OT - Physics Question on Anti-Matter

[Ed Kolis]

A ton of mass or weight is not the same as a ton of explosive force, so that conversion would have been misleading anyway

[capnq]

Well, there's got to be some conversion factor between the two. Whatever that number is, you've still got a big BOOM.

[Baron Munchausen]

Wow, here we have the resources to figure out what it really takes to blow up a planet. The 'death star' beam is stoopid, of course. It takes enough energy to accelerate the planet's entire mass to its own escape velocity to make it explode. For an earth-sized planet this is equivalent to several months output by our sun. (!) A simple 'beam' cannot possibly deliver this much energy. And anyway, if it's delivered from outside, it just burns away one side of the planet, sending the rest spinning away somewhere. The only practical way to really explode a planet is to deliver enough anti-matter to the core to make an explosion big enough to shatter the planet.

So, if someone can figure out how much energy is needed to accelerate the earth's mass to it's own escape velocity, then back-convert that to matter/anti-matter reaction, we would then know how much anti-matter a super-high-tech ablative delivery device (the 'bunker buster' is a toy compared to this problem... ) has to deliver to the planet's core.

[Will]

Well, it's a bit more complicated than that. First, it's gonna be a nasty volume integral, since the gravity will be different along points from the surface to the core. Then, there isn't an easy way to tell how much of the energy from the annihilation will be converted to kinetic energy instead of heating up bits of former-earth. And it would probably not be the case that the annihilation happens all at once, or that the energy flux would be uniform across the unit sphere, so you cannot be certain where the center of gravity will be.

Anyway, with all that, I would say that it is safe to assume that the amount of anti-matter needed is bounded by the mass of the Earth.

[Thy_Reaper]

All my data is from Google, so ask it to back me up

Earth has a mass of 5.9742 x 10^24 kg.
Escape velocity is 11 km/s approx.
7.228782 × 10^32 (72,278,200,000,000,000,000,000,000,000,000) Joules are needed to blow the planet up.
Based on e = mc^2, 8.0431047 × 10^15 kilograms of a matter/anti-matter mix is needed to detonate the planet, so just inject 4.02155235 x 10^15 kg of anti-matter into the core.
That's 4,021,552,350 million kilograms of anti-matter... ouch.

Well, good luck on getting that