# Law of conservation of Energy please explain how it is

1. Sep 26, 2007

### d_jnaneswar

hi guys,

I have a doubt, and searched this forum, but couldnt find an answer.

Law of conservation of energy states that energy can neither be created nor destroyed. In other words, energy can convert from one form to another, but as a whole, in a system, its quantity does not change.

Am I right?

How can we apply this to the Universe? How can we say that it is certainly true for the entire universe?

Another question.

In the archives, I came across a thread that had a rough discussion on planets and energy spent to keep them in orbit.

The question is, is gravitational force based on energy? Doesnt earth need a constant source of energy to keep a massive object like moon in orbit?

The other thread said that the work done by earth on moon is zero since..
a) work done on an object moving in a circle is zero.
b) force on moon is perpendicular to the direction of movement of the moon and so, the energy spent is zero in that direction (assuming that moon travels in a perfect circle).

If this is so, then earth does not spend energy in keeping the moon there. yet, the moon stays there fighting the centrifugal pull. The answer is gravitational force. But if gravitational force doesnt equal the energy of the centrifugal pull or any other pulls in the opposite direction, how can it stay in orbit?

Also, if earth doesnt spend energy on it to keep it in orbit, doesnt that mean that gravitational pull is not involved with energy on an object? Then what about potential energy?

You see my doubt? I am a bit confused here. Please explain the relationship between gravity and energy.

Gravity is G*m1*m2/d*d right? (where G is gravitational constant). Its been almost 15 years since I read this formula, so please correct. And energy/work is Force * distance. which means work = mass * acceleration * distance. right?

DJ

2. Sep 26, 2007

### Seele

Well in attempt to answer your first question completely and satisfactory, it would conditional if you could be a bit more specific in your questioning. Though you are correct in saying that energy is never lost, merely converted to a different form. When you speak of applying energy conservation to the universe, do you mean its constituents or the universe itself?

Upon the ignition of the Big Bang, there was most definitely an excess surplus of particles, constantly in a state of annihilation with one another. Though no energy is lost in this scenario, for despite an electron and its opposite counterpart, the positron destroying each other, as a consequence many other simpler particles are formed, for instance that of photons. As far as asking where the energy from the big bang derived from is inconsequential, perhaps it arrived here from a membrane-to-membrane collision; though wherever it came from, it certainly did not materialize from nothingness.

Though I wish you would be more specific in your questionings, as then perhaps I could better aide you in understanding.

3. Sep 27, 2007

### gdpudasaini

Don't be confuse

Man don't worry i will be solving your confusion. But today i am in hurry but i had mentioned some points here to solve it. Listen energy is simply difined as the capacity to do work according to classical physics. But in the world of quantum physics energy is something that contains neutral particle called pgoton with no mass at all.If the universe is closed and finite then law of conservation of energy must hold and if not it is violated which we don't want. What you have to remember is that the total mass and energy of such universe is constant as mass and energy are interconvertable according Special theory of Realativity in equation E=mc2. I will give detail explantion later.
Thanks

4. Sep 27, 2007

### Wallace

Energy as we normally think of it is a Newtonian 3 dimensional quantity that is not in general conserved when we have to use General Relativity, such as in understanding an expanding universe. See this thread for more information (this exact question is discussed).

You are trying to equate forces with energy. This cannot be done, it's like trying to add a velocity and an acceleration, it makes no sense. The energy of an object in orbit does not change since neither their kinetic or potential energies are changing, hence no work (the addition or subtraction of energy) is done.

5. Sep 27, 2007

### gdpudasaini

how

Do you have a simple explanation for non conservation of energy in general relativity?

6. Sep 27, 2007

### genneth

7. Sep 27, 2007

### Wallace

A simple example (which is mentioned in the above link) is redshift. As the Universe expands all photons lose energy due to redshift (since photon energy is given by E=hf and f decrease as the photons redshift). This energy does not 'go' anywhere, it is simply lost hence energy is not conserved.

Note that the Universe is not lawless and there are conservation laws in GR, they just aren't Newtonian ones (like conservation of energy) you may be more familiar with.

8. Sep 27, 2007

### d_jnaneswar

Thanks a lot guys.

Regarding force of earth on moon. I understand that since acceleration is zero, and force = mass * acceleration, and work done is force times distance, right? Since acceleration is zero (towards earth), force is zero and so work done by earth on moon is zero. But does that mean that earth is not doing any work on the moon? Does that mean that the moon will stay in orbit even if earth is not there? Does that mean earth does not have a force on the moon?

