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.
Re: OT - Physics Question on Anti-Matter
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