# The Naked Scientists Forum

### Author Topic: Where does the energy from a gravitational field go?  (Read 8896 times)

#### jeffreyH

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##### Where does the energy from a gravitational field go?
« on: 09/11/2014 14:57:14 »
Mass is considered the source of the gravitational field. The field is considered to extend to infinity. The field radiates outwards from the source. The field must have energy. If this energy source is the mass then shouldn't the energy of the mass decrease over time? If there is an equivalence between mass and energy wouldn't the mass decrease? The earth, the sun and the planets have been producing gravity that radiates away for a very long time.
« Last Edit: 14/11/2014 14:06:43 by chris »

#### evan_au

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##### Re: Where does the energy go?
« Reply #1 on: 10/11/2014 10:17:39 »
Gravity is a field that is produced by mass. By itself, a lone mass produces a static gravitational field that extends to infinity, but it  cannot do work or "produce energy". So there is no "leak" that drains energy or mass out of the massive object.

If you now introduce another mass into this gravitational field, it can exchange kinetic energy & gravitational potential energy as it moves through the field. But the exchange is pretty much exact, and the objects travel in a repeated elliptical orbit around their common center of gravity. Still no energy is lost (at least, it's not measurable for objects less than the mass of Jupiter).

However, if the masses are neutron stars in a tight orbit, you find that they do radiate significant energy away into space, in the form of gravitational waves - as "wiggles" in the gravitational field that propagate away to infinity. But this does not cause the objects to become measurably lighter - the radiated energy comes from the two orbiting neutron stars getting closer to each other.

This is analogous to electric charge. By itself, a single charge has an electric field that extends to infinity, but does not radiate anything away; accelerating charges will radiate electromagnetic energy as wiggles in the electromagnetic field that propagate away to infinity.

#### jeffreyH

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##### Re: Where does the energy go?
« Reply #2 on: 11/11/2014 21:59:00 »
Gravity is a field that is produced by mass. By itself, a lone mass produces a static gravitational field that extends to infinity, but it  cannot do work or "produce energy". So there is no "leak" that drains energy or mass out of the massive object.

If you now introduce another mass into this gravitational field, it can exchange kinetic energy & gravitational potential energy as it moves through the field. But the exchange is pretty much exact, and the objects travel in a repeated elliptical orbit around their common center of gravity. Still no energy is lost (at least, it's not measurable for objects less than the mass of Jupiter).

However, if the masses are neutron stars in a tight orbit, you find that they do radiate significant energy away into space, in the form of gravitational waves - as "wiggles" in the gravitational field that propagate away to infinity. But this does not cause the objects to become measurably lighter - the radiated energy comes from the two orbiting neutron stars getting closer to each other.

This is analogous to electric charge. By itself, a single charge has an electric field that extends to infinity, but does not radiate anything away; accelerating charges will radiate electromagnetic energy as wiggles in the electromagnetic field that propagate away to infinity.

OK then some questions. What exactly IS a field? How does gravitational acceleration relate to inertial acceleration? A force is felt when acceleration is caused by an external agent other than gravity. No force is felt when in free fall. If relativistic velocities due to external forces increase mass then what change in mass IF ANY occur during gravitational acceleration. If the gravitational acceleration reaches relativistic speeds do we have the same increase in mass. What then of the relationship between kinetic and potential energy in acceleration under force and under gravitation?

#### PmbPhy

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##### Re: Where does the energy go?
« Reply #3 on: 12/11/2014 13:15:58 »
Quote from: evan_au
Gravity is a field that is produced by mass. By itself, a lone mass produces a static gravitational field that extends to infinity, but it  cannot do work or "produce energy".
Why not? The electric field and the gravitational field are well-known for doing work on particles.

#### yor_on

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##### Re: Where does the energy go?
« Reply #4 on: 12/11/2014 20:54:58 »
Pretty nice questions Jeffrey.

Maybe a field is a conceptual description of 'something' joining everything we can measure? Everything becomes a abstraction, the more you read about it, well, it does to me :) And before anyone wants to shoot down that one, why not tell me what thoughts consist of? To me it seems as if the universe is ordered around abstractions, emergences as I like to think of it, taking place. A information universe creating hierarchies of abstractions under a arrow. The base should be physics, as I think then.

'Energy' is either a 'coin of exchange' we use to describe transformations, or possibly something 'material', or maybe both? I don't know there? it's a working concept in Relativity, and in all physics as I gather. Think Pete referred to 'mass' some time, as being everything we could measure, from EM to matter.

