Quote:
Originally Posted by CraigS
And it works both ways. I'm not clear on your response above.
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OK..
Since the single picture is worth a thousand words, and because I think this fundamental issue must be resolved properly, I put some effort into attached drawing, to clarify things, the way I see them.
The gravitational energy well is represented with the curves, the masses are circles.
Small mass resides at the surface of the Big mass (or it is in the circular orbit).
m, M, small and Big mass, respectively.
Ee is the energy required to pull out the small mass out of the well.
Ep is potential energy of the small mass, and it equals zero (because the small mass is on the surface of the big mass - lowest energy state).
E_total = Ee + Ep (Ep is zero before collapse of the Big Mass)
F0 and F1 iare the indications of field strengths (only they are inverse proportional to the value of F1^2 )
Also, because this is the closed system, the total energy balance before and after any change (including collapse) must be the same, right?
If we allow the big mass to collapse from Ro to R1 and if we keep the small mass at the same distance from the gravity centre of the Big mass (Ro.. let's assume it is in circular orbit around Big mass), the things are now different in terms of:
1) the potential energy of the Big mass changed (the matter is now deeper in its energy well.. the individual particles will now need more energy to escape the gravity well, as correctly pointed out by Steven).
2) If the small mass remained at the same place (or circular orbit), it acquired potential energy (Ep) which came from collapse of the big mass (??).
However, Ee (escape energy from the well ) remained exactly the same. This is in contradiction to what Steven said earlier, citation is below:
Quote:
Originally Posted by sjastro
You require energy to keep the small mass at the same distance plus the energy to remove the mass out of the well.
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The same goes for field strength at this point - it didn't change.
It would be good if someone could present the equation that fully accounts for energy bill in the system described above - I will try to do it later.