Err.. maybe.
However, if we stick to Gauss law, the field strength is determined by number of field lines per unit of surface (cm^2).. but the total flux (energy packed in the well) remains the same (because the big mass is the same in amount, regardless the change in density.
So your analogy is not quite correct, because the field strength at place where the small mass was is still the same.
However it appears that the potential energy of the small mass changed.
It came from the potential energy of the big mass which is now smaller, due to shrinkage.
So, after shrinkage of the big mass, and if we allow the small mass to fall to the lowes possible energy state, yes, we will have to use more energy to remove the small mass out of the well.
So, the first part of the total energy of the small mass is already there (added by collapse of the big mass. The small mass didn't move).
I need only the second part (after "plus ") to remove the small mass from the well.
This is not more than needed before collapse of the big mass.
As I commented in my earlier post (maybe my remark went un-noticed because it was edited later), we should be more clear when answering questions like this. Cryptic and not well-enough explained answers, however correct, will just create a huge confusion among some people (including myself).
Point taken.
And it works both ways. I'm not clear on your response above.
Responding to a call for help is part of community and contribution.
Confusion is part of learning. So is asking questions.
And it works both ways. I'm not clear on your response above.
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.
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.
Then there be people such as myself who with the clearest of answers find myself in a huge state of confusion!
Brian
That is so cool, Brian !
We're all confused !!
Maybe we're all on the same playin' field after all .. that's a terrific place to learn from eachother !
Having said that, Steven's answers are very clear to me, also.
We're lucky to have him around.
Oh and Bojan, also - thanks for taking the time and effort to outline things as you have. I'll have a look at your post when I get the chance. Thanks kindly, Bojan.
Hi Craig, two questions, are you self taught or did you pick this up in university? (if the first then there just might be hope for me) what is a 'bartelized' dob?
Brian
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)
A few points here. Ee is the kinetic energy. Since gravity is a conservative force E_total = Ee + Ep is constant everywhere for the small mass in the gravitational well.
Quote:
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 (??).
It has nothing to do with the potential energy of the large mass. When the small mass moves up the well Ee is converted into Ep, that is the small mass KE is converted into potential energy. It is why E_total is constant.
Conversely if it moves down the well Ep is converted into Ee.
Quote:
However, Ee (escape energy from the well ) remained exactly the same. This is in contradiction to what Steven said earlier, citation is below:
If the small mass has the value Ep=0 when the large mass contracts and remains at the same point in the deeper well, Ep is no longer zero. This means the small mass is performing work, that is KE is being converted into PE. The small mass loses KE equalling the difference in the depths of the well before and after contraction.
..
..
If the small mass has the value Ep=0 when the large mass contracts and remains at the same point in the deeper well, Ep is no longer zero.
OK so far.
Quote:
Originally Posted by sjastro
This means the small mass is performing work, that is KE is being converted into PE. The small mass loses KE equalling the difference in the depths of the well before and after contraction.
Now we came to the sticky point (for me and for some others, I am sure). Even if the distance of masses centres remain the same?
So what is happening to the proposed circular orbit?
Or, does the shape of the well change, apart from just being extended downwards? The curve was supposed to indicate the energy as a function of the distance from the centre. If this is so then I've got it.. if not.. well then I have a problem
Because I always believed in a principle that the extended mass (star) can be replaced with point like mass of equal value, without small mass (planet) ever noticing the difference, for the purpose of orbit calculations (and that involves potential and kinetic energies of course - all according to classical mechanic)
Ok now it is official, I started this thread looking for an explanation in simple English. Now we are into diagrams, algebra and serious philosophical chat... I'm lost!
But I am learning however for a while I am just going monitor the discussion but please do not stop cause I am loosing ignorance with each and every comment.
Brian
Now we came to the sticky point (for me and for some others, I am sure). Even if the distance of masses centres remain the same?
So what is happening to the proposed circular orbit?
Or, does the shape of the well change, apart from just being extended downwards? The curve was supposed to indicate the energy as a function of the distance from the centre. If this is so then I've got it.. if not.. well then I have a problem
Because I always believed in a principle that the extended mass (star) can be replaced with point like mass of equal value, without small mass (planet) ever noticing the difference, for the purpose of orbit calculations (and that involves potential and kinetic energies of course - all according to classical mechanic)
I don't see the relevance of orbits in this discussion. I have been referring specifically to the separation of a small mass from a large mass. It is in keeping with the 2 mass model to explain the significance of the cosmological term "Omega". The well is based on this criteria.
