at the bottom of the gravity well has us at a big disadvantage.
Kinetic kill missiles could also be effective. Basically a KKV doesn't worry about a warhead, and instead relies on delivering the kinetic energy of an object traveling at thousands of miles per hour to the target.
As @WilliamKappler said, you can't just drop any old rocks down and expect them to reach the ground. You need something very large, with a high metal content, and preferably a metal with a high melting point.
But the aliens probably know that if they can travel across interstellar space.
They could probably grab a few of the larger asteroids and divert them toward Earth. It would be a be a lot easier than mining the moon for the right kind of materials, and it's worked a few times before.
Why not just use the simple solution? Shoot a gun at the sky! I oversimplify, as it's obvious that a regular handgun round won't go into orbital height, but all you need is a device that will shoot large aerodynamic projectiles at a high speed. This would be relatively cheap (quite a bit cheaper than massive laser arrays), and there wouldn't be much they could do about it, short of starting to throw rocks at it. But if you make enough of those installations, in a matter of minutes, at least one will hit the enemy ship hard enough to cause a hull breach. This velocity doesn't have to be very high, especially if an explosive is mounted on the projectile, or just a sharp, durable tip.
The only major concern about this is that they may start to bomb out the installations on the ground, but, as mentioned by Jim2B, there's enough clutter on Earth to hide the installations, until the moment of firing. In fact, the entire acceleration mechanism could be kept deep underground, with only a small bit poking out. This would be effectively invisible from space.
Furthermore, you have to consider the "rock-paper-scissors" of aerial warfare:
Ground anti-aircraft installations beat fighters (usually, or at least are armored enough that fighters can't do much about them)
Bombers can reliably destroy ground installations, assuming you have enough so that a few can come close enough that if they are shot down, the explosion of their contents once it hits the ground it is still close enough to assure destruction of the target.
Fighters can reliably destroy bombers, as bombers are meant to be anti-facility, not anti-plane, and fighters are designed to be anti-plane.
Thus, a small force of fighter jets, even available by today's technology (though it depends how high they are) should be able to make it high enough to attack the "bombers", as fighters CAN make it to orbital height (they just need to get enough speed and then pull up). All you need is one or two fighters to make it within firing range, and then they fire everything they have at the bomber, which probably would be enough to breach the airtight hull. If that fails, ramming the ship at full speed while simultaneously detonating all the on board missiles would almost certainly be enough.
Would Aliens use rocks as a bombardment method, consider the following: (not mine, all credit to whoever wrote the original)
Rocks are NOT ‘free’, citizen.
Firstly, you must manoeuvre the space vessel within the asteroid belt, almost assuredly sustaining damage to the ship’s paint from micrometeoroids, while expending the fuel.
Then the rock in question must be inspected to ascertain its condition. Should it pass muster, the ship must prepare the potential ordinance for movement. Finally, the ship may begin manoeuvring the warship to abut the asteroid at the prepared face (expending yet more fuel), and then begin boosting the stone towards the offensive planet.
After a few days of expending a prodigious amount of fuel to accelerate the asteroid into an orbit to hit the planet, the ship may then return to the planet via superluminous warp travel and await the arrival of the stone, still many weeks (or months) away.
After twiddling away the time and consuming food in the wasteful pursuit of making sure that the planet does not launch a deflection mission, they may finally watch the ordinance impact the planet (assuming that the ship does not need to attempt any last-minute course correction upon the rock, using yet more of the fuel).
Given a typical (class Bravo-CVII) system, we have the following:
Two months, O&M, Titan class warship: 5.2 Million Credits
Two months, rations, crew of same: 1.2 MC
Paint, Titan class warship: 2.5 MC
Dihydrogen peroxide fuel: 0.9 MC
Total: 9.8 MC
Contrasted with the following:
5 warheads, “Planetary Destruction Grade”: 2.5 MC
One day, O&M, Titan class warship: 0.3 MC
One day, rations, crew of same: 0.0 MC
Dihydrogen peroxide fuel: 0.1 MC
Total: 2.9 MI
Given the same result with under one third of the cost, will have saved a massive amount of money and almost a full month of time, during which the warship may be bombarding an entirely different planet.
Bursarius Tenathis,
Purser Level XI,
Office of Interplanetary War Costings.
Since we are familiar with our planet and know how to tune our weapons to work on it, we can assume that a sufficiently warned humanity has the capacity to build and deploy soft UV laser weapons with the capacity to vaporize any ship it can hit.
The range limitation will not be one of our laser's power, sensor targeting, or cooking ourselves with our own waste heat. It will be the limitation imposed by light speed delays and alien ship maneuverability. For a first order approximation, assume this to be several light-seconds to several light-minutes (it depends upon whether you assume high acceleration or low acceleration alien ships).
