The power of the Jupiter projectile

Question

I recently re-watched an awesome show - Diebuster. At one point in the show, one of the characters uses Jupiter as a projectile, slamming it into one of the aliens, but to no avail.

I can't find a good picture of that scene for some strange reason.

Anyway, this question is not about how such a feat would be achievable, or even about whether or not it is possible, rather it is about just how powerful such a projectile would be. How much damage would Jupiter do as a projectile, assuming it is travelling at a speed fast enough to be perceivable by the human eye or to be at least considered projectile speeds (I'm not sure the exact numbers)?

Answer 1

You are going to do a lot of damage. To restate the calculations PipperChip has done:

$$ E_k = \frac{1}{2}mv^2 $$ $$ E_k = \frac{1}{2} \times 1.89 \times 10^{27} \times 13000^2 $$ $$ = 1.6 \times 10^{35} \text{J} $$

That's quite a lot of energy - enough to destroy 665 Earths. And that's just the energy Jupiter has at its orbit velocity.

However, if you're going to move it, you also need a lot of energy. Most likely this energy is also pretty significant: not only is Jupiter incredibly heavy, it's a gas giant, so you can't just hire a rocket to give it a push - it'll go right through. With that kind of technology and energy to throw around, it would be a foolish alien to mess with you.

Answer 2

There are, at least, a few ways to measure the damage a weapon can do. Perhaps the simplest, and most easily transferred between varying weapon types, is the energy behind the blast. This is often normalized per kg because you can often get bigger explosions by simply adding more explosives. Another good way is to measure the energy in terms of how much TNT you would need to produce that energy.

TNT (the explosive) has an energy of 2.8 megajoules per kg. Dynamite is at 7.5 megajoules per kg, or about 2.67 times as explosive as TNT. Let's talk about kinetic rounds.

Kinetic rounds do not use explosive force, but they do carry the common currency of energy. Obviously, kinetic rounds use kinetic energy, not "explosive" energy like TNT. Since both objects are often measured in how much energy they hit the target with, you can make the comparison.

To determine the kinetic energy of something, you use can use: $$E_{k}=\frac{1}{2}mv^2$$ Where m is the mass of the object and v is it's velocity.

For Jupiter, going at the speed of a bullet from a high-powered rifle (mach 1), gives you about $1.09899149 × 10^{32} J$. That is $3.925 * 10^{25}$ kg of TNT. However, Jupiter is so big that this speed is really slow. Jupiter orbits at $13\frac{km}{s}$, whereas the speed of sound is a measly $.340 \frac{km}{s}$.

If you shot jupiter at .1c, one-tenth the speed of light ($2.998*10^{7} \frac{m}{s}$), you get $8.530 * 10^{41} J$. That is $3.046 * 10^{41}$ kg of TNT.

For reference, the Tsar Bomba, considered the most powerful man-made explosion in the world, was 50 megatons of TNT. That is 209.2 PJ ($209.2 * 10^{15}$ J). That also assumes that nothing else blows up when Jupiter hits, as it's mostly (~89%) $H_2$. (Oxygen is not naturally present in large amounts in Jupiter, so it would not explode like the Hindenburg did.)