The role of KE and PE in circular orbits is very different when compared to separating masses.
For circular orbits, the PE+KE =constant rule is also applicable. Orbits however do not have to exist in the lowest PE state. The PE of an orbit is proportional to the radial distance.
PE and KE are constant at every point in the orbit. Hence there is no conversion of PE to KE and vice versa. The only criteria for a closed orbit is that KE<PE.
Getting back to your original point, I agree, if you shrink the central mass, the orbit is unaffected.
I don't see the relevance of orbits in this discussion. ...
...
Getting back to your original point, I agree, if you shrink the central mass, the orbit is unaffected.
Regards
Steven
Steven, thanks for your answer
Well, there is a relevance, because your later clarification created some confusion, I am sorry but I have to say this. And I only tried to sort it out taking another view angle, because confusion is not what we want to have here in science forum.
So, as far as orbits are concerned, that is exactly what I wanted to see.
Therefore, the conclusion is, the energy to remove the small mass from gravitational well in our little case is the same regardless the Big mass is shrank or not.
It is the energy needed to put the small mass from circular orbit around the Big mass into parabolic one.
Please correct me if I am wrong here and please show me where and why....
After this is sorted out, we can move to more complicated things, like omega.
A few points here. Ee is the kinetic energy. Since gravity is a conservative force E_total = Ee + Ep is constant everywhere for the small mass in the gravitational well.
It has nothing to do with the potential energy of the large mass. When the small mass moves up the well Ee is converted into Ep, that is the small mass KE is converted into potential energy. It is why E_total is constant.
Conversely if it moves down the well Ep is converted into Ee.
If the small mass has the value Ep=0 when the large mass contracts and remains at the same point in the deeper well, Ep is no longer zero. This means the small mass is performing work, that is KE is being converted into PE. The small mass loses KE equalling the difference in the depths of the well before and after contraction.
Hence Ee does not remain the same.
Regards
Steven
Have you guys ever heard of the Cavendish experiment
This is similar to Gauss' Law for electric fields:
"The electric flux through any closed surface is proportional to the enclosed electric charge."
The smaller 'closed surface', encloses more 'field lines', (for a constant charge or gravity), thus the field strength goes up as the radius (r) of the 'closed surface' decreases. If the point mass stays at the same place, the potential difference between where the point is and where the shrunken 'closed surface' now is, is greater and thus results in a greater attractive force on the point. Hence a greater force is needed for it to escape.
The 'closed surface', I think, is the key in the model. The numbers of field lines passing thru this surface determines the field strength.
Hope this helps.
Cheers
It has yet to be demonstrated that gravity has field lines or that is related to EMF, so how does Gauss come into it
so how
Steven, thanks for your answer
Well, there is a relevance, because your later clarification created some confusion, I am sorry but I have to say this. And I only tried to sort it out taking another view angle, because confusion is not what we want to have here in science forum.
So, as far as orbits are concerned, that is exactly what I wanted to see.
Therefore, the conclusion is, the energy to remove the small mass from gravitational well in our little case is the same regardless the Big mass is shrank or not.
It is the energy needed to put the small mass from circular orbit around the Big mass into parabolic one.
Please correct me if I am wrong here and please show me where and why....
You are not comparing apples to apples.
In a circular orbit, the direction of the velocity is perpendicular to the central force. No work is being performed. This is opposite to the the mass moving radially in the field.
A circular orbit exists because it is in a dynamic equilibrium without having to be in lowest PE state, a mass in the field is in the most stable equilibrium when it is in the lowest PE state.
A circular orbit is subject to orbital inertia. The interaction of gravity with orbital inertia is very different when compared to the linear inertia of a mass moving in the field.
The energy supplied for converting a circular orbit to parabolic orbit is due to external non conservative forces. The KE+PE = constant rule no longer applies. This is contrary to the effects of gravity on the inertia of masses in the absence of external forces on which the Universe is modelled on.
The energy supplied for converting a circular orbit to parabolic orbit is due to external non conservative forces. The KE+PE = constant rule no longer applies. This is contrary to the effects of gravity on the inertia of masses in the absence of external forces on which the Universe is modelled on.
Regards
Steven
OK, now I think I see where the difference is (and I hope it is more clear to others as well).
Summa summarum:
Our little system is not closed (it is open to external influence).
Universe is a closed system.
Thanks..
