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Author Topic: will a uniformly accelerating spaceship gravitational field influence another?  (Read 7158 times)

Offline MikeS

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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?

It has uniform motion and hence inertia until you cause it to accelerate (stop) and it has uniform motion (zero) after you stop it, so it still has inertia.   But I don't see how you can define inertia for an accelerating body?   However we use acceleration to measure the objects inertia.
« Last Edit: 12/04/2012 09:14:22 by MikeS »
 

Offline Pmb

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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.
Why do you assume that "local" means "is the same as"?
 

Offline yor_on

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I'm proposing that we have two identical objects accelerating with the same amount, as from some defined 'inertial frame of reference', as ? Well, I use Earth here, but we can use whatever you want to define as 'inertial' Pete. And I'm also assuming that the gravitational potential outside those objects is as similar as it can be.

Then, from the aspect of that 'inertial frame of reference' (Earth) their accelerations should be equivalent as I assume, and we can also assume that they find themselves being 'still' relative each other (possibly, depending on how you think of a acceleration, as displacements of/from a uniform motion to another, or not?:)

Maybe there are some things missing in this description, but for a starter it will do :)
 

Offline yor_on

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Mike, we better ignore inertia for this.

I think we can use momentum instead? Inertia is a description similar to rest mass in that it is a invariant local property of a object, expected to be the same everywhere, according to a main stream definition. You might say that the 'inertia' only is definable from a 'uniform motion' in relativity.  Although I thought of it differently :)

But using momentum does describe it as I think of it.
==

To see my point consider if different uniform motions will give you a different 'inertia'? When it comes to a local acceleration it won't as I see it. But if you're trying to stop two objects in a uniform motion, that you define as having different speeds relative you. Will the 'force' you apply be the same for making them 'unmoving' relative you?

But I keep losing the track here :)
So momentum will do for this I think?
« Last Edit: 17/04/2012 13:31:26 by yor_on »
 

Offline Pmb

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Mike, we better ignore inertia for this.

I think we can use momentum instead? Inertia is a description similar to rest mass in that it is a invariant local property of a object, expected to be the same everywhere, according to a main stream definition. You might say that the 'inertia' only is definable from a 'uniform motion' in relativity.  Although I thought of it differently :)

But using momentum does describe it as I think of it.
==

To see my point consider if different uniform motions will give you a different 'inertia'? When it comes to a local acceleration it won't as I see it. But if you're trying to stop two objects in a uniform motion, that you define as having different speeds relative you. Will the 'force' you apply be the same for making them 'unmoving' relative you?

But I keep losing the track here :)
So momentum will do for this I think?
Inertial mass M is defined as M = p/v
« Last Edit: 17/04/2012 19:35:16 by Pmb »
 

Offline yor_on

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So you know what inertia is then Pete :)
I've actually seen different definitions for it, as it been bothering me for a while.

Here's one good.

" Mass has two meanings, both of which can be viewed as proportionality
factors. "Inertial mass" is the factor that determines how much force
it takes to produce a given acceleration in an object, according to
Newton's first law of motion:

  F = ma

"Gravitational mass" is the factor that determines how much
gravitational force is developed between two objects at a given
distance, according to Newton's law of gravity:

  F = -GMm/r^2

where G is the gravitational constant, r is the distance between the
objects, and M and m are the masses of the two objects.

Inertial mass and gravitational mass are the same. (This is still the
subject of experiments seeking to verify it more and more precisely,
because it is intimately connected with Einstein's general theory of
relativity.) Because of this, the two equations above combine into

 a = GM/r^2

On the surface of the earth, M (the mass of the earth) and r (the
radius of the earth) are fixed, and so a (the acceleration due to
gravity) is a constant, which we call g."

From Doctor Rick, mathforum.org

So according to this inertia is equivalent to (rest) mass, as I read it?

If I use that definition then what we have in different uniform motions as I try to stop a object moving relative me is not its inertia, as that will differ relative the perceived 'speed'. Against it we have the fact that no matter your uniform motion (in space) you should expend the same amount of energy in a acceleration, or 'displacement' if you like, to start to move relative whatever frame you earlier found yourself being still relative.

Well, as I think of it.

In relativity "All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not accelerating in the sense that an accelerometer at rest in one would detect zero acceleration. Measurements in one inertial frame can be converted to measurements in another by a simple transformation (the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity).

In general relativity, in any region small enough for the curvature of spacetime to be negligible one can find a set of inertial frames that approximately describe that region."

This contains several ideas that makes sense, but inertia boggles me mind :)

And then you have its mass, which governs its resistance to the action of a force, and its moment of inertia about a specified axis, which measures its resistance to the action of a torque about the same axis. with accompanying math from PF :) as well as the definition of 'Moment of Inertia' in engineering.

