Where does the energy of gravity come from?

[edpell]

How about this. We have two steel balls attached to each other with a wire. They are spinning around each other in empty space. No gravity involved. The force that causes the acceleration comes from the tension in the wire. The force of the wire of ball1 is equal and opposite the force on ball2. There is no net force.

If you believe the acceleration is doing work then after some time we should see some effect of that work. But nothing changes the temperatures remain the same. The velocities remain the same. So where is the energy going? Work = force (dot product) distance. In this case force and distance are perpendicular so the (dot product) is zero.

 

[Don Hicks]

The moon moves when an object slingshots around it. Gravity is not a force, it is the curvature of space due to matter.

This is a great demonstration of the effects of gravity; however, it does not explain how gravity does what it does.

As to the question of whether gravity is a force, step off the fifth floor of a building at sea level on planet Earth and tell me if there is not a force at play. For that matter, help a buddy move his stuff into an upstairs apartment and tell me what you are fighting as you climb the stairs with his futon.

The real answer is not a definition of what gravity does, but an explanation of how gravity does it. Conquering gravity would liberate the human race.

 

[Don Hicks]

How about this. We have two steel balls attached to each other with a wire. They are spinning around each other in empty space. No gravity involved. The force that causes the acceleration comes from the tension in the wire. The force of the wire of ball1 is equal and opposite the force on ball2. There is no net force.

If you believe the acceleration is doing work then after some time we should see some effect of that work. But nothing changes the temperatures remain the same. The velocities remain the same. So where is the energy going? Work = force (dot product) distance. In this case force and distance are perpendicular so the (dot product) is zero.

Ok, there is no gravity (perceptible gravity) at play, so why is this part of the discussion?

It is a good thought experiment, but the true energy in this example was applied at the beginning when the balls were originally flung in the “orbit” you have created. They will eventually slow down as effects from other objects play on them, but, aside from the centrifugal force that would separate the two if the wire were cut, there appears to be no other forces at play. What am I missing?

 

[DaveC426913]

Ok, there is no gravity (perceptible gravity) at play, so why is this part of the discussion?

It is a good thought experiment, but the true energy in this example was applied at the beginning when the balls were originally flung in the “orbit” you have created. They will eventually slow down as effects from other objects play on them, but, aside from the centrifugal force that would separate the two if the wire were cut, there appears to be no other forces at play. What am I missing?

That's why he's bringing it up. Same arrangement, different cause. It makes it easier to show why gravity is doing more work since it's easy to see that the connecting wire is doing no work.

 

[edpell]

They will eventually slow down as effects from other objects play on them

Newton's first law is still good "objects in motion will stay in motion". There is no friction they just keep going and going...

 

[DaveC426913]

Newton's first law is still good "objects in motion will stay in motion". There is no friction they just keep going and going...

Not friction - tidal forces. The objects will eventually stop their rotation with their long axis aligned with the closest gravity well.

 

[Bussani]

I had a similar question that I couldn't answer, and here might be the perfect place to answer it.

Let's say you had a huge stationary object in space, like...a solid ball the size of the solar system, just to go over the top. It has gravity, obviously, due to its ridiculous mass. Then you throw something towards it with a certain amount of force. As it gets closer, the object should start to accelerate due to the gravity of the giant object, right?

So the question is: where is that increase in kinetic energy coming from? It can't just appear out of nowhere, can it? But it's also not stealing any mass or gravity or anything from the giant ball.

 

[edpell]

At the start the small ball has potential energy. As it moves faster and faster the potential energy is converted to kinetic energy. The potential energy is stored in the field. The gravity field. Just like a spring. But a spring that is distributed over near by space and has no material substance but does have tension/compression.

 

[Bussani]

At the start the small ball has potential energy. As it moves faster and faster the potential energy is converted to kinetic energy. The potential energy is stored in the field. The gravity field. Just like a spring. But a spring that is distributed over near by space and has no material substance but does have tension/compression.

Hm, I see. Is that potential energy in the gravity field of the moving object, the giant ball, or both?

