# B How does gravitational potential energy work?

#### TheQuestionGuy14

Gravitational energy is the potential energy a physical object with mass has in relation to another massive object due to gravity, so, does an object outside a gravitational field have no gravitational potential energy?
For example, the Earth is 4.5 billion years old, so it's gravity stretches 4.5 billion lightyears, meaning objects further than this aren't affected by Earth's gravity. Once Earth's gravity reaches them, do they gain potential energy? How does this work?

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#### DaveC426913

Gold Member
does an object outside a gravitational field have no gravitational potential energy?
There is no such thing as being outside a gravitational field. Gravity from every single atom (in principle) extends throughout the universe.

For example, the Earth is 4.5 billion years old, so it's gravity stretches 4.5 billion lightyears,
The mass that makes up Earth has existed since the Big Bang (as energy, and then as atoms) - albeit being distributed throughout larger volume of space. Every one of those atoms has been exerting its gravitational pull on everything else in the universe (in principle).

The large volume of dust and gas that is destined to become Earth has been acting upon that object's individual atoms even before the atoms coalesced into the object, so the gravitational potential has always been there.

#### sophiecentaur

Gold Member
For example, the Earth is 4.5 billion years old, so it's gravity stretches 4.5 billion lightyears,
The majority of the mass of the Earth was 'somewhere else' before it got together to form the Earth. There has been a tiny amount of mass change due to Energy changes but we can ignore that here.
I'm not sure how "Advanced Cosmology" you want to go but there's a reasonable classical argument that says that every tiny piece of mass has always affected every other tiny piece of mass (back to the big bang, at least).
Taking that into account, do you want to elaborate on your question?
(I see that I have more or less repeated what Dave has already written but the fact that we came up with similar answers should help to convince you!! )

#### TheQuestionGuy14

There is no such thing as being outside a gravitational field. Gravity from every single atom (in principle) extends throughout the universe.

The mass that makes up Earth has existed since the Big Bang (as energy, and then as atoms) - albeit being distributed throughout larger volume of space. Every one of those atoms has been exerting its gravitational pull on everything else in the universe (in principle).

The large volume of dust and gas that is destined to become Earth has been acting upon that object's individual atoms even before the atoms coalesced into the object, so the gravitational potential has always been there.
Ok, thanks, that makes sense.

#### TheQuestionGuy14

The majority of the mass of the Earth was 'somewhere else' before it got together to form the Earth. There has been a tiny amount of mass change due to Energy changes but we can ignore that here.
I'm not sure how "Advanced Cosmology" you want to go but there's a reasonable classical argument that says that every tiny piece of mass has always affected every other tiny piece of mass (back to the big bang, at least).
Taking that into account, do you want to elaborate on your question?
(I see that I have more or less repeated what Dave has already written but the fact that we came up with similar answers should help to convince you!! )
Thanks, I understand. I assume the same applies to other fields like the electric field aswell?

#### sophiecentaur

Gold Member
Hmm. Not sure about that because there are both positive and negative charges (of course) in nearly all matter so the effect at a distance of a particular charge can actually be zero due to other charges. Gravity is a bit special.

#### DaveC426913

Gold Member
Well, the net effect of gravity can be zeroed out as well, say, by having mass equally distributed about the target mass.

#### Ibix

Well, the net effect of gravity can be zeroed out as well, say, by having mass equally distributed about the target mass.
But that doesn't zero the potential, just the force.

#### DaveC426913

Gold Member
But that doesn't zero the potential, just the force.
Yes.

Can the same be said about the EMF?

#### Ibix

Yes.

Can the same be said about the EMF?
You can zero the electric potential because the signs can be opposite - half way between an electron and a positron, for example. You can only zero the gradient of the gravitational potential.

Gold Member

#### Ibix

Inflation is a phenomenon in the very early universe, needs general relativity to discuss, and gravitational potential is not defined in any situation where it is a relevant effect.

#### TheQuestionGuy14

The majority of the mass of the Earth was 'somewhere else' before it got together to form the Earth. There has been a tiny amount of mass change due to Energy changes but we can ignore that here.
I'm not sure how "Advanced Cosmology" you want to go but there's a reasonable classical argument that says that every tiny piece of mass has always affected every other tiny piece of mass (back to the big bang, at least).
Taking that into account, do you want to elaborate on your question?
(I see that I have more or less repeated what Dave has already written but the fact that we came up with similar answers should help to convince you!! )
Sorry if I'm bothering, but can I ask, how exactly has every particle always affected every other particle, back to the big bang? I know I said I understood but now that I thought about it for a bit, I'm confused.

