Importance of Specific Grav. Binding Energy (??)

[Widdekind]

Please ponder a planet's Gravitational Binding Energy (Joules):

 

U = (2/5) G M² / R

 

Now, please ponder that planet's Specific GBE (J / kg):

 

U = (2/5) G M / R

 

It turns out, that for the Earth, the S-GBE is roughly 15x the Energy-per-Mass released by exploding TNT. Thus, even if the whole world was turned into TNT, and detonated, it wouldn't be blown apart, but would reform, from the fragments, from gravity. Earth is "strongly gravity bound" (as it were).

 

Now, according to Ollivier, Encrenaz, et al, in Planetary Systems — detection, formation, and habitability of extra-solar planets (pp. 209-213), for rocky worlds of terrestrial-type bulk chemical composition, R ~ M^0.27. So, as it happens to happen, for a world about twice the mass of the Moon (i.e., M ~= 0.024 M_earth), the S-GBE becomes comparable to the chemical energy stored in TNT.

 

QUESTION:

 

Is the chemical energy, per mass, stored in TNT characteristic of common chemical kinds of bonds ?? And, if so, is there some sort of significance, to this transition, for worlds w/ the Moon's mass, where the S-GBE starts exceeding the characteristic specific energy of chemical bonds ??

 

I suspect this has some sort of significance, since it marks the transition from "strongly gravity bound" worlds to "weakly gravity bound" worlds, relative to the energy scales associated w/ chemical bonding. So, maybe Moon-mass worlds begin to become "brittle", b/c they're basically bound by bonds of chemical, not gravitational, origin — to wit, maybe Moon-mass worlds are like large single slabs of surface rock, as seen on Earth ("a big ball of crustal rock").

 

 

Is there some sort of theorem, that rocks forming under "low pressure" conditions cannot create strong chemical bonds ?? Could GPE be some sort of source for any necessary input energies, for forming rock crystals which are chemically bound ??

[swansont]

U = (3/5) G M^2 / R

http://en.wikipedia.org/wiki/Gravitational_binding_energy

http://scienceworld.wolfram.com/physics/SphereGravitationalPotentialEnergy.html

 

The energy in TNT is, to first order, the same as in many substances with carbon and hydrogen in it. So yes, it is sort of characteristic, because the individual bonds you are breaking and forming are the same.

 

A chocolate chip cookie actually has more energy, on an equal mass basis, than TNT.

[Widdekind]

2/5 --> 3/5. So, the Earth's S-GBE is actually ~20x the S-BE of TNT, so the threshold mass, where S-GBE = S-BE_tnt is closer to one Moon mass.

 

According to Wired Chemist, the Bond Energy of Si-O, a quite common constituent of rocky worlds of terrestrial type, is 452 KJ / mol. Now, a molecule of Si-O masses 44 AMU (roughly), and so a mole of those molecules is 44 g (6e23 x 44 = 2.64e25 AMU = 0.044 kg). So, the "S-BE" of Si-O is ( 452 KJ / mol ) / ( 0.044 kg / mol ) = 1e7 J / kg = 10 GJ / ton, or about 2.5x the S-BE of TNT.

 

So, as Swansont said, the S-BE of TNT is quite characteristic of common chemical bonds, not only of C-H compounds, but even of Silicates as well. Using these revised numbers, the threshold mass (S-GBE = S-BE_si-o) is 3-4 M_moon. More massive worlds will be "Gravity Bonded", whereas smaller worlds will be "Chemically Bonded".

 

In-so-far as the stronger mutual self-gravity, of rocky material, in "Gravity Bonded" worlds, will translate, ultimately, into some sort of Pressure (as gravity pushes the rocky materials up against each other)... then "Chemically Bonded" planetoids could conceivably behave more like stones on the surface of Earth, at "low pressure"; and, conversely, "Gravity Bonded" planetoids might be more like stones under high pressure.

 

How does pressure affect the property of rocks ?? Is there any evidence of such differences, in bulk properties, between the Earth ("Gravity Bonded") and the Moon ("Chemically Bonded") ??

 

 

 

 

Extras: According to Wikipedia, 1 eV / AMU = 100 MJ / kg (roughly).