And your definition too. All of them seems sort of valid to me? But then again, none of them touches uniform motion and what I should call that 'resistance' to 'stopping' as I apply a 'force' to make that object stand still relative me. As I see all uniform motion to be the same, as can be proved by accelerating something from a 'inertial frame' where its 'relative motion', meaning that 'inertial frames' uniform motion through space, doesn't matter.
=

Sorry, had to add some text above to make the citation more understandable. As well as a link to that very nice and concise first citation.
« Last Edit: 18/04/2012 11:28:56 by yor_on »
 

Offline Pmb

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So you know what inertia is then Pete :)
If someone uses the term inertial mass as a synonym for rest mass then I disagree with them, for many reasons.

There are three terms which contain the term mass in them. They are (roughly):

1) inertial mass: m = m_i - determines how much momentum a body has. This is how Newton defined momentum in fact

2) active gravitational mass: m = m_a - the source of gravity

3) passive gravitational mass: m = m_p - What gravity acts on. Same as inertial mass.

It should be noted inertial mass density does not have the same value as active gravitational mass density.
« Last Edit: 18/04/2012 15:32:05 by Pmb »
 

Offline yor_on

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Ahh, I knew I didn't want to discuss this one :)
Yeah, I used inertial mass as you use relativistic mass, in my first way of thinking of it.

But inertia, as in a resistance to motion, must be directly coupled to the rest mass it consists of. And if it is so, and it not is so that this 'inertia' can be considered to grow in a acceleration, then it will be a function of the objects rest mass.

And that we can test by imagining different uniform motions of equivalent objects (in a equivalent portion of 'space'), relative some inertial frame, and then try to move that object, in its own frame, by mounting a equivalent rocket to it to see what 'force' is needed for it to begin to accelerate.

If the force locally are the same in all uniform motions, as defined differently from our 'inertial observer', then the inertia must belong to the rest mass, as I think of it :)

But then again..
Inertia is weird.
 ==

The point is that the inertial frame 'stopping them' will in deed need a different force, but locally, as defined by the force needed to locally accelerate this object, all uniform motions should be the same. And that defines the inertia as a local expression of rest mass to me, if I'm thinking right here :)

==

Hmm I'm not sure at all of that definition rereading it? As you accelerate you will find that you need more energy to accelerate, the closer you comes to lights speed in a vacuum, and as all accelerations can be described as 'displacements' from uniform motions?

Thinking that way we might use this instead.

Inertia must then be directly connected to your 'relative motion', which becomes truly weird in that inertia to know it will need a 'gold standard' of what 'relative motion' is? But it will be a fit to how I thought of it first, as responding to your (relative) motion by expressing a higher 'resistance'

You might assume it a geometrical expression relative the SpaceTime around you possibly?
I find Inertia quite frustrating.
==

Let us put it like this. You define two uniform frames of motion, two equivalent earths :)
One of them moving double the speed of the other according to you measuring.

On each one you have a 'frictionless' table.
On each table you have one kg of invariant restmass, equivalent to each other.

Will you need more force to move the kg on the planet that you have defined to move 'faster', relative the other?
Or won't it matter? :)

Then we have the planets themselves, if we now mount a really big rocket to each one.
Will the force needed for a first displacement differ between them, assuming the two scenarios equivalent in all other aspects, except the speed, as measured from some 'inertial frame of reference'?
« Last Edit: 22/04/2012 20:56:50 by yor_on »
 

Offline yor_on

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You know Pete, you are using classical mechanic's here, right?

"In the theory of relativity, the quantity invariant mass, which in concept is close to the classical idea of mass, does not vary between single observers in different reference frames.

In classical mechanics, there are three types of mass or properties called mass: Inertial mass; passive gravitational mass; and active gravitational mass. Although inertial mass, passive gravitational mass and active gravitational mass are conceptually distinct, no experiment has ever unambiguously demonstrated any difference between them."

The invariant mass is what I use thinking of inertia, assuming it to be the same in all frames of reference. Then I assume that this mass also will be what defines inertia as well as the local 'gravity' described by it.  All of those concepts should then, to me, be the same as in 'coupled' to each other. Invariant restmass, Inertia, gravity, invariant descriptions. But I'm not sure I understand Inertia at all. From a 'SpaceTime perspective' a inertial motion describes a straight path as I think of it, all uniform motions being geodesics.

Those geodesics are the absolute same as I see it, all relative motion becoming arbitrarily definitions, relative a observer. But then we have 'energy' and that 'stress' that motion places on SpaceTime. We also has a constant called 'c' that defines a limit of 'relative motion' so looked at from that perspective SpaceTime must have a way to define 'relative motion', especially if one expect different 'speeds' relative oneself to represent different inertia. It also has to do with frames of reference in that you may define motion as arbitrary relative any other single object, but what about defining it from all of SpaceTime?

For example, momentum of some inertial (uniformly moving) object. Is that a (invariant, well sort of, assuming a constant uniform motion) property of that object or is it a property between 'frames of reference'?
=

To see my point here you need to reread what I wrote. The easy answer is that it is a property belonging to the object itself, depending on its 'motion', but the other answer will be that it can only exist as a property between frames of reference. And as there is no way for you to measure the momentum without using a reference frame, as relative some arbitrarily defined 'speed'' I wonder about a lot of things :)
« Last Edit: 22/04/2012 23:04:37 by yor_on »
 

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