Moon stays in orbit because the resultant force on it towards the earth is zero, because there are other forces pulling it away. But for the moon not to get pulled away, doesnt earth exert force to keep it in orbit?

I am not trying to equate force and energy. I am simply confused about the whole thing thats all.

Two guys are pulling a box in two opposite ways. Their force upon it is equal and so the box stays stable. Does that mean that the work done on it by either guy is zero? Equations do point out that it is.

How ever, earth exerts Gravitational force on the moon that keeps it stable in orbit. Now, what does this mean?

For moon to stay in orbit against all the pull it has to get out of it, earth needs to pull it towards itself, right? Earth needs to exert force on it right? That force is gravity. But how does force come about?

I think I need to know what Gravity is, first of all. Thinking slowly, i dont seem to understand my own question!

Thanks for all the replies guys. I think I will go look at my mechanics text book first. This seems like a fundamental confusion between what is a force and what is energy. Still, any light on this would be really helpful.

DJ

9. Sep 28, 2007

### gdpudasaini

Don't be confuse

Ok I am back. Yesterday I was in hurried so couldn’t explain in detail, now I am going to do. Listen you are wrong in your first assumption that the energy of the system is constant. You certainly know the equation E=mc2 which shows that mass and energy are interconvert able. So in the entire universe the universe contains same mass and energy (remember same mass and energy but not only energy) since Big Bang. In other words mass and energy of the universe is always constant.

You will come across this sort of problem many times when you regard the laws of classical physics holds true in all condition. Remember the laws of classical physics doesn’t holds true any more in the extreme condition like Big Bang and over the large distance like universe. This was why Modern Physics was born.

I don’t know where you read that Earth spends energy to keep the moon in its orbit. (Can you give me the address?) As far as I know it is not so rather General Relativity (GR) predicts that a massive object moving in space and time gives off gravitational waves from which it loses energy. Yes I know what you are thinking now: “then the Earth also must be losing energy then why it doesn’t collapse to the sun” Listen the rate at which the Earth emits its gravitational waves is very small (enough to run a small electric heater). So calculations easily shows that the Earth will loose its energy completely and fall inside sun after billion billion billion billion years which is very longer than the age of the sun (5 billion years from now).
Gravitational energy is something that is naturally present in an object and no object in this universe loses it until it has mass. So there is no way that the Earth has to spent energy to keep the moon in its orbit. Also you knew that the Work done by the Earth on the moon is zero. Certainly there is no chance that any energy is lost.

What a silly question are you asking now? If centrifugal force ( given my mv.v/r) is not balanced by the gravitational force then not only the moon fly away in space but whole symmetry of the nature is broken down which is impossible. You must have heard as notion that “Nature loves symmetry”. From the atom to the galactic super cluster this sort of symmetry where centrifugal force is always balanced by the attractive force strictly holds. Otherwise the laws of nature would break down and the whole universe would not exist. But as we all know this is not the case. In case of the moon the moon is orbiting round the earth at a right distance where gravitational force is exactly balanced by the centrifugal force. But this is not always the case. The reason why the meteorites or asteroid fall on the earth can be explained by this fact. When meteorites come close to the earth then Earth’s gravitational pull acts upon the them, their centrifugal force is not enough to balance the Earth’s gravitational pull( As centrifugal force is directly prop. to mass). You may be thinking then from the right distance from the Earth gravitational force should be balanced by the centrifugal force ( CF inversely prop. to radius square). But in case of meteorites this distance is very far where gravitational force of earth is no longer strong. That’s the reason why the Earth and other planets have a certain no. of satellites.

It was lengthy but I hope you got proper answer of your question.

10. Sep 28, 2007

### Chronos

The net energy of the universe is always conserved. Photons redshift because space expands. The total energy content of the universe is fixed, IMO.

11. Sep 28, 2007

### genneth

The idea of energy in GR, on the cosmological scale, is ill-defined. In general, our intuitive idea of energy only makes sense when you can find a large, flat region of spacetime.

12. Sep 28, 2007

### d_jnaneswar

gdpudasaini :

Thanks a lot everyone!

DJ

13. Sep 29, 2007

### Wallace

This is entirely incorrect, the total energy of the Universe does not stay constant as explained in this thread and in those linked from this thread. To take another reason why, as the Universe expands there is more space and hence more vaccuum energy in the universe in total.

errm sorry but this is also wrong, gravity does not 'balance the centrifugal force' since this is a fictious force that does not exist in the Earth-Moon system. The Moon orbits the Earth due to the centripedal force this provided by the gravitational attraction between the two bodies but this is the only force in operation. The second part of the above answer is too confused to even deal with, suffice to say that this is not an accurate description of Newtonian physics.

