Gravitational Binding Energy vs total mass energy

[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 without leaving a trace of its existence would require 5.4 *10^41 J right?

 

[Bandersnatch]

Hi tacsec, welcome to PF

No, that's not what these numbers mean. Gravitational binding energy of Earth is the energy 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.

 

[tacsec]

Hi tacsec, welcome to PF

No, that's not what these numbers mean. Gravitational binding energy of Earth is the energy 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.

Okay. So let's 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?

 

[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.

 

[Matterwave]

Okay. So let's 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?

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".

 

[Bandersnatch]

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

 

[tacsec]

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

What falls under vaporize? GBE?

 

[Bandersnatch]

Yeah.

 

[tacsec]

Yeah.

Gotcha.