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Thread: Newtonian Gravity And Massive Objects

  1. #1 Newtonian Gravity And Massive Objects 
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    I'm doing some casual research on gravity this weekend, and I came across some figures for the acceleration due to gravity near a neutron star, generally between a few trillion m/s<sup>2</sup> and thirty trillion m/s<sup>2</sup>. I assume these figures will be at the surface radius of the neutron star, but the most glaring issue I'm having is, wouldn't such an acceleration quickly push an object's velocity many thousands of times past c?

    I'm not factoring in any relativistic properties here because I'm not intimately familiar with them, but I'll start with what I know. The mass of the object would increase by its Lorentz Factor as its velocity approaches c, but the acceleration due to gravity on an object is constant and irrelevant of its mass (correct me if I'm mistaken here, I'm basing this on Newtonian logic, the whole baseball vs. bowling ball in free-fall bit).

    So what prevents hugely-massive objects from sling-shotting other mass into warp speeds?


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  3. #2 Re: Newtonian Gravity And Massive Objects 
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    Quote Originally Posted by Frenchi
    I'm doing some casual research on gravity this weekend, and I came across some figures for the acceleration due to gravity near a neutron star, generally between a few trillion m/s<sup>2</sup> and thirty trillion m/s<sup>2</sup>. I assume these figures will be at the surface radius of the neutron star, but the most glaring issue I'm having is, wouldn't such an acceleration quickly push an object's velocity many thousands of times past c?
    If the mass is so high that it could accelerate a falling object to above C, then it's a black hole.


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  4. #3 Re: Newtonian Gravity And Massive Objects 
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    Quote Originally Posted by Scifor Refugee
    If the mass is so high that it could accelerate a falling object to above C, then it's a black hole.
    That's where I'm getting hung up. That's an enormous acceleration, but multiple websites list it in the trillions of m/s<sup>2</sup>. Just to clarify, does this mean that there isn't really anything stopping gravity from super-accelerating objects past c? Obviously though there's the side effect of never escaping the gravity well.
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  5. #4 Re: Newtonian Gravity And Massive Objects 
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    Quote Originally Posted by Frenchi
    That's where I'm getting hung up. That's an enormous acceleration, but multiple websites list it in the trillions of m/s<sup>2</sup>. Just to clarify, does this mean that there isn't really anything stopping gravity from super-accelerating objects past c? Obviously though there's the side effect of never escaping the gravity well.
    But how long would an object experience that acceleration? A neutron star might have a mass of 4E30 kg and a radius of 10 km. That would give it a surface acceleration due to gravity of about 2.7 trillion m/sec, according to Newton. But an object falling toward its surface from far away would only be able to accelerate up to about 2.3E8 m/sec before it struck the surface and stopped - so you can't quite go faster than light due to falling toward the neutron star.
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  6. #5 Re: Newtonian Gravity And Massive Objects 
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    Quote Originally Posted by Scifor Refugee
    But how long would an object experience that acceleration? A neutron star might have a mass of 4E30 kg and a radius of 10 km. That would give it a surface acceleration due to gravity of about 2.7 trillion m/sec, according to Newton. But an object falling toward its surface from far away would only be able to accelerate up to about 2.3E8 m/sec before it struck the surface and stopped - so you can't quite go faster than light due to falling toward the neutron star.
    What if the object was already traveling at a significant percentage of c? Could a neutron star's gravity "complete" an objects approach to c?
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  7. #6 Re: Newtonian Gravity And Massive Objects 
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    Quote Originally Posted by Frenchi
    What if the object was already traveling at a significant percentage of c? Could a neutron star's gravity "complete" an objects approach to c?
    Well, Newtonian physics allows an object to accelerate to just below C and then get the final "nudge" over C from the gravity of an object. But according to relativity, the velocity could never reach C; the massive object would still cause some acceleration, but not enough to make the object hit the speed of light. The main difference between a neutron star and a black hole in this situation is that with a very powerful rocket you could still blast off from the surface of a neutron star and escape.
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  8. #7 Re: Newtonian Gravity And Massive Objects 
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    Quote Originally Posted by Scifor Refugee
    But according to relativity, the velocity could never reach C; the massive object would still cause some acceleration, but not enough to make the object hit the speed of light.
    Could you elaborate on this? I figured there must be something of the sort (a property of gravity in relativity that would prevent accelerating an object past c), I just had no idea what it might be.
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    The main concern here is the velocity addition formula.

    Anyway, colinear non-relativistic velocities add like this:


    That is, throw a ball forward at 10 m/s from a car moving at 20 m/s and it's going 30 m/s.

    Colinear relativistic velocities add like this:


    That is, throw a ball forward at 200,000,000 m/s from a car moving at 200,000,000 m/s and the final speed isn't 400,000,000 m/s, it's about 276,805,111 m/s. (You'll notice that for very small values, this is almost the same as the first equation.)

    So an object falling towards a neutron star at 1,000,000,000 m/s/s adds about another 1,000,000 m/s to it's velocity every 1/1000 second, but it does so by the second formula, which will never give a final speed over (or even equal to) 1c.
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  10. #9  
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    Quote Originally Posted by MagiMaster
    The main concern here is the velocity addition formula.
    Ah, fantastic. Thanks Magi and Scifor for your insight =)
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