#### yor_on

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##### Re: Where does the energy go?
« Reply #5 on: 12/11/2014 21:12:01 »
If it's a coin of exchange, then you can talk about a loss in form of heat, as per entropy. If it's something more than that, then ? But it seems to be about hierarchies too, doesn't it? Still, there is something really weird in getting 'free lunches', as in a energy conservation without loss, that as we then have to count in heat as another product of that 'energy' getting transformed. Because we do get work out of it. I also wonder about that one. assuming it is correct free lunches exist, although they have an end :)

#### jeffreyH

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##### Re: Where does the energy go?
« Reply #6 on: 12/11/2014 21:34:25 »
The relationships between mass energy, potential energy and kinetic energy are not straightforward. The movement of energy, whether angular momentum, velocity or acceleration, changes over time and via the influence of gravitation. The rates of change form a complex gradient that is not easy to determine because of the number of variables that may be involved. The biggest challenge is to develop a model that can predict all the various changes accurately with the support of experimental evidence. So where does the energy go?
« Last Edit: 12/11/2014 21:36:09 by jeffreyH »

#### alancalverd

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##### Re: Where does the energy go?
« Reply #7 on: 12/11/2014 23:30:46 »
definition
Quote
The region in which a particular condition prevails, especially one in which a force or influence is effective regardless of the presence or absence of a material medium.

Quote
The field must have energy.
Not true - indeed meaningless. You need to expend energy to move a particle that interacts with the field.

#### jeffreyH

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##### Re: Where does the energy go?
« Reply #8 on: 12/11/2014 23:59:55 »
definition
Quote
The region in which a particular condition prevails, especially one in which a force or influence is effective regardless of the presence or absence of a material medium.

Quote
The field must have energy.
Not true - indeed meaningless. You need to expend energy to move a particle that interacts with the field.

This is the kind of answer that I like. I've actually learned something. Thanks Alan.

#### jeffreyH

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##### Re: Where does the energy go?
« Reply #9 on: 13/11/2014 00:40:33 »
So in reacting with a gravitational field it could be hypothesized that there is a dilation in the rate of change of any particle. This decrease in the rate of change would be of the same percentage for any particle at an equivalent point in the field. Which would preserve the observed constancy of the speed of light. If the rate drops by 0.01% for an electron then it drops by the same percentage for the photon or any other interacting particle.

#### jeffreyH

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##### Re: Where does the energy go?
« Reply #10 on: 13/11/2014 02:38:30 »
If we take the centre of gravity of a perfect sphere and have a plane running through it. We can then define x, y and z axes tilted so each is axis has the same angle to the plane. If we then set a path that when projected onto the intersection of pairs of axes is at 45 degrees all axes that describe the path perpendicular to the plane then change at the same rate. As a baseline for mapping the effects of rates of change this can map a straight line path. This can then be adapted for curved trajectories. Extending this path out to an imaginary spherical surface the mass within the surface can be defined to be of any size with a radius of choice. Comparisons are then easy to make against the baseline straight path. It would be interesting to see what effects we could model on the interchange of energy under various conditions. To include the electric, magnetic and gravitational fields. With an equivalent value for rate of change at equidistant points the effects on energy of multi-mass systems would be fairly straightforward. Just an idea.

#### PmbPhy

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##### Re: Where does the energy go?
« Reply #11 on: 14/11/2014 02:47:20 »
Quote from: alancalverd

Quote
The field must have energy.

Not true - indeed meaningless. You need to expend energy to move a particle that interacts with the field.

Not true at all. The gravitational field most certainty does have energy. That's a well-known fact in gravitational physics. See:
http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/Mathematical_Thinking/possible_scalar_terms.htm

#### jeffreyH

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##### Re: Where does the energy go?
« Reply #12 on: 15/11/2014 15:36:07 »
Quote from: alancalverd

Quote
The field must have energy.

Not true - indeed meaningless. You need to expend energy to move a particle that interacts with the field.

Not true at all. The gravitational field most certainty does have energy. That's a well-known fact in gravitational physics. See:
http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/Mathematical_Thinking/possible_scalar_terms.htm

This post made my day. The equations on the page you linked to were exactly what I needed.

#### JohnDuffield

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##### Re: Where does the energy from a gravitational field go?
« Reply #13 on: 15/11/2014 16:16:17 »
A field definitely consists of energy, and this energy is positive. But the expression uG = g²/(8πG) isn't correct I'm afraid. Take a look at the picture of gravitational potential:

CCASA image by AllenMcC, see http://commons.wikimedia.org/wiki/File:GravityPotential.jpg

The spatial energy density increases towards the middle, and is at a maximum in the middle where gravitational potential is lowest. However g depends on the gradient in gravitational potential, and is zero in the middle.

#### jeffreyH

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##### Re: Where does the energy from a gravitational field go?
« Reply #14 on: 15/11/2014 16:27:38 »
The middle is the centre of gravity and therefore within the mass itself. If this is a particle then your argument makes no sense.

#### JohnDuffield

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##### Re: Where does the energy from a gravitational field go?
« Reply #15 on: 15/11/2014 16:31:40 »
Yes it's inside the mass itself. Just imagine a mineshaft that goes all the way through the middle of a cold rocky planet. At the centre point you don't fall down, you just float around.

The depiction is a depiction of gravitational potential for something like a planet, it doesn't make much sense for a particle like an electron.

