The world government discovers that a mile wide asteroid will strike the earth in a couple months. Assuming that the impact is imminent and nothing can be done to stop it, what could the governments do to save as many as possible?
The same technology level as today. The impact will hit the ocean. The speed is 25 kilometers per second. It will hit the earth head on some where between japan and California.
A mile wide asteroid is bad, but it's literally not the end of the world. In fact, impacting in the sparsely populated Pacific Ocean its immediate impact will be relatively minor compared to falling in a densely populated area.
To put this in perspective, the "dinosaur killer" at Chicxulub was about 6 miles wide, made a crater 110 miles wide, and had the energy of about 100 teratonnes of TNT.
Your asteroid is about on the scale of the one that created the 14 mile wide Haughton Impact Crater. This is still pretty big, but it's not extinction event bad. Because volume (and thus mass) is the cube of the diameter, your asteroid has 1/6th the diameter of the Chicxulub asteroid, but 1/216 the mass. That's still a lot, but it's not the end of the world.
Plugging the numbers into The Earth Impacts Effect Program tells the rest of the story...
The impact will have the seismic effect of a magnitude 8.4 earthquake. By comparison the 2011 Tōhoku earthquake which caused the Fukushima meltdown was a 9.0 earthquake (much more powerful, it's not a linear scale) and sent a tsunami and surge over 100 miles. However, anything close enough to be affected by a resulting tsunami will be well inside the heat and shockwave. @YoustayIgo found an updated calculator which included tsunami calculations, boy was I wrong.
The asteroid impact hitting the ocean will shove aside so much water it will create an enormous tsunami. At 400 km from the impact, where you're likely to survive the heat and shock, the tsunami will arrive 40 minutes later with a maximum height of 150 meters. At 1000 km it's at 60 meters. At 2000 km it's still a towering 30 meters. Tsunami height drops linearly with the distance, so at 4000 km it's still 15 meters. At 6400 km, the distance from Tokyo to Hawaii, it's 9 meters similar to the wave heights experienced after the 2011 Tōhoku earthquake (the one that caused the Fukushima meltdown). The good news is you have 10 hours of warning after the impact. The bad news is it hits the entire Pacific Rim.
The good news is since the Pacific Ocean is sparsely populated, few people will be affected by initial impact. If the point of impact can be calculated, they can be evacuated.
The bad news is the whole Pacific coastline is flooded. Everyone, and as much of their stuff as possible, will have to be evacuated away from the Pacific coast to high ground. Like, far away. It will be a refugee problem on the scale never seen before. Major cities such as San Francisco and Los Angeles will need to be evacuated and their tens of millions of people cared for. The people of major island nations such as Japan, Taiwan, and Indonesia may have no where to go. Governments will have to stockpile food, water, shelter, and sanitation facilities at a scale never seen before.
The good news is all that water will recede rapidly. The bad news is all infrastructure, bridges, roads, power lines, sewage, buildings, fuel stations... will be trashed leaving the Pacific Coast uninhabitable by modern humans.
When they start to rebuild, they will find a major environmental disaster. All the toxic chemicals of modern life we leave lying around in pools or sealed in storage will now be released and smeared over the countryside. Nuclear material; all sorts of toxic chemicals; heavy metals; petroleum products like oil, fuel and asphalt. Governments will have to do their best to remove as much as possible in the months before the event, but much was never made to be transported. They will not get them all.
The world will be left with a refugee crisis on a scale they have never seen, and some of the most fertile and productive land in the world now a toxic wreck. The loss of food and economic production would put the world into a depression exacerbating the refugee crisis. Millions will die of starvation, disease, and exposure. The question now is how the world reacts to this, and how they rebuild.
The disaster scale stated here is quoted from Astronomy Notes, Space and Purdue Universitywebsites. The last website is specially of interest to anyone who wants to calculate effects of an impact without having to deal with a lot of formulas or assumptions.
I entered the values (1 mile projectile, impact at 90° angle, in ocean of depth 3 km -average-) and calculated the effects at 500 km from the site of impact. I put the asteroid density equal to dense rock (ice and porous rock are lighter while metals are heavier than dense rock). These were the results:
Foregoing things such as crater shape and size, a fireball would be visible from 500 km. The fireball would be 2.6 times the size of sun's size (the visual size of sun, as seen from Earth). The fireball would have have a radius (diameter is twice the radius) of 5.73 km. The thermal radiation (heat blast) would continue for a shocking 5.49 minutes!
The impact will create a direct earthquake of magnitude 7.9 at richter scale (at 500 km from point of impact).
The air blast would reach after 25.3 minutes with a wind speed of 87 mph. Which is easily enough to shatter glass windows and create enormous dust storms.
and now the freakiest part ...
That is a seriously horrific tsunami wave, if you ask me. A 242 feet high wave (for minimum amplitude) raging at 600 km/h speed ...
1- Prepare for monster tsunamis. Now that you know beforehand, you can better prepare your defenses against it. I will not go into tsunami defense here, but it would be logical to evacuate some cities/islands too close (400 km or less) and try to move as many people from other beach cities.
2- Prepare for top scale relief operations in all countries with beach cities. While the region shielded between Far Eastern islands and Americas (Mainland South Asia, Arabia, Africa and Western Europe) would be saved from the brunt, Western Americas and Eastern Asia would be the hardest hit. Prepare relief operation with this in mind.
3- Mentally and psychologically prepare for a world map without Japan, Indonesia, Malaysia and most of New Zealand. These islands would continue to physically exist. But it would be at least a decade before anything like human settlements would be built there.
4- Persuade shipping companies and navies that having ships and submarines (specially nuclear weapons carriers) during that week is a very bad omen and would result in magical disappearance of those vessels.
5- Mentally prepare to be thrown 40 years back wrt technological progress and standard of living.
6- Make complete copies of the internet (excluding cat videos and zombie outrage news) and distribute a copy to every country in the world.
7- Prepare large stocks of grain and potatoes in Asia and Europe.
8- Shutdown any and all nuclear reactors 2 days in advance all over the globe and pull out all the nuclear fuel from them.
9- Disarm nuclear warheads a week ago. (Persuade all military leaders and belligerent politicians that they will get ample time to rearm them once the catastrophe is over but in case of a nuclear disaster, they will only be repenting in hell).
10- Cancel all flights 2 days prior to the expected impact date. You don't want to add to life and economic losses.
11- Reassure that the stock in Svalbard Seed Vault is viable. Also try and prepare more indigenous seed vaults in all countries around the globe. These would be smaller (only containing seeds of crops and natural flora in the country).
12- And most important of all (unless you are in a government job or have registered as volunteer for relief work), find a secluded cave somewhere far inland in Asia ... and pray, pray, pray ...
