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Author Topic: Velocity dependant gravitational acceleration  (Read 1609 times)

Offline Pmb

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Velocity dependant gravitational acceleration
« on: 07/02/2013 11:03:03 »
I was wondering if you good folks were aware that the gravitational acceleration of a body in free-fall, while being independant of the bodies chemical composition is a function of the bodies velocity, i.e. a - a(v)?

There's a new version of Exploring Black Holes comming out and I'm trying to convince the authors to put this fact into the text. I was wondering if you agree that this fact should be in the text? If so then how should it be presented? If this fact cannot be derived using the techniques introduced in the text should it be left out?


 

Offline imatfaal

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Re: Velocity dependant gravitational acceleration
« Reply #1 on: 07/02/2013 15:01:37 »
well if you could explain it to us I am sure you could explain it to the readers of that great text book.  give it a shot
 

Offline Bored chemist

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Re: Velocity dependant gravitational acceleration
« Reply #2 on: 07/02/2013 16:59:31 »
"I was wondering if you good folks were aware that the gravitational acceleration of a body in free-fall, while being independant of the bodies chemical composition is a function of the bodies velocity, i.e. a - a(v)?"
I wonder if the people who launch satellites are aware of that.
How big an effect are you saying velocity has?
 

Offline Pmb

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Re: Velocity dependant gravitational acceleration
« Reply #3 on: 07/02/2013 22:26:33 »
Quote from: imatfaal
well if you could explain it to us I am sure you could explain it to the readers of that great text book.  give it a shot
The question is whether you think itíd be good to have it in the text or not?

Quote from: Bored chemist
I wonder if the people who launch satellites are aware of that.
How big an effect are you saying velocity has?
The effect is too small to be worrisome to them.

Iíll create a web page to put the derivation in. Itís very involved/messy and as yet Iíve only done it the simple way in my head. In fact I didnít know I could do it this easily until after I posted that question this morning.

Basically you solve the metric for dr/dt and take the derivative with respect to t and it will be a function of r and dr/dt
 

Offline JP

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Re: Velocity dependant gravitational acceleration
« Reply #4 on: 07/02/2013 23:14:51 »
Is there any intuition for this?  I know if you were trying to accelerate a craft from rest using a rocket, you get diminishing returns at higher speeds (with respect to dv/dt WRT the rest frame) due to approaching the speed of light.  Is it at all similar to that?
 

Offline Pmb

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Re: Velocity dependant gravitational acceleration
« Reply #5 on: 08/02/2013 21:18:43 »
Quote from: JP
Is there any intuition for this?
That depends on your intuition.  A person who has studied special relativity knows that accleration is velocity dependant. I.e. let a' and v' be the acceleration and
velocity of a particle in S' and let a and v be the acceleration and
velocity of a particle in S. Then a is a function of both a' and v'. In GR there is a bit of a difference in that the gravitational acceleration (which is an inertial acceleration) is a function of v.

Quote from: JP
I know if you were trying to accelerate a craft from rest using a rocket, you get diminishing returns at higher speeds (with respect to dv/dt WRT the rest frame) due to approaching the speed of light.  Is it at all similar to that?
No.

Something occured to me after I started this thread. The vlue of the 3-velocity can have different values. If we use the coordinate value r where r is the r in the Schwarzschild metric then we'll get a different value that one would get if we used the distance traveled. So it's much easier to show that dr2r/dt2 is a function of dr/dt. I'll try to work it out in terms of the physical displacement dL (aka "shell" distance) rather than dr which is a coordinate displacement. One also has to distinguish which time one uses. In the first version of the text the authors used local time (or "shell" time).

The text asks the reader to derive an expression for the gravitational acceleration using an initial "shell" velocity, i.e. dr_shell/dt_shell, of zero. This problem is the same with only one fact changed, i.e. the initial "shell" velocity is not zero.
« Last Edit: 09/02/2013 01:00:47 by Pmb »
 

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Re: Velocity dependant gravitational acceleration
« Reply #5 on: 08/02/2013 21:18:43 »

 

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