Science a GoGo's Home Page Forums General Discussion General Science Discussion Forum Gravitational Potential Energy What is it exactly?

It seems that bandying mathematical formulae about gets nowhere significant.
Here is a non-mathematical suggestion:

At the time of the Big Bang we are told that all the matter and energy of the Universe occupied a very small area. The energy of the BB forced this matter and energy to expand. GPE is simply the equal and opposite force which, provided there were no "interference", would tend to bring everything back together.

Of course, this implies acceptance of the BB, the expanding Universe and equal and opposite forces, but, heck, where would we be without a little "faith"?

BTW, preearth, it's good to see you haven't deserted us. It's been very quite around here, and you do tend to liven things up.

Hi Bill; as you know I am pushing a new theory which is encountering some significant resistance.

I get a lot of crap from a lot of people and tend to get a bit cranky at times.

The Geek, in particular, makes me cranky,... particularly, his making up "facts" he feels no one can check.

For example, he has made up "facts" which he claims come from papers that are not available to the public.

In one case, when the paper was made available, his "facts" were not to be found in it.

Of course, if his "facts" were actually in the paper, he could have included the paper as an attachment to the thread, so that all could see it,... but he didn't.

Also, in the "Einstein was NOT first to publish E=mc^2" thread, he gave as "proof" of his claims, a passage in Italian.

If he understood the passage he was quoting, then he had to be able to read Italian. If he could read Italian, then he could have translated the passage for us and more clearly verified his claim,... but he didn't.

These instances show he is a dishonest debater and that annoys me.

I have to say I am not surprised that your "new theory" is raising a few objections. Perhaps it is best to see this resistance as the refiner's fire in which your theory can be assayed.

Regarding your comments about Bryan; I prefer to eschew "ad hominem" attacks, and stick to discussion of the relevant issues.

Bill S. said; "I prefer to eschew "ad hominem" attacks, and stick to discussion of the relevant issues."

If you don't want to call a liar, a liar, and end up believing his lies, that's your concern.

I am not that stupid.

Thanks.

How did we get from name calling to "believing his lies"?

Seems a natural progression to me.

If you are trying to draw me into some sort of slanging match, you really are wasting your time.

If you are unwilling to discuss things in a reasonable manner, I am wasting my time trying.

The ball is in your court.

Whatever happened to the original point of all this, which I seem to remember (could be wrong!) was something like:

Preearth says the gravitational potential energy of two planets moving from very close to combining may not be converted into enough heat to melt the crust.

Somebody else saying the gravitational potential energy of the two planets moving from very close to combining would have to be converted to enough heat to melt the crust.

How about a simple calculation like this:

1) Find the gravitational potential energy of the two planets just touching (using several methods if need be)
2) Find the gravitational potential energy of the combined planet (using the same method(s) as in 1).
3) Find the difference, and make sure it's the same for all methods. If not, got back and identify the wrong ones.
4) Assume all the energy is converted to heat and so find the amount of heat energy created
5) Estimate an upper bound on the time taken to combine.
6) Apply a radiative cooling model (or a suitable approximation), and calculate the temperature gradient through the surface of the combined planet.
7) See if the surface of the combined planet has a layer of similar thickness to continental crust which never exceeds the melting point of that material.
8) Conclude that the energy calculation either disproves Preearth's hypothesis, or is compatible with it.

Easy peasy!! Who wants to work through this with me?

Bonus part) If it disproves it, then increase the time taken to combine. For a slow enough process it won't disprove the hypothesis. This can give a quantified lower limit on the time taken to combine.

Sounds like a fascinating project. I don't have the maths to be much help, but I look forward to watching things happen.

I reckon. I hope PreEarth will be keen too. I'm happy to have a good go at the maths. It seems a shame to see arguments degenerate into irrelevant details that aren't going to make a difference either way.

This potential energy -> melting crust seems like something so easy to quantify. I'm sure it won't require any supercomputer mantle convection modelling, just a best/worst case scenario.



"No sense of harmony, no sense of time ..."

Go for it, Kallog. Preearth seems like the sort of person who would have the maths to make it a lively exchange. I may have to limit myself to the occasional "What?".

Here is something on this from way back.

Here is a cute calculation that comes up in showing the impact between the two planets (i.e., Heaven and PreEarth) would not necessarily melt the entire surface of the larger planet that coalesced from them (i.e., Earth).

It is simple enough for high schools students to understand and it illustrates the power of (even simple) mathematics.

