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### Author Topic: will a uniformly accelerating spaceship gravitational field influence another?  (Read 7149 times)

#### yor_on

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##### will a uniformly accelerating spaceship gravitational field influence another?
« on: 07/04/2012 09:15:28 »
Assume two ships accelerating uniformly beside each other, and in the same direction.
Each one will have its own local (same) 'gravity', equivalent to the acceleration.

Do those fields influence each other?

#### CliffordK

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #1 on: 07/04/2012 10:02:43 »
NO

If you are talking about gravity due to acceleration.
Say, a couple of m/s2

Then two side-by-side ships would be independent, and not affect each other.  There would be no difference between that and building one ship twice as large.

If a spaceship was tailgating another spaceship, it is possible that the exhaust from the first ship would slow down the second ship.  However, the gravity felt inside the ship would solely be dependent on the actual acceleration of the vessel.

Two rotating artificial gravity modules would also be independent in space and not affect each other.

Did you have a different hypothesis?  Why?

#### syhprum

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #2 on: 07/04/2012 11:23:22 »
Although there would be the normal gravitational attraction between the two vehicles due to their masses (very small) is it possible that psuedo gravity generated by their acceleration would also have an attractive effect ?.
If they were accelerating at 9.82 m/s/s the occupents would feel the same gravity as they would from a 6*10^24 Kg body 6400 Km away, I think this is a GR question.
« Last Edit: 07/04/2012 11:31:43 by syhprum »

#### yor_on

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #3 on: 07/04/2012 13:08:54 »
Energy is mass according to Einstein.

Is there energy expended in a acceleration?

#### CliffordK

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #4 on: 07/04/2012 17:25:28 »
The force of attraction between two bodies at rest, at the same velocity, or undergoing the same acceleration would be the same, except that the consumption of fuel would mean a decreasing mass.

The artificial gravity created by constant acceleration is due to inertial differences.  I can not imagine how it could possibly extend beyond its reference frame, the ship itself.

The acceleration is changing the weight of the occupants,  but it is not changing the mass of the occupants.

Isn't relativity based on velocity, rather than acceleration.

#### Phractality

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #5 on: 07/04/2012 17:38:19 »
If they are accelerating uniformly relative to Earth, their mass in Earth's reference frame will increase as they approach the speed of light. So both their inertia and the force of attraction between them will increase proportionately in Earth's reference frame, and the gravitational acceleration toward one another will remain constant.

Sorry about that. The gravitational force pulling the ships toward one another is proportional to the square of their mass, while the inertia is directly proportional to the mass. So the acceleration of the ships toward one another should be directly proportional to their mass. If special relativity increases the gravitational mass, as the ships approach c in Earth's reference frame, then gravity between the ships should cause them to orbit one another more rapidly in Earth's reference frame. This seems paradoxical. As the ships approach the speed of light in Earth's reference frame, the ships clocks must run slow in Earth's reference frame. But the orbital period of the ships has to be proportional to the passage of time on the ships. As clocks on the ships run more slowly, the ships should orbit one another more slowly. If gravitational mass of the ships is constant, but their inertial mass is increasing, their orbital period will slow in proportion to the time dilation.

Of course, to simplify the problem, I'm pretending they don't use up any fuel. In reality, their rest mass will decrease by the amount of fuel consumed.
« Last Edit: 08/04/2012 21:02:36 by Phractality »

#### MikeS

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #6 on: 08/04/2012 09:01:17 »
Assume two ships accelerating uniformly beside each other, and in the same direction.
Each one will have its own local (same) 'gravity', equivalent to the acceleration.

Do those fields influence each other?

Perhaps fields is the wrong word when talking about warped space-time (gravity).

(1)As I understand it there are no fields to interact (assuming the spaceships not to have sufficient mass or speed to produce noticeable space-time warp).
A spaceship accelerates primarily within spacial dimensions.  The effect is short range and only felt by something in contact with the ship.
A gravitating mass accelerates primarily within the time dimension (space-time).  This is gravity and it is long range.

(1) this is only approximately correct as all mass warps space-time.  However, a space ship is unlikely to warp space-time enough to be noticeable.  (Unless having considerable mass or travelling close to the speed of light.)

So, the answer to the question is essentially no.
« Last Edit: 08/04/2012 09:11:18 by MikeS »

#### Phractality

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #7 on: 08/04/2012 21:09:00 »
I have always assumed that relativistic mass applies to both inertia and gravity. Apparently, I was wrong. See the edited version of my previous post.

#### yor_on

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #8 on: 09/04/2012 08:16:00 »
I think we can use 'fields' for it?

The other way is to define it as creating 'geometrical warp-holes' of a sort :) as we then approach it purely geometrically, but 'fields' feels more intuitive for this. As for inertia and 'Gravity' being two sides of the same coin, they should be, shouldn't they? But to push/deflect something moving from/at its 'side' must always be easier than to try to push/deflect its motion, meeting it up front, so to speak. And if you accelerate something its inertia (resistance to motion) must grow, until it becomes infinite near lights speed, well, as I see it.