#### DaveC426913

Gold Member
Sorry if I'm bothering,
Not a bother. That's what we're here for.

but can I ask, how exactly has every particle always affected every other particle, back to the big bang?
The Big Bang started from a very small, dense state - all the mass was very close together - within each others' gravitational influence. The actual details are a bit more complicated but that's the gist.

#### sophiecentaur

Gold Member
how exactly has every particle always affected every other particle, back to the big bang?
Gravity works that way. It never dies down to nothing.
The force per unit mass (g) is
g= Gm1 m2/d2
which is the good old inverse square law, with G being the universal gravitational constant, the m's are the masses and d is the distance between. Gravity always causes an attractive force between all pairs of masses and all the forces add up (multiple vectors adding together). As the formula shows you, it goes on for 'ever' - in the classical world. The details will change with modern theories about the geometry of the universe but this a very good start at understanding the system.

#### TheQuestionGuy14

Not a bother. That's what we're here for.

The Big Bang started from a very small, dense state - all the mass was very close together - within each others' gravitational influence. The actual details are a bit more complicated but that's the gist.
Gravity works that way. It never dies down to nothing.
The force per unit mass (g) is
g= Gm1 m2/d2
which is the good old inverse square law, with G being the universal gravitational constant, the m's are the masses and d is the distance between. Gravity always causes an attractive force between all pairs of masses and all the forces add up (multiple vectors adding together). As the formula shows you, it goes on for 'ever' - in the classical world. The details will change with modern theories about the geometry of the universe but this a very good start at understanding the system.
So when the universe expanded after the big bang, did all the particles stay in every other particles gravitational field? They didn't leave the fields?

#### DaveC426913

Gold Member
So when the universe expanded after the big bang, did all the particles stay in every other particles gravitational field? They didn't leave the fields?
I see where you're going.

Since the Inflationary Epoch expanded at a rate greatly exceeding the speed of light - and gravitational waves only propagate at the speed of light - is it not possible that portions of the universe were isolated from each other?

Sure, but our observable universe is defined as only that portion in which all parts are within reach of each other.
Gravitational waves travel at the same speed as - and thus reaches as far as - light. i.e. If we can see light from it, then it affects us gravitationally.

As always, see sig line:*

#### TheQuestionGuy14

I see where you're going.

Since the Inflationary Epoch expanded at a rate greatly exceeding the speed of light - and gravitational waves only propagate at the speed of light - is it not possible that portions of the universe were isolated from each other?

Sure, but our observable universe is defined as only that portion in which all parts are within reach of each other.
Gravitational waves travel at the same speed as - and thus reaches as far as - light. i.e. If we can see light from it, then it affects us gravitationally.

As always, see sig line:*
Ah, I see. So, correct me if I'm wrong, but every particle in the observable universe has always been affected by every other particles gravity. Would I be correct?

#### sophiecentaur

Gold Member
Ah, I see. So, correct me if I'm wrong, but every particle in the observable universe has always been affected by every other particles gravity. Would I be correct?
I reckon so.

#### Mister T

Gold Member
Sorry if I'm bothering, but can I ask, how exactly has every particle always affected every other particle, back to the big bang?
To varying amounts, most of them negligible.

#### TheQuestionGuy14

I reckon so.
And currently, space is expanding at an accelerating rate, doesn't that mean objects within the observal universe will eventually leave it and no longer be casually connected to Earth, meaning they'd leave Earth's gravitational field? What will happen to their (teeny tiny amount of) gravitational potential energy?

#### DaveC426913

Gold Member
And currently, space is expanding at an accelerating rate, doesn't that mean objects within the observal universe will eventually leave it and no longer be casually connected to Earth, meaning they'd leave Earth's gravitational field?
Yes, I believe so.

What will happen to their (teeny tiny amount of) gravitational potential energy?
It will reach zero - as intuited by the fact that such an object will no longer be tugged upon by the Earth.

#### TheQuestionGuy14

Yes, I believe so.

It will reach zero - as intuited by the fact that such an object will no longer be tugged upon by the Earth.
I see, but wouldn't it reading zero mean it lost its potential energy?

#### DaveC426913

Gold Member
I see, but wouldn't it reading zero mean it lost its potential energy?
Sure.

#### TheQuestionGuy14

Sorry for all the questions, I'm just really interested.

So, I know we're talking in terms of Relativity now, with the expansion of the universe and stuff, and in relativity implies there is no global conservation of energy. But, doesn't this loss of potential energy violate local conservation of energy? If I was on a far away planet, about to leave Earth's gravitational field, and I had an extremely accurate and hypothetical device that could measure the potential energy a particle has, wouldn't I see it lose potential energy, violating local conservation of energy?

"How does gravitational potential energy work?"

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