# Gravitational Binding Energy vs total mass energy

1. Nov 30, 2014

### tacsec

The Gravitational Binding Energy of Earth is 2 * 10^32 J.
But the total mass energy of Earth is 5.4 *10^41 J.
So the shatter the planet into pieces it would require 2*10^32 J of energy, and to completely destroy the planet with out leaving a trace of its existence would require 5.4 *10^41 J right?

2. Nov 30, 2014

### Bandersnatch

Hi tacsec, welcome to PF

No, that's not what these numbers mean. Gravitational binding energy of Earth is the enrgy needed to remove every single bit of matter that makes up our planet to infinity.

The energy content of mass is what you'd get if you managed to convert all the mass into electromagnetic energy - e.g., if half of it turned into antimatter and annihilated with the other half.

Note that in the second case, the energy is still gravitating, so the total will get reduced by the amount equal to the binding energy as the light produced by annihilation travels away to infinity.

Whether either of those cases counts as "completely destroying" is up to your personal interpretation.

3. Nov 30, 2014

### tacsec

Okay. So lets say you vaporize Earth completely. Is the minimum amount of energy required the GBE? Or let's say you shatter the planet. Is that the GBE?

4. Nov 30, 2014

### jerromyjon

The GBE is just the "gravity holding all the atoms together" energy. The atomic energy as in annihilation of every atom in Earth would be mc2.

5. Nov 30, 2014

### Matterwave

If you deposited the gravitational binding energy of the Earth to the Earth, you would, in principle, destroy the Earth so badly that it would never even re-gravitate and re-create itself since every piece of the Earth will fly "to infinity".

6. Nov 30, 2014

### Bandersnatch

And to answer the question directly - I'd say that falls under "vaporize", as long as we're not too concerned with precision.

7. Dec 5, 2014

### tacsec

What falls under vaporize? GBE?

8. Dec 5, 2014

Yeah.

9. Dec 5, 2014

Gotcha.