And it seems that the toughest thing is to meet it from the front, much in a similar way to how a Lorentz contraction is defined to 'work' only in the direction of its motion, and not 'sideways'.

It's not the mass that grows, as I think of it, but the inertia surely must.
Or we can use relativistic mass/energy and define it as it is this that 'grows' here.

So we have a equivalence to 'gravity' inside each ship, but you all seem to assume that this gravitational potential has to be restricted to the local 'insides' of the respective ships only?

Except you Phracticality :)
If I get you correct?

#### MikeS

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #9 on: 09/04/2012 12:00:16 »
yor_on

What I said was
"a space ship is unlikely to warp space-time enough to be noticeable.  (Unless having considerable mass or travelling close to the speed of light.)"
It's all relative.

A spaceship accelerating at 1g (through space) gains velocity.
The surface of the Earth accelerating at 1g (through time) does not gain velocity.

Gravity is a long range effect but it requires a very large mass or a small mass travelling at very high velocity (close to c) for it to become a noticeably effect.

quote
"As for inertia and 'Gravity' being two sides of the same coin, they should be, shouldn't they?"
Gravity and acceleration in a sense yes but essentially the same side of the same coin.
Inertia is in a sense a property of mass as is gravity.  So I suppose you could consider them to be opposite sides of the same coin in as much as gravity is concerned with making objects accelerate.  Inertia is concerned with objects not accelerating.

Interesting point I need to give it more thought when I have time but my initial impression is inertia and gravity are not the same thing but may well be different aspects of the same thing.
« Last Edit: 09/04/2012 12:02:39 by MikeS »

#### yor_on

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #10 on: 09/04/2012 16:27:34 »
I need to correct myself here, although I'm not sure I'm agreeing with myself now either:)

Inertia, is it a property intrinsic to matter?
If it is it can't really grow with an acceleration, can it?

Then there is only the momentum that can grow.

So what is it that 'slows' you down infinitely, as you come forever closer to lights speed in a vacuum?
Relative mass is one expression, momentum another, what more?
==

To see my point imagine it as 'forces' having 'arrows' that point towards the way they want to go. A momentum will always point in the direction of the motion of the 'force', whereas inertia will act the opposite, as I see it.
« Last Edit: 09/04/2012 16:55:25 by yor_on »

#### MikeS

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #11 on: 10/04/2012 06:23:07 »

So what is it that 'slows' you down infinitely, as you come forever closer to lights speed in a vacuum?
Relative mass is one expression, momentum another, what more?
==

What more? Time you run out of it.
Think of space time as two vectors, one for space the other for time.  The more you use of one the less you have available of the other.  As your speed approaches c so you run out of time as time approaches infinite dilation.

Another way of thinking of it.
Approaching c mass increases towards infinity.  This requires energy to approach infinity to further increase acceleration.  By the mass/energy equivalence principle mass further increases towards infinity.  Infinite mass means infinite gravity and zero passage of time.

As you approach c you literally run out of time.

#### MikeS

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #12 on: 10/04/2012 07:21:06 »
yor_on

Inertia.
A property of matter by which it continues in its existing state of rest or uniform motion in a straight line, unless that state is changed by an external force.

Any freely moving object whether it has or does not have mass follows a geodesic in space-time.  It will continue in this geodesic unless acted upon by an external force.
So, it would appear that a geodesic in space-time and inertia are essentially the same thing.  Inertia then like gravity is a property of warped space-time.  Gravity is the geodesic, inertia is why objects follow the geodesic.  The geodesic represents the path of least resistance.

What do you think?

#### yor_on

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #13 on: 10/04/2012 08:51:31 »
Sort of elegant Mike, although I need to think about it some more. A geodesic is indeed (a result of)  'gravity', and when objects following a geodesic is acted upon they find inertia. But then you have something accelerating, if acted upon that too will find a inertia, but it is not following a geodesic. The idea has a certain symmetry to me though, and SpaceTime seems very much to be about symmetries.
« Last Edit: 10/04/2012 08:53:21 by yor_on »

#### syhprum

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #14 on: 10/04/2012 09:06:01 »
I think we could simplify this Question and instead of spaceships ask do highly accelerated particles in the LHC bunch due to gravitational attraction or do coulamb forces overwhelm this effect.

#### yor_on

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #15 on: 10/04/2012 11:20:54 »
Sweet idea Syhprum :) as with very high energies there must be a complimentary 'locally' strong gravity. What energies and what rest mass would we be talking about there? From that one should be able to calculate the 'gravity' at the end points of their trajectories, colliding I mean. And also, maybe, (?) be able to see if they've diverged due to experiencing gravitational 'forces' in their paths, although considering their accelerations I suspect that effect might be negligible, as too small to be noticed by our instruments?

