Sci-Fi Sanity Check

A friend wrote me an email a few days ago asking for a sci-fi sanity check. He had been reading a series of sci-fi books where some interesting physics was used to destroy a hostile alien race. He was wondering if the the methods used were credible and could actually be used in a hypothetical space battle. Below are his questions followed by my responses.

Question 1:

"First, they had a fleet of ships fire nuclear weapons while travelling close to the speed of light towards the battle. The idea was that the wavelength of the energy from the blast would experience an intense doppler effect, and hit the enemies at an incredibly high frequency. This gave the weapons far more devastating effects than would have otherwise been possible."

Response 1:

This question is one that I looked at and said, "Oh, there is an easy answer to that." But the more I thought about it the more complex it became. So I went and asked a real nuclear physicist in my department and we both thought about it for a while and concluded that the issue is irrelevant anyway, though there are some interesting physics questions underneath that made us scratch our heads, but none of which would make a better weapon.

The first problem is a misconception of where most of the energy in a nuclear blast goes. When an atom bomb goes boom it does release a significant amount of gamma radiation. That is just something that happens. When the uranium or plutonium fissions it will release a gamma ray, which is very energetic as far as electromagnetic radiation goes, and very dangerous, but the vast majority of the energy actually is carried away by the fission products. That is, the daughter isotopes of the nuclear reaction carry most of the energy in the form of kinetic energy. The gamma radiation will fry you, but the thing that actually creates the blast is the huge number of particles with huge kinetic energies that will rip you apart. The gamma radiation will ionize the atoms in your body, but the thing that will literally blast you to smithereens is the fissioned material with huge amounts of kinetic energy.

The gamma radiation will only carry away like 10% of the total energy from a nuclear blast, the rest is in the kinetic energy of the atoms after they split apart.

So if you accelerated it to high speeds the only part of the blast that would be doppler shifted would be the radiation. The particles that make up the most dangerous part of the nuclear weapon would not be doppler shifted. So the radiation (gamma rays) from a nuclear weapon that has been accelerated to the near the speed of light would get columnated, doppler shifted, and would be more energetic in the direction of motion, but you would have to be going at like 99.9998 % the speed of light before the doppler shift would make the radiation that much more dangerous than it already was. For example if the bomb was traveling at 90% the speed of light then it would only raise the energy of the gamma radiation by a factor of 4. To make a significant difference you would literally need to be going 99.9998% the speed of light. At that speed that energy of the photons would be shifted by a factor of 1000, but only on an extremely narrow beam directly directly in front of the blast. A deviation by as little as 0.5 degrees would decrease the doppler shift by a factor of 10 (an overall increase of only a factor of 100). So aiming would have to be extremely precise, which means the detonation would have have to occur right on target or any doppler advantage would be lost.

But the main issue with this scenario, and the thing that makes everything I discussed above pointless, is that at relativistic speeds the kinetic energy far exceeds any possible yield from the atom bomb. For every kilogram of plutonium there is a theoretical total yield of about 20 kilotons of TNT, which comes to about 8x10^13 joules of energy. A kilogram of lead moving at 10% the speed of light has kinetic energy of about 5x10^14 joules, or almost 10 times as much energy as you would get from an atom bomb.

If you take that up to 90% the speed of light, 1 kg of lead would have kinetic energy of about 1x10^17 joules, or about 20 megatons of TNT, which is about the yield of the largest hydrogen bomb the US ever tested. At relativistic speeds the kinetic energy of the case that holds the bomb would have orders of magnitude more energy than anything the atom bomb could produce. So accelerating an atom bomb to relativistic speeds in order to take advantage of the doppler effect is kind of like strapping a stick of dynamite to the front of a semi truck traveling at 100 mph. It's not the dynamite that will kill you.

The key is that at relativistic speeds everything has such high kinetic energy that normal stuff like atom bombs are tiny in comparison. Just getting a hunk of metal up to relativistic speeds would make it much more dangerous than any atom bomb.

Question 2:

"The second thing they did was accelerate a barren planet to a significant fraction of light speed (I recognize there are issues with that too, but they never tried to give a scientific explanation for doing that) and send it through the star where their adversaries lived. The result of the high speed mass applying high pressure and force as it passed through was to cause an increase of fusion (because of the mass pushing stellar material together really hard) which released a tremendous burst of additional energy, causing it to become a supernova."

...Yes? It is conceivable. The star would have to be pretty big to begin with, but in order to get a planet to do that it would need to be going really, really, really, really fast. Like 99.9998% the speed of light. In order to get the level of pressure needed to make that happen you would either need a really big planet (basically another star) or an earth sized planet traveling at 99.9998% the speed of light.

But then we run into the same problem as before. At that speed the planet would have a HUGE amount of kinetic energy. We are talking about 10^44 joules of kinetic energy. To put that in perspective, that is the same amount of energy as a type Ia supernova. So yes, crashing a planet into a star at 99.9998% the speed of light would probably cause the star to undergo a massive amount of fusion setting off a supernova. But in order to do that the planet would need to have kinetic energy equivalent to a supernova to begin with. It's kind of like dropping an atom bomb on an atom bomb in the hope of getting the second atom bomb to go off. If you got the planet going that fast, hitting a star with it would be pointless since just about anything you hit with it would release enough energy that it would create a supernova sized explosion.

If your goal is to obliterate an enemy planet with a supernova sized blast, and if you could get an earth sized planet up to 99.9998% you wouldn't have to aim it at the star in the hope of setting off a chain reaction that would fuse all the hydrogen in the star. Just have it hit anything, a planet or a star, within a relatively short distance, say 3-4 light years, and that will release enough energy to make a supernova equivalent explosion and cook the alien planet. If your goal is to kill your enemy with an atom bomb, and you have an atom bomb, then just drop your bomb. Don't go for Pinky and the Brain level of complexity and drop it on another bomb hoping to set it off.