The problem is to estimate the rise in the temperature caused by placing the planet PreEarth next to the planet Heaven and letting gravity transform them into the Earth.

(Note, that if two large enough planets are placed side by side and left alone, then gravity will pull them into one planet. So here we are placing PreEarth next to Heaven and gravity is pulling these two into a new planet which just happens to be the Earth.)

We will make the simplifying assumption that both the planets Heaven and PreEarth were spherical with uniform density.

This makes the math simple and the argument easy to follow.

The gravitational binding energy of a planet, U, is the energy released by the assembly of the planet from atoms which were originally an infinite distance away. Or, alternatively, it is the energy needed to disassemble the planet into atoms by moving each an infinite distance away.

The gravitational binding energy of a spherical planet with uniform density, is given by the formula;

U = 0.6GM^2/R, where

G = 6.67428 x 10^-20 km^3/(kg s^2) is the gravitational constant,
M is the mass of the planet in kg,
R is its radius in km.

U is here measured in megajoules, MJ.

Earth Radius R_E = 6371 km.
Earth Mass M_E = 5.97369 x 10^24 kg.
Approximate Earth Binding Energy = 0.6*G*M_P^2/R_P = 22.430 x 10^25.

PreEarth Radius R_P = 5200 km.
PreEarth Mass M_P = 3.48280 x 10^24 kg.
Approximate PreEarth Binding Energy = 0.6*G*M_P^2/R_P = 9.341 x 10^25 MJ.

Heaven Radius R_H = 4680 km.
Heaven Mass M_H = 2.48456 x 10^24 kg.
Approximate Heaven Binding Energy = 0.6*G*M_H^2/R_H = 5.282 x 10^25 MJ.

The energy necessary to separate PreEarth and Heaven to infinity, is:

G*M_P*M_H/(5200+4680) = G*M_P*M_H/9880 = 5.846 x 10^25 MJ.

The idea is to take PreEarth and Heaven at the point of first contact, that is, when they are just 9,880 kilometers apart, dissemble them to infinity, then bring everything back from infinity and assemble Earth.

So, the energy released from the point of contact through the formation of the Earth, is:

Energy Released = (22.430 - 9.341 - 5.282 - 5.846) x 10^25 = 1.961 x 10^25 MJ.

This is (1.961 x 10^25)/(5.97369 x 10^24) = 3.2827 megajoules per kilogram.

Suppose an average specific heat of 1330 J/kg°K.

Then we have that the Earth experiences a 3282700/1330 = 2,468 degree (average) rise in the temperature.

I emphasize that this temperature rise is due solely to the energy released by just placing PreEarth next to Heaven and letting gravity transform them into the Earth.

It is worth mentioning that the temperature rise will not be uniform.

Any pre-impact kinetic energy of Heaven (relative to PreEarth) will cause an additional rise in temperature.

To be continued,...

Note that in the above calculation, the latent heat of melting of the rock has not been taken into account. This will reduce the temperature rise somewhat.

Sorry some of this doesn't make any sense to me because of my level of english or there is extreme confusion?

What I can't understand is why all the Newtonian equations trying to understand Gravitational Potential Energy we all do realize they are wrong and won't make sense at this level ... right?

If I am understanding you correctly what you really need to look at is Bill S's favourite the somewhat scary Friedmann equations
(http://en.wikipedia.org/wiki/Friedmann_equations)

Go down to the bottom section they do a rescale for you if you can't do the maths and there is effective potential energy for something in space.

I think that's what you are trying to work.

Trying any of this with newtonian law is ridiculous it's a given it's wrong.

For "favourite", read "nemesis"!

BTW. Towards the close of last year I offered a non-mathematical suggestion as a possible answer to the original question.

"At the time of the Big Bang we are told that all the matter and energy of the Universe occupied a very small area. The energy of the BB forced this matter and energy to expand. GPE is simply the equal and opposite force which, provided there were no "interference", would tend to bring everything back together.

Of course, this implies acceptance of the BB, the expanding Universe and equal and opposite forces, but, heck, where would we be without a little "faith"?"

No one responded; is that because it is too naive to deserve comment?

The problem is what is the force in effect you are asking the age old question question of the direction of entropy which leads directly into the "arrow of time".

I accept the argument but it becomes a bit like discussing religion origins I have no basis to discuss.

I suspect if you actually do the analysis it ends a bit like Doug Sweetsers analysis of Julian Barbour's theory that there is no such thing as time it is an illussion (http://www.science20.com/standup_physicist/julian_barbour_versus_minkowski_and_me-80765).