# A maximum speed in Newtonian Physics

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Say we have 2  bodies ,mass=M composed of a set of smaller bodies ,mass=m set in a vacuum, what might be the maximum speed of separation  from the respective centres of gravity.?

Is it possible to say whether  this speed would approach a limit given the effect of gravity or would this depend on the value of M ,m and ,I suppose n (the number of smaller bodies)?

Or ,in Newtonian physics does it follow that the maximum speed of separation is without limits (infinite)?

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Newtonian mechanics has no constraints on speed.

In your example however, and depending on how the accelerating force is applied, there is a maximum acceleration that can be sustained, without the larger body, M, losing gravitational cohesion.

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2 hours ago, MigL said:

Newtonian mechanics has no constraints on speed.

In your example however, and depending on how the accelerating force is applied, there is a maximum acceleration that can be sustained, without the larger body, M, losing gravitational cohesion.

Are there other scenarios in Newtonian physics where a separation velocity  is calculated to be able to increase without a limit?

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22 minutes ago, Halc said:

I cannot parse what you have in mind with the M and the little m's. A rock is composed of a bunch of molecules, which is a set of smaller masses making up a larger mass. That fact seems totally irrelevant to the limit the separation velocity of a pair of rocks.

GR limits separation speed locally to c, but non-locally, this is not the case. Hence there are distant galaxies increasing their proper distance from us at a rate of greater than c. No object can have a peculiar velocity greater than c.  Peculiar velocity is local in a sense: it is its velocity relative to the center of mass of all matter within some radius (typically the size of the visible universe, or possibly the Hubble radius) centered at the location of the object.

It is academic/historical  but I am limiting the question to how it would appear to a pre Einstein physicist (so Newtonian).

I think they assumed the world was composed of bodies composed of smaller components with mass.

That is why I set it up as two bodies trying to engineer a separation velocity among any pair of the component bodies.

I know this is wrong and outdated  ,but I am trying to get into the head of a Newtonian physicist  and understand whether they would have concurred there was a maximum speed of massive particles  or whether they would have said  there was no limit to how great this separation velocity  (from a standing start) could be.

Edited by geordief

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3 hours ago, geordief said:

Are there other scenarios in Newtonian physics where a separation velocity  is calculated to be able to increase without a limit?

No.
As far as I know, in Newtonian mechanics, if you are moving down the road at v, and you throw a ball forward at v, the ball will be measured to be moving at 2v with respect to the road.
The deviation starts to be non-trivial as v approaches relativistic speeds.
In Newtonian mechanics v + v = 2v even if v=c , while SR tells us that is an impossibility.

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1 minute ago, MigL said:

No.
As far as I know, in Newtonian mechanics, if you are moving down the road at v, and you throw a ball forward at v, the ball will be measured to be moving at 2v with respect to the road.
The deviation starts to be non-trivial as v approaches relativistic speeds.
In Newtonian mechanics v + v = 2v even if v=c , while SR tells us that is an impossibility.

I see ; not infinite but greater than c?

What about if there were an infinite number of "v" s that were added ?

Any scenario that would allow for that?

Would that imply a theoretical infinite speed in Newtonian physics? (I don't think Newton was aware of the relativistic addition of velocities even if that was known before Einstein....)

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Not following you.

Newtonian mechanics adds speeds linearly and there is no asymptotic limit at c, like there is in SR.
You could add speeds as high as you want, without limit.
But to reach infinite ( Newtonian limit ) speeds you'd still need infinite energy.

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32 minutes ago, MigL said:

Not following you.

Newtonian mechanics adds speeds linearly and there is no asymptotic limit at c, like there is in SR.
You could add speeds as high as you want, without limit.
But to reach infinite ( Newtonian limit ) speeds you'd still need infinite energy.

OK ,thanks.

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On 9/20/2020 at 11:20 AM, geordief said:

Are there other scenarios in Newtonian physics where a separation velocity  is calculated to be able to increase without a limit?

Increasing velocity, acceleration, requires a force- F= ma.  How is force being applied in your scenario?

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14 minutes ago, HallsofIvy said:

Increasing velocity, acceleration, requires a force- F= ma.  How is force being applied in your scenario?

If I was trying to arrange such a scenario  I have the intuition that any such force would approach a limit in practical terms.

Actually ,in the initial inflationary epoch ,I wonder if  there were objects separating from each other and if there was a velocity attached to those separations?

Did the term "speed"  even apply to those conditions?

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1 hour ago, geordief said:

If I was trying to arrange such a scenario  I have the intuition that any such force would approach a limit in practical terms.

Actually ,in the initial inflationary epoch ,I wonder if  there were objects separating from each other and if there was a velocity attached to those separations?

Did the term "speed"  even apply to those conditions?

Anything having to do with GR is decidedly non-Newtonian. You can’t mix them together.

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1 minute ago, swansont said:

Anything having to do with GR is decidedly non-Newtonian. You can’t mix them together.

I didn't know that the inflationary epoch  was covered by GR. It is ,then?

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1 minute ago, geordief said:

I didn't know that the inflationary epoch  was covered by GR. It is ,then?

Expansion is GR. That’s not going to stop being the case for inflation, which is still expansion. It’s not going to revert to being Newtonian, that’s for sure.

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1 minute ago, swansont said:

Expansion is GR. That’s not going to stop being the case for inflation, which is still expansion. It’s not going to revert to being Newtonian, that’s for sure.

So ,even the maximum separation speed **during inflation  would be comparable to that obtaining now ,just many times higher?(so many ,many multiples of c) but the actual  maximum speed  then would likewise be the same as now ....ie c?

*I think that is the term (or the term I am looking for) where  on account of expansion objects recede (and become invisible) at speeds greater than c

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9 minutes ago, geordief said:

So ,even the maximum separation speed **during inflation  would be comparable to that obtaining now ,just many times higher?(so many ,many multiples of c) but the actual  maximum speed  then would likewise be the same as now ....ie c?

*I think that is the term (or the term I am looking for) where  on account of expansion objects recede (and become invisible) at speeds greater than c

We know that recession velocities can exceed c, which is not a problem because one is not referring to a single frame of reference. Locally, i.e. in flat spacetime, the speed limit is c

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