#### jeffreyH

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##### Re: Where does the energy from a gravitational field go?
« Reply #16 on: 15/11/2014 20:41:29 »
A field definitely consists of energy, and this energy is positive. But the expression uG = g²/(8πG) isn't correct I'm afraid. Take a look at the picture of gravitational potential:

CCASA image by AllenMcC, see http://commons.wikimedia.org/wiki/File:GravityPotential.jpg

The spatial energy density increases towards the middle, and is at a maximum in the middle where gravitational potential is lowest. However g depends on the gradient in gravitational potential, and is zero in the middle.

The author is talking about 2 contributions. One from the mass and one from the field itself. I can see your point perfectly well which is why g alone does not represent the density. The equation is of the wrong form. At least someone has been brave enough to attempt to formulate it.

#### jeffreyH

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##### Re: Where does the energy from a gravitational field go?
« Reply #17 on: 15/11/2014 22:39:38 »
The energy equation has to start from this:

http://www.sjsu.edu/faculty/watkins/orbital.htm

#### jeffreyH

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##### Re: Where does the energy from a gravitational field go?
« Reply #18 on: 16/11/2014 01:16:13 »
If we take the radius of a perfect sphere with zero rotation to be unity we have 1/SQRT(1). Therefore the equation is unity at the surface. So in 1/SQRT(r) as r increases we have a factor that we can use with energy in a simplistic manner. This is really too simplistic but it is a reasonable starting point. The unity in v*1/SQRT(r) in the above site is the key to how the energy decreases with relation to kinetic energy. This differs between motion in the direction of the field lines and motion at an angle to the field lines. Curvature will present itself only with angular motion through the field. So in essense we need two equations to properly describe the interactions.

#### PmbPhy

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##### Re: Where does the energy from a gravitational field go?
« Reply #19 on: 16/11/2014 04:10:18 »
Quote from: jeffreyH
Excellent! :)

Quote from: jeffreyH
The middle is the centre of gravity and therefore within the mass itself. If this is a particle then your argument makes no sense.
What is the gravitating body that you're talking about? The center of gravity isn't always the center of mass.

#### alancalverd

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##### Re: Where does the energy from a gravitational field go?
« Reply #20 on: 16/11/2014 09:00:43 »
Quote from: alancalverd

Quote
The field must have energy.

Not true - indeed meaningless. You need to expend energy to move a particle that interacts with the field.

Not true at all. The gravitational field most certainty does have energy. That's a well-known fact in gravitational physics. See:
http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/Mathematical_Thinking/possible_scalar_terms.htm

Slight problem here. The dimensions of energy are ML2T-2 but those of gravitational field intensity are LT-2 and gravitational field potential L2T-2. No energy is involved until you introduce a mass into the field.

#### PmbPhy

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##### Re: Where does the energy from a gravitational field go?
« Reply #21 on: 16/11/2014 10:21:50 »
Quote from: alancalverd
Slight problem here. The dimensions of energy are ML2T-2 but those of gravitational field intensity are LT-2 and gravitational field potential L2T-2. No energy is involved until you introduce a mass into the field.
Hi Alan,

Thank you SO much for catching that and noting it.
« Last Edit: 16/11/2014 10:25:58 by PmbPhy »

#### PmbPhy

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##### Re: Where does the energy go?
« Reply #22 on: 16/11/2014 10:24:43 »
Quote from: evan_au
By itself, a lone mass produces a static gravitational field that extends to infinity, but it  cannot do work or "produce energy". So there is no "leak" that drains energy or mass out of the massive object.
I want to add to this that this is true because the mass is alone. That's why he put in a "lone" mass.

#### evan_au

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##### Re: Where does the energy from a gravitational field go?
« Reply #23 on: 16/11/2014 10:37:20 »
Quote from: JeffreyH
The middle is the centre of gravity and therefore within the mass itself.
This is true for a sphere (eg planet or star).

However, there are some exception cases, for example, the letter "C".

If you made a 3D solid "C", the center of gravity is in the middle of the "C", but it is not within the mass itself, because there is a big hole in the middle.

#### PmbPhy

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##### Re: Where does the energy from a gravitational field go?
« Reply #24 on: 16/11/2014 11:43:38 »
Quote from: JeffreyH
The middle is the centre of gravity and therefore within the mass itself.
This is true for a sphere (eg planet or star).

However, there are some exception cases, for example, the letter "C".

If you made a 3D solid "C", the center of gravity is in the middle of the "C", but it is not within the mass itself, because there is a big hole in the middle.
Dear Evan,

I believe that you have the wrong idea about what the center of mass and center of gravity are. Please see

Center of gravity; http://scienceworld.wolfram.com/physics/CenterofGravity.html

Center of mass: http://scienceworld.wolfram.com/physics/CenterofMass.html

The center of mass of a ring is at the geometric center of the ring where there is no mass. It's also the center of gravity too. Eeek!! :)

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##### Re: Where does the energy from a gravitational field go?
« Reply #24 on: 16/11/2014 11:43:38 »