This leads me to another question. Let's say you had an impossible bottomless pit, with a constant gravitational pull all the way down and no end. Also no air, so no terminal velocity to interfere with this. If you dropped something into this pit, would it eventually hit a point where it stops accelerating, when all of this potential energy has become kinetic energy? In short: is there a limit to how much a gravitational pull can accelerate a particular object?

I know the situation is impossible, but I'm just trying to visualize how this potential energy in the gravity fields works.

 

[DaveC426913]

Hm, I see. Is that potential energy in the gravity field of the moving object, the giant ball, or both?

This leads me to another question. Let's say you had an impossible bottomless pit, with a constant gravitational pull all the way down and no end. Also no air, so no terminal velocity to interfere with this. If you dropped something into this pit, would it eventually hit a point where it stops accelerating, when all of this potential energy has become kinetic energy? In short: is there a limit to how much a gravitational pull can accelerate a particular object?

I know the situation is impossible, but I'm just trying to visualize how this potential energy in the gravity fields works.

It's not impossible. Not in space. An object can fall from infinity toward another object.

No, the object need never stop accelerating.

Until the two objects are actually touching, there is always some potential energy.

 

[Bussani]

Ahh, I see. Thanks a lot for the reply.

 

[Livethefire]

I'll restate the problem I'm having.
Take any two obvious large objects as an example, the two easiest are the Earth and the Moon, locked in an orbit around each other, by gravity. Simple. The question becomes... as the Moon is not being allowed to take off on a tangential course, it is being constantly being accelerated towards the Earth. Simple, again. The energy required must be supplied from somewhere, and the question is where?
Mass and energy are two sides of the same thing, as there is no other source for the energy required, matter has to be converted to energy, but where is the loss of mass?

Answer: Gravitational Potientual Energy

Energy is an extremely useful book keeping system. Yes energy/work is needed to apply a force or vice versa. However physicists note that there are Four Fundemental Forces of nature- essentially by default these Fundamental forces have ability to do work. This ability comes from the property of an object, which can include mass (gravity), charge (coloumb)... etc etc The list goes on.

 

[edpell]

Hm, I see. Is that potential energy in the gravity field of the moving object, the giant ball, or both?

This leads me to another question. Let's say you had an impossible bottomless pit, with a constant gravitational pull all the way down and no end. Also no air, so no terminal velocity to interfere with this. If you dropped something into this pit, would it eventually hit a point where it stops accelerating, when all of this potential energy has become kinetic energy? In short: is there a limit to how much a gravitational pull can accelerate a particular object?

I know the situation is impossible, but I'm just trying to visualize how this potential energy in the gravity fields works.

To answer the first part mostly the small ball falls to the large ball but the large ball does fall a little towards the small ball. So I would say the net motion is due mostly to energy from the field of the large ball and a little from the field of the small ball. It might be correct to say that the motion of the small ball is due 100% to the field of the large ball and the motion of the large ball is due 100% to the field of the small ball, but I would have to think carefully about that.

Since the pit is infinite the initial potential energy is infinite so no problem it keeps gaining energy. But as to the question how much velocity does it gain per unit time (in the shafts inertia frame of reference)? I would say once it gets to say (1-10^30)c the gain in velocity per unit time (as stated above) is very small (but never zero).

 

[edpell]

Answer: Gravitational Potientual Energy

Energy is an extremely useful book keeping system. Yes energy/work is needed to apply a force or vice versa. However physicists note that there are Four Fundemental Forces of nature- essentially by default these Fundamental forces have ability to do work. This ability comes from the property of an object, which can include mass (gravity), charge (coloumb)... etc etc The list goes on.

No work is done. The definition of work is force (dot product) distance. In this case since the force is always orthogonal to the distance the dot product is always zero.

How are you defining work?

 

[Livethefire]

No work is done. The definition of work is force (dot product) distance. In this case since the force is always orthogonal to the distance the dot product is always zero.

How are you defining work?