14. Sep 29, 2007

### JesseM

The "Earth-Moon system" is a set of objects, not a coordinate system--there's nothing that says you can't analyze these objects from the point of view of a rotating coordinate system where you have a fictitious centrifugal force. For a perfectly circular orbit, it will be true in a coordinate system where both objects are at rest that the gravitational force exactly balances the centrifugal force. This doesn't work so well in the case of elliptical orbits, though, since their angular velocity is not constant and it'd be hard to figure out the fictitious forces in a rotating coordinate system with a non-constant angular velocity (though I'm sure you could do it if you really wanted to). In general it's easier to analyze non-circular orbits in Newtonian mechanics the standard way, using an inertial coordinate system where there are no fictitious forces...for elliptical orbits the best conceptual way of thinking about it might be to use the fact that angular momentum is conserved, see here for example (although if you want to use this in a proof, you first have to show why angular momentum must be conserved). An orbit like the moon's basically happens because the moon is constantly trying to move on a tangent to the orbit due to its linear momentum (or just due to Newton's second law, which says objects "want" to move in straight lines in the direction of their current velocity and will only deviate from straight lines if a force is acting them), and if it did move on a straight-line tangent its radial distance from the Earth would constantly increase, but meanwhile the Earth's gravity is causing it to fall towards the Earth in the radial direction, so these things are balancing out in such a way that it never escapes but also never falls all the way in and hits the Earth.

Last edited: Sep 29, 2007
15. Sep 29, 2007

### Chronos

Vacuum energy is an attempt to balance the energy density of the universe. It's a convenient way to preserve the critical density in an expanding universe. I view this as an unphysical solution. It is more palatable to consider a MOND-like effect over cosmological distances. Space is space - it only exists with respect to mass. Remove mass and the concept of space is meaningless.

16. Sep 30, 2007

### nemesis2010

Is it not so that, unless a force is exerted, an object will continue to move in a straight line in space? So, to keep an object in orbit, a continuous force must be exerted to keep that object from flying out into a straight line motion. To create a force, energy must be converted from one form to another. The kind of energy conversion that must take place to hold the moon in orbit is gravity. But what is unclear is, which enrgy is being converted into which in order for gravity to exerts its force.

17. Sep 30, 2007

### wolram

The theory is that the Earth bends spacetime and creates a gravity well, just by taking
away the Earth the moon would follow some other path, is there any convertion of energy?

18. Sep 30, 2007

### JesseM

Yes, this much is true.
No, energy does not need to be converted from one form to another in order for a force to be exerted. For a radial force like the force of gravity in Newtonian physics, there is only a conversion of potential to kinetic energy if the object's distance from the source of gravity changes--so in the case of a circular orbit, neither the kinetic energy nor the potential energy is changing. And the source of the gravitational force is not expending energy, that's just a natural property of its mass (just like the repulsive force of a positve charge on other positive charges is just a natural property of electrical charge).

Last edited: Sep 30, 2007
19. Oct 1, 2007

### gdpudasaini

not at all

Yeah man you are absolutely right that unless a force is exerted on a body it won’t orbit in a circular path like moon instead fly away in space in a uniform straight line. I totally agree on this fact. But what you are wrong is that gravitational energy is being converted into other unknown form of energy to keep the moon in its orbit. You certainly know Newton’s Universal Law of Gravitation from which we can easily deduce the following formula. F=GMm/r2. If you look carefully in this equation you would find that if there don’t exist a second mass (i.e. either M or m is zero) then clearly F=0. So gravitational force is something that exists only between two masses instead of single one. There is no existence of gravitational force in a single object.

Also if look more carefully this equation than you would notice that the gravitational force depends upon the mass of the objects held together (keeping r constant). So gravitational force last until the existence of the masses. So in case of Earth and Moon there is the existence of gravitational force between them until their mass exists. Since mass has been a constant quantity since their birth there always exists force that keeps the moon in orbit. Since mass can’t be destroyed and so is the gravitational force. So it has been clear that no energy must be converted in other form of energy to keep the moon in orbit so that Earth is not spending any energy to keep the moon in orbit. It would be easy if you imagine the force of attraction between to oppositely charged particle. When one such charged particle (say negative) is brought near to other (say positive) then negatively charged particle exerts a force on positively charged one(assuming that the charge in negative one is more than that of charge in positive one). Then can you imagine that energy is lost by the negative one? Of course no! That’s what in case of Earth and Moon too.

Thanks a lot to put you query.

20. Oct 4, 2007

### TR345

Movement of mass is energy. The velocity of the moon remains constant and so no energy is lost right?