But accelerating something in a particle chamber there must be a strong local gravity. What will it do to a particle near light?

#### MikeS

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #16 on: 10/04/2012 11:24:27 »
Sort of elegant Mike, although I need to think about it some more. A geodesic is indeed (a result of)  'gravity', and when objects following a geodesic is acted upon they find inertia. But then you have something accelerating, if acted upon that too will find a inertia, but it is not following a geodesic. The idea has a certain symmetry to me though, and SpaceTime seems very much to be about symmetries.

Thank you.

If it's accelerating it's not following a geodesic and therefore inertia does  not apply.   ???

#### MikeS

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #17 on: 10/04/2012 11:31:56 »
I think we could simplify this Question and instead of spaceships ask do highly accelerated particles in the LHC bunch due to gravitational attraction or do coulamb forces overwhelm this effect.

I don't know but I suspect that coulomb forces would still overwhelm the effect to a large extent.

#### yor_on

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #18 on: 10/04/2012 12:42:27 »
Now that's tricky Mike :)

If we assume that inertia is a intrinsic property of matter you must be wrong. If we assume that inertia is 'the tendency of a body to maintain its state of rest or uniform motion unless acted upon by an external force' then you might formulate it that way?

So, what is it?

A intrinsic property, or a special circumstance?

#### MikeS

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #19 on: 10/04/2012 15:43:11 »
Now that's tricky Mike :)

If we assume that inertia is a intrinsic property of matter you must be wrong. If we assume that inertia is 'the tendency of a body to maintain its state of rest or uniform motion unless acted upon by an external force' then you might formulate it that way?

So, what is it?

A intrinsic property, or a special circumstance?

I never said it was.  It is an intrinsic property of space-time that affects matter.

#### yor_on

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #20 on: 10/04/2012 15:55:34 »
It all depends of course. Normally I would call inertia a property belonging to matter, but then the question is if it is there existing in a acceleration too? If it is a 'intrinsic' property it should. And then the next question will be if it is thought of as some type of unvarying property, as the modern definition of a rest mass? If it is so then momentum and 'energy' can be used to describe what properties we expect to raise in a acceleration, but not the inertia.

But if I imagine something moving and I then stop it. Is it its inertia that comes to rule in a uniform motion? But not in a acceleration? :) I would call that pretty weird if it was so?

#### yor_on

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #21 on: 10/04/2012 16:05:32 »
It can't be unvarying as you can have different 'uniform motions' as defined relative Earth for example. The inertia of a object moving faster than its twin should differ? Da* I'm not sure I understand the definition of inertia at all? As a resistance to motion I can see it, but when it comes to uniform motion versus an acceleration?

#### yor_on

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #22 on: 10/04/2012 17:39:16 »
Okay, I'm changing track here it seems :)

Didn't mean to do that, let's get back to the original question instead. We can use 'relativistic mass' or 'momentum' to define anything moving. And as relativity defines all 'motion' as questionable :) unless as defined relative something 'inertial' as being in a 'uniform motion'? Inertia hurts me head. but so do 'motion' ::))

So, are we happy with defining a accelerating ships 'gravity' to its own 'intrinsic' properties, ignoring the mass, or do we think that two accelerating ships/particles will influence each other gravitationally to a higher degree the faster they move relative Eh, Earth :)

It also have an importance for the view in which we imagine all accelerations as continuous displacements of a uniform motion, as it seems to me?

#### MikeS

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #23 on: 12/04/2012 08:02:18 »
Okay, I'm changing track here it seems :)

clip
So, are we happy with defining a accelerating ships 'gravity' to its own 'intrinsic' properties, ignoring the mass, or do we think that two accelerating ships/particles will influence each other gravitationally to a higher degree the faster they move relative Eh, Earth :)

It also have an importance for the view in which we imagine all accelerations as continuous displacements of a uniform motion, as it seems to me?

It seems to me that if the ships are traveling close enough to c then they would exhibit sufficient mass to warp space-time 'noticeably' enough to influence each other.  Although their mass would always warp space-time, the effect would not become noticeable until their speed approached c.

Think of the two ships travelling parallel to each other.  Imagine a line (world line) through the center of each ship in line with it's direction of travel.  At low speed the world lines lines intercept a long way into the future of the ships.  Approaching c the world lines intercept close to the ships.  The ships world lines intercept due to their mass warping space-time.

#### MikeS

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #24 on: 12/04/2012 08:59:13 »
yor_on

When you talk about the inertia of an accelerating body is that a meaningful idea?  The accelerating body must have inertia but surely, it cannot be apparent under acceleration.  Acceleration must mask the effect of inertia?

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##### Re: will a uniformly accelerating spaceship gravitational field influence another?
« Reply #24 on: 12/04/2012 08:59:13 »