You are in charge of the world, with technology about the same as we have now, except that a while back the leaders of the world decided that nukes are too powerful, so they destroyed them all and noone knows how to make them anymore.
The space program has also died out, so you do not have any probes.
When some astronomers tell you that there is a large asteroid coming in 5 days and the impact will kill all human life on Earth, what do you do to prevent the impact?
If the asteroid is still 5 days away it might need a very small angular deflection to have it miss Earth.
You obviously need "something" able to reach the asteroid to do anything useful (barring magic, of course).
We are developing fairly powerful lasers, but they might not be enough to break the body.
Your best bet is a swarm of the rockets used to penetrate bunkers, these will drill a fair hole on the surface of the asteroid thus providing a highly directional explosion; effectively a rocker burst. If You can hit the side of the asteroid with enough such charges you might be able to deflect its trajectory enough to miss Earth without need to obliterate it.
Based on the answers given to this question, considering you rule out space technology, you (and the planet you rule) are pretty much doomed.
Unless you're a Jedi, you won't be able to move this thing with just the power of your mind. You'll have to send something up there to do something about the asteroid. Either retrofit an existing rocket or build one from the ground up (though again, you may not have time to start from scratch) and make sure it is capable of delivering objects beyond Earth orbit. Also, create a payload. This is going to be the thing that will interact with the asteroid
Nevertheless 5 days notice is not enough even to launch a rocket. Consider that when US went to the Moon (and they knew with a huge notice that somebody was going to be sent out there) the only preparation they did for the event of a malfunction of the spaceship was a funeral speech.
You find a deep hole, stock it with food and supplies, and hope to survive the impact. There is nothing you can do. If the object was years out, a small change in its vector would cause it to miss the Earth. Five days out, we could launch all of our nukes at it, and MAYBE break it up enough that most of the larger pieces would evaporate in the atmosphere. With five years of warning, humanity could deflect it. Five day won't even be enough to get the ammo and food shipped to your bunker..
If we assume that the asteroid is the equivalent of the Chicxulub impactor (so not quite big enough to kill all life on earth, but probably enough to wipe out humanity), aimed at the centre of the Earth (for working out the worse-case scenario), and that the Earth's gravity had no effect on the asteroid (for ease of working it out), we wouldn't be able to do anything about it.
This asteroid would be 15km wide, and if we assume that it is roughly spherical (for ease of calculation...see jokes about spherical cows) and has a density of 2000 kg/m3, the mass would be 1.77 trillion tonnes. If we could act instantly, we would have 5 days to deflect it by about 7000 km, so 1400 km/day or 16.2 m/s. The energy required to move mass m (in kg) at velocity _v (in m/s) is at least 1/2mv2. For 1.77 trillion tonnes (=1.77 x 1015 kg) by 7000km in 5 days, it would require 4.645 x 1017 Joules, equivalent to about 110 megatonne explosion, assuming we can focus all of that energy onto the asteroid rather than simply having it throw out equally in all directions.
However most of the energy from such an explosion would probably break up the asteroid into smaller fragments, rather than moving it, so resulting in a rain of fiery asteroid fragments impacting the Earth, rather than a single large one. It could be done with rockets pushing it, in theory, but that's out of the question (literally), so I'm not sure we can put up the necessary amount of energy in the right spot.
Given modern day Earth the only hope of possibly pulling this off would be if there was a large (considerably bigger than anything we've ever flown) deep space rocket ready for launch. Strip it's cargo, replace it with nukes (and good luck disabling the safeties on enough boom for the job) and head out. The astronauts (if it wasn't manned they're in suits and laying on padding--it's a one-way mission anyway so the lack of a re-entry system is irrelevant and they need nothing but air, water and power) push the bombs in the right directions (they have to be spread apart to avoid fratricide) and hope it's a very, very solid rock as the required deflection is going to put an awful lot of stress on it and if it breaks up there's no hope of stopping it.
Pak already showed we need 110 megatons for 5 days out assuming 100% efficiency, I would be amazed if we could get the intercept even two days out so we need 275mt and then 10x this for the efficiency of the crude use of them we are making. Given the most efficient bombs built we still need over 450 tons of bomb--that's a lot of rocket!
ZioByte, touched on it, but a large laser array could do the trick. But it doesn't have to destroy the asteroid, merely heat it to the point of vaporizing part of the asteroid. This vapor will act as a small jet deflecting the asteroid from Earth.