Probably the laser weapon of choice will be the free electron laser tuned to fire beams in the highest frequency that passes out of the atmosphere with minimal absorption (probably something in the soft UV band).
These installations will be over 1 km long and buried under lots of protective ground. Since once we fire the weapon, the aliens will try to target and kill our laser, it makes sense to have as many beam paths as possible under ground with many pop-up mirror turrets that fire the beam into space. The aliens will kill our cheap and easy to fix turrets but they won't know where the actual beam generator is.
But our problems start after we zorch several of the alien ships. Assuming we don't manage to kill them all in a surprise attack, as soon as they realize near Earth space is deadly to them, they'll attack through asteroid bombardment staying well outside of our laser range.
Our massive lasers have little chance of doing significant damage to their ships at the range of our asteroid belt and even less of actually hitting their ships.
At ranges beyond a few light minutes, the only thing that is going to work are missiles, or even better missile buses.
A forewarned humanity will boost these into space and hide them throughout the solar system, especially in locations we think the aliens might use for bases. A surprised humanity will just have to clear out near Earth space and launch them with the hopes that the aliens can't scrag our missile buses before they get out of the atmosphere and can maneuver.
The missile bus will use Nuclear power propulsion (it will have to be nuclear pulse propulsion or nuclear salt water reactor based to get both the necessary acceleration and $I_{sp}$). That'll be bad for our environment but at least we can fight back.
The bus will contain multiple independent seeker warheads (probably kinetic but depending upon the planned engagement velocity, it may require nuclear warheads). During main boost and prior to the terminal engagement, the bus will provide propulsion for all of the seeker heads. As the bus approaches the target and prior to becoming vulnerable to counter fire, the seekers will separate. It is likely the bus and one or more of the seekers will contain high end seeker programming to integrate all sensor input (all seekers will contain sensors) and determine an engagement strategy for the whole cluster.
We've been lead to believe the space is the ultimate high ground and that someone bombarding a planet from space has the advantage. But there are some aspects to this we have ignored and even more things to consider
Most of the details of how a space bombardment would proceed will depend upon the alien's objectives. As has been answered elsewhere, there are precious few reasons for aliens to bother coming here the first place. There are fewer to cause them to want to attack us and there are almost none that will cause them to attack us using anything but overwhelming bombardment from space.
About the only ones I can think of are:
Ask yourself what the aliens want to do.
They're just plain evil and want to exterminate humans - Orbital bombardment isn't the way to go. It is a useful supplement and a relatively cheap but effective way to destroy primary targets, but for widespread destruction you'll need something more thorough. Nuclear weapons are much better for the purpose.
If you're well-hidden it could be very hard to make a precise strike. This goes very well with the strategy of building underground bunkers, which not only obscures your location but may also protect you from the blast if they do find out where you are.
Their orbital weapons can't just drop out of the sky. It could potentially take a long time to align them and then deorbit onto Earth. Even when executed with maximum precision there is still a practical barrier to rapid strikes barring an absolutely massive network of orbiting weapons. As long as you constantly move, it will be very hard to kill you.
Earth is really big. It's hard for humans to perceive how big it truly is, but you can take my word for it. This works well with the underground-bunkers strategy because if you can avoid detection then there's simply no way for them to hit you. If you do detect a strike incoming, you still have a considerable amount of time to evacuate, so a highly mobile base will be a necessity.
These weapons are great for knocking out a dense settlement fast. Avoid grouping together. Big cities cannot be quickly evacuated and can be wiped off the map with significant casualties easily. Instead, have a large number of low-lying bases. If this strategy is employed, avoiding conspicuous targets is even more important.
This strategy is a little stupid, but before you evacuate all of Earth's former cities and go into hiding, launch thousands of pounds of debris into space. Pray that it creates a Kessler syndrome-esque cascade of destruction that makes launching orbital weapons very hard. Launching thousands of nuclear weapons and detonating them is also a great idea because it will increase the amount of protective shrapnel floating around in LEO, forming a sort of smokescreen consisting of hypersonic radioactive space junk. The downside is you may never be able to go to space again.
During the cold war the Americans experimented with all sorts of ways to destroy ICBMs from space in an attempt to render them obsolete. One system that may be of interest is the Brilliant Pebbles. They serve a similar purpose, destroying projectiles in space, and there is already a lot of research on it (though most of it is classified) so it could be very helpful in defending against the orbital weapons.
There is also a myriad of other bizarre high-tech anti-ICBM technologies from the Cold War Star Wars era. These are all potentially great ways to destroy reentering orbital impactors.
Blunt moon rocks burn up fairly quickly in the atmosphere. For an effective orbital strike ammunition, you'll want as much mass and velocity as possible. You can achieve both by making your weapons more aerodynamic, meaning more mass arrives to the surface intact and it loses less velocity to friction. You'll want long rods of something with high heat resistance like tungsten rods.
