Jupiter, Bullets, Antimatter

There's been some discussion around the web of Jupiter apparently getting walloped by something, probably a comet. As with the more famous Shoemaker-Levy 9 impact, the result is a small dark blot in the clouds of the Jovian upper atmosphere. Small is a relative term - small spots on the surface can easily be as big as the Earth or bigger. Impacts are some of the most violent events in the solar system, and they release their energy entirely via conversion from kinetic energy.

Here on earth people sometimes discuss the history of high energy weapons in terms of energy per weapon mass. Conventional bombs using chemical reactions start the list, fission and fusion with nuclear reactions are more powerful by several orders of magnitude, and the as-yet purely hypothetical antimatter weapons would beat even nuclear weapons by a factor of maybe 100 or so. There the list usually stops. You can't squeeze more energy out of a lump of mass than with total conversion to energy.

But there's no reason you have to extract only the internal energy. An ordinary bullet is still the most common implement of warfare despite not releasing any internal energy at all. The damage is done by kinetic means. Comets smashing into planets do precisely the same thing.

The equation for kinetic energy is:

Now since nothing can go faster than the speed of light, you might expect that letting v = c gives a maximum kinetic energy for a given quantity of mass. But that formula is a purely classical one - if we're going to be accurate and consider the speed of light limitations then we need to use the exact relativistic kinetic energy formula:

The lower case Greek gamma is a quantity that varies with the velocity in the following way:

It increases without bound as v get closer and closer to the speed of light. From the relativistic kinetic energy equation, we can see that the kinetic energy is going to be equal to the rest energy at gamma = 2. This is going to happen at just over 86% of the speed of light. By the time you get up to 99% of the speed of light or so, the kinetic energy is so large, the energy you'd get via total annihilation of antimatter is starting to look pretty small in comparison.

This is mostly theoretical though. To get that much energy out you have to put that much energy in in the first place. That's not possible at the moment for anything bigger than subatomic particles. But it is interesting to think that in some ways both bullets and comets are very scaled down instances of a kind of energy that can pound-for-pound outmatch antimatter to whatever degree you want.