# How much asteroid can we divert from the Earth?

There are many movies with the Earth being saved by sending a bomb out blow up the asteroid. What realistically could we do to that degree today? Do we have interplanetary missiles? if so how much of an asteroid can we move?

• This conversion might be more costlier than to build new rockets. Aug 5, 2018 at 10:33
• This makes me want to ask how big of a rock we could absolutely theoretically destroy with all the existing nukes... on a different SE. Though I do not know which... Aug 5, 2018 at 22:50
• Depends on how good you are with a baseball bat. Aug 6, 2018 at 10:41

In the simple case (no other encounters before impact) you need to generate no more (and maybe a lot less depending on where it's going to hit) than a bit over 6500 kilometers worth of deflection. Note the absence of time units.

Deflection, however will normally be measured in meters per second. Note that this does have time units.

Lets apply some numbers to get a better picture: You send out your bomb, it does a standoff detonation that imparts 1 meter per second to the offending rock. (Note that you do not want to blow it up in most cases!! Unless you can blow it to bits small enough that they won't make it through the atmosphere you actually make it worse.)

What does this do? If the rock was more than 6,500,000 seconds from impact that 1 m/s adds up to enough to cause a miss. That's 75 days.

Now, lets look at rock that is 10x as big. Lets send out the same missile. We only get .1 m/s deflection. Success means we need to intercept at least 750 days (just over 2 years) out.

Lets scale our rock up by 10x again. Now the same missile generates only .01 m/s and has to intercept almost 21 years before impact.

See how it's not a simple answer to how much asteroid can we move?

We have no such missiles sitting around, if a dangerous rock were detected we would have to build it, although not totally from scratch as we have already built something pretty similar--the Deep Impact mission. Replace the impactor with a nuke and include a rangefinder to set it off at the right point.

Also, you need to ensure you don't blow up the target. Since you can't be sure of what you're shooting at you want to make sure that the velocity imparted by the missile is well below the escape velocity of the rock so that if you break it it will put itself back together. (If you blow off small bits at high speed they'll miss anyway and don't matter.) This might necessitate multiple shots even if one could carry enough boom.

Since we have never shot at a rock with a bomb we don't truly know what will happen. NASA figures 10% of the energy of the bomb can be imparted on the target (this is basically an Orion drive.)

Note that this has one huge advantage over any other currently considered approach in that it's much easier to make a good guidance system than to match velocities with something going fast the wrong way. Lets look at the worst case--a comet going backwards. That could require 60 km/sec just to match and that's more than NASA could do. An Orion drive, however, cares not a bit that the warhead is closing on the pusher plate at 60 km/sec so long as your detonation timer is accurate to the sub millisecond range.

• Something seems to be wrong. To get 1/10 of deflection velocity, the rock's mass should be 100 times bigger. The energy is the same. But a rock with 10 times the diameter will have 1000 times the mass. Scaling the mass by 100x is 4.64x the diameter.
– Uwe
Aug 5, 2018 at 19:54
• @Uwe Ultimately, you have to impact momentum to the target to move it. I don't know much about bomb-asteroid interactions, but it seems likely that (for these kinds of recoil velocities) the momentum transfer will be constant when something goes throws a lot of bomb outputs against a large surface. But I'm not sure when "large" sets in... Aug 5, 2018 at 22:35
• @Uwe I meant to increase the mass of the rock 10x, not the diameter of the rock 10x. We don't really care what the size or shape of the rock is, only how much it weighs. Aug 5, 2018 at 22:41
• @BobJacobsen Don't look for bomb-asteroid interactions, look at Orion drives. You don't have a nice pusher plate, just the offending object itself but that only means erosion and so what? If anything a larger rock will receive slightly more energy from the bomb. Aug 5, 2018 at 22:44