Well, I was kind of answering my own question.
I wasn't focusing on the concept of the orbit, rather just the aspect that two masses will attract due to a force.

I realize what your getting at , and it was my inability to really focus on the question. Sorry.

 

[Nick666]

Could this energy of gravity involve somehow dark matter/energy ?

 

[Rasalhague]

And that makes no sense which is what we've been trying to tell you. Your equations don't help explain how the Sun is able to keep the Earth moving in a circular manner as opposed to flying straight. Or the Earth and the Moon, etc. To say that no energy is needed to maintain a circular orbit is nonsensical. It obviously requires energy.

Take a table. If I kick the bottom of the table, in outer space it will move in the direction it was kicked. But Earth's gravity is continuously pulling it downward. This is work being done. Work requires energy. There is no matter --> energy conversion that explains this as far as I know, and petridge pointed this out as well. So where does it come from?

I've raised this issue up in a conversation with a Stanford PhD physics professor about this. She didn't know how to answer it and said things like 'we don't know much about gravity' and 'we have this concept of potential energy.' If you have better credentials than that, by all means give a real answer, don't just refer to some equation as proof that you don't need to account for it.

Think of the simple case where the difference in mass between the two bodies is so great that the effect of the smaller mass, m, on the greater, M, can be ignored. Let's suppose mass m is in a circular orbit around M.

By definition of potential energy (and taking our "zero of potential energy" as infinity),

U = - \int_{r}^{\infty} \textbf{F} \cdot \textup{d}\textbf{r} = \frac{-GMm}{r},

where U is potential energy due to gravity, F gravitational force, M the greater mass, m the smaller mass, dr an infinitesimal change in the position of m (the position considered as a position vector, r, extending from the centre of mass of the system, here effectively the centre of mass of M, to the centre of mass of m), r the magnitude (length) of this position vector r, G the gravitational constant (which relates the units). In other words, the potential energy of the satellite m is the work that would be done by the force of gravity if it was to move m from infinitely far away to its current position.

By definition of kinetic energy,

T = \frac{1}{2}mv^2,

where T is the kinetic energy of the orbiting body with mass m, and v its speed, defined as the magnitude of its velocity with respect to the more massive body.

By definition of circular motion,

\frac{\mathrm{d} r}{\mathrm{d} t} = 0

at all points in the orbit. This just means that the distance of the satellite from the more massive body doesn't vary over time.

Less obviously,

\frac{\mathrm{d} v}{\mathrm{d} t} = 0.

That is, the speed of the satellite is constant over time. This follows from Kepler's 2nd law in the special case of a circular orbit; the radius of the orbit doesn't change, so the only way that an equal area can be swept out over an equal time is if the speed is constant.

http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion#Second_law

Therefore

\frac{\mathrm{d} }{\mathrm{d} t} \left(T + U) = 0.

Kinetic energy is constant, and potential energy is constant, so their sum is constant.

 

[bonjour]

I saw this thread when I was looking for "is gravity energy?"
A conclusion I had come to on my own.
I believe gravity is just energy, specifically kinetic energy.

 

[flufffrost]

I have been thinking about two different possibilities. For one thing, isn't it possible our understanding of energy is incomplete? I mean we say all this stuff about how there must be conservation of energy and all these equations that show this and that, but aren't those all just "proven" by real-life examples we've all seen? I mean to say that we might not be able to answer this question because there is not a good enough understanding of energy.
Also, Einstein's idea that matter warps space-time meant to show that yes, when space is flat and good and all, an object will continue to move in a straight line. However, when space is curved (as it supposedly is around planets), the path of least resistance so to speak is a curved one. Forgive me if I have misinterpreted this idea.
Still, this does not address the question as to where this energy comes from. I liked the example given above regarding two metal balls attached by a wire--if spun and left in space, they will continue to spin for eternity because of all the velocity dot stuff. However, it seems to me that the question we are addressing is where did the energy for that original spin come from? This initial spin force is analogous to the Sun changing the direction of a comet. Where does it get the energy to do that? Do we know enough about energy to answer it? Or does it not need energy?


ps sorry for the long post!

