Gravitational Binding Energy vs total mass energy

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Discussion Overview

The discussion revolves around the concepts of Gravitational Binding Energy (GBE) and total mass energy of Earth, exploring their meanings and implications in the context of destroying the planet. Participants examine the energy required for different scenarios, such as shattering or completely vaporizing Earth, and the interpretations of these energy values.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants assert that the GBE of Earth is the energy needed to remove all matter to infinity, while the total mass energy represents the energy obtainable from converting all mass into electromagnetic energy.
  • There is a suggestion that the interpretation of "completely destroying" the planet varies among participants, with some questioning whether vaporization or shattering counts as complete destruction.
  • One participant proposes that depositing the GBE into Earth would prevent it from re-gravitating, implying a form of destruction that leaves no remnants.
  • Another participant states that vaporizing Earth could be considered as requiring the GBE, depending on the precision of the definition used.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definitions and implications of GBE versus total mass energy, with multiple competing views on what constitutes complete destruction of Earth and the energy required for various scenarios.

Contextual Notes

Participants express uncertainty regarding the definitions of terms like "vaporize" and "shatter," and how these relate to the energy values discussed. There is also ambiguity in the interpretation of what it means to completely destroy the planet.

tacsec
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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?
 
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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.
 
Bandersnatch said:
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?
 
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.
 
tacsec said:
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".
 
And to answer the question directly - I'd say that falls under "vaporize", as long as we're not too concerned with precision.
 
Bandersnatch said:
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?
 
Yeah.
 
Bandersnatch said:
Yeah.
Gotcha.
 

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