 

[flufffrost]

Could this energy of gravity involve somehow dark matter/energy ?

perhaps the "vacuum" energy that is thought to be causing the universe to expand quicker and quicker has something to do with it? seems improbable.

 

[flufffrost]

Think of the simple case where the difference in mass between the two bodies is so great that the effect of the smaller mass, m, on the greater, M, can be ignored. Let's suppose mass m is in a circular orbit around M.

By definition of potential energy (and taking our "zero of potential energy" as infinity),

U = - \int_{r}^{\infty} \textbf{F} \cdot \textup{d}\textbf{r} = \frac{-GMm}{r},

where U is potential energy due to gravity, F gravitational force, M the greater mass, m the smaller mass, dr an infinitesimal change in the position of m (the position considered as a position vector, r, extending from the centre of mass of the system, here effectively the centre of mass of M, to the centre of mass of m), r the magnitude (length) of this position vector r, G the gravitational constant (which relates the units). In other words, the potential energy of the satellite m is the work that would be done by the force of gravity if it was to move m from infinitely far away to its current position.

By definition of kinetic energy,

T = \frac{1}{2}mv^2,

where T is the kinetic energy of the orbiting body with mass m, and v its speed, defined as the magnitude of its velocity with respect to the more massive body.

By definition of circular motion,

\frac{\mathrm{d} r}{\mathrm{d} t} = 0

at all points in the orbit. This just means that the distance of the satellite from the more massive body doesn't vary over time.

Less obviously,

\frac{\mathrm{d} v}{\mathrm{d} t} = 0.

That is, the speed of the satellite is constant over time. This follows from Kepler's 2nd law in the special case of a circular orbit; the radius of the orbit doesn't change, so the only way that an equal area can be swept out over an equal time is if the speed is constant.

http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion#Second_law

Therefore

\frac{\mathrm{d} }{\mathrm{d} t} \left(T + U) = 0.

Kinetic energy is constant, and potential energy is constant, so their sum is constant.

in reply to Rasalhague's post with the equations regarding potential and kinetic energy, I was wondering if this constant of kinetic and potential energy example can be applied to a comet going in a straight line that is bent and pulled in by the Sun's gravity (therefore changing its velocity, which requires an output of energy)?

 

[Matterwave]

The change in velocity is exactly offset by the change in potential energy.

In circular motion neither T nor U changes. This is a special case. In general orbits (ellipse, or hyperbola, or parabolas) T and U are dynamics. But T+U always remains constant. If you lose T you gain U and vice versa.

 

[Frame Dragger]

I have been thinking about two different possibilities. For one thing, isn't it possible our understanding of energy is incomplete? I mean we say all this stuff about how there must be conservation of energy and all these equations that show this and that, but aren't those all just "proven" by real-life examples we've all seen? I mean to say that we might not be able to answer this question because there is not a good enough understanding of energy.
Also, Einstein's idea that matter warps space-time meant to show that yes, when space is flat and good and all, an object will continue to move in a straight line. However, when space is curved (as it supposedly is around planets), the path of least resistance so to speak is a curved one. Forgive me if I have misinterpreted this idea.
Still, this does not address the question as to where this energy comes from. I liked the example given above regarding two metal balls attached by a wire--if spun and left in space, they will continue to spin for eternity because of all the velocity dot stuff. However, it seems to me that the question we are addressing is where did the energy for that original spin come from? This initial spin force is analogous to the Sun changing the direction of a comet. Where does it get the energy to do that? Do we know enough about energy to answer it? Or does it not need energy?


ps sorry for the long post!

Do a little reading on the Stress-Energy Tensor (Momentum-Energy Tensor). That describes how spacetime is distored by (no shock here) energy. You'll note that beyond a constent for energy, physics doesn't offer an explanation as to what energy is. The best definition for energy is that it's what distorts and is guides by spacetime. Energy is not a 'thing', but a concept to describe how Work is done. What is energy is right up there with 'what is time, really?'... that is for metaphysics and philosophers... or physicists of the distant future.

 

[NYSportsguy]

First of all let's get some concepts clear here:

1) Energy: is a scalar physical quantity that describes the amount of
Work that can be performed by a force, an attribute of objects and systems that is subject to a conservation law.

2) Work: is the amount of energy transferred by a force acting through a distance. Like energy, it is a scalar quantity.

FORMULA for WORK: W = F (force) x d (distance of displacement)3) Force: In physics, the concept of force is used to describe an influence which causes a free body to undergo an acceleration. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or which can cause a flexible object to deform. An applied force has both magnitude and direction, making it a vector quantity.

Formula for FORCE: F = M (mass) x A (acceleration)

 

[bonjour]

Sportsguy, qould it be fair to say that "work" is the measurement of a condensed singular action? I say condensed because a singular action would be the 2 elementary particles reacting to one another, and of course that happens on too large a scale to be measured.

 

[NYSportsguy]

(cont.) As Stated very well by posters Rasalhague and Matterwave above, in a closed field, the total potential + kinetic energy of that field must always add up to the same amount. If you increase the potential energy, the kinetic should decrease...and vice-versa.

Similar to magnets that attract each other, if you move them apart they gain potential energy as they go further and further apart while losing kinetic energy at the same time. Now when you move those same magnets closer to each other; they lose that potential energy and gain the equivalent kinetic energy.

Overall the systems adds up 0 in either case.

 

[Frame Dragger]

(cont.) As Stated very well by posters Rasalhague and Matterwave above, in a closed field, the total potential + kinetic energy of that field must always add up to the same amount. If you increase the potential energy, the kinetic should decrease...and vice-versa.

Similar to magnets that attract each other, if you move them apart they gain potential energy as they go further and further apart while losing kinetic energy at the same time. Now when you move those same magnets closer to each other; they lose that potential energy and gain the equivalent kinetic energy.

Overall the systems adds up 0 in either case.

And...?

 

[NYSportsguy]

Say you were to slingshot around the moon and gain momentum. In so doing you would have gained Energy from gravity. Basically because energy is conserved there has to be some way that the force of gravity "radiating" out from the moon would come in contact with a space shuttle and speed it up. How does this work?

Once again, you would have gained kinetic energy form that field but decreased an equal amount potential energy in the process. Overall the amount of energy in the gravitational field remains constant.

Momentum = mass x velocity

 

[flufffrost]

The change in velocity is exactly offset by the change in potential energy.

In circular motion neither T nor U changes. This is a special case. In general orbits (ellipse, or hyperbola, or parabolas) T and U are dynamics. But T+U always remains constant. If you lose T you gain U and vice versa.

So, you guys are saying that the Earth's pulling of the moon is a closed system given by the fact that the sum of kinetic and potential energy remains constant (forgive me once more if I have misinterpreted, I really don't know much about physics but I like to read physics discussions). Still, work is being done. When an asteroid is pulled in by Earth's gravity, gravity has accelerated it a given distance of displacement from what would have been its natural course. So doesn't energy either have to come in from somewhere or somehow be re-transferred to the Earth?

 

[DaveC426913]

So, you guys are saying that the Earth's pulling of the moon is a closed system given by the fact that the sum of kinetic and potential energy remains constant (forgive me once more if I have misinterpreted, I really don't know much about physics but I like to read physics discussions). Still, work is being done.

No. No work is being done because the CoM of the (Earth/Moon) system has remained stationary.

When an asteroid is pulled in by Earth's gravity, gravity has accelerated it a given distance of displacement from what would have been its natural course. So doesn't energy eitherc have to come in from somewhere or somehow be re-transferred to the Earth?

Depends on whether you include the asteroid in the system or not. If you do not, then yes work is done (the CoM of Earth/Moon has moved due the external influence of the asteroid); if you do, tehn no work is done (because the CoM of Earth/Moon/asteroid has not moved).