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Planets and other bodies in the universe have different ranges of gravitational fields. What is the maximum speed that can be achieved because of acceleration due to gravitational field.

In other words which is the strongest and largest gravitational field discovered in the universe till date. What is the maximum speed An object accelerating in these fields can gain?

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    $\begingroup$ This is just a guess, but a black hole could accelerate objects arbitrarily close to light speed (with respect to most other objects in our universe) as they approached the event horizon. $\endgroup$ – barrycarter Jan 18 '16 at 6:34
  • $\begingroup$ Suppose it accelerates over a great distance and achieves speed near to that of speed of light, Is it possible that it will further accelerate? Is it possible it will continue at that speed without accelerating or convert to energy rather. $\endgroup$ – Anupam Rekha Jan 18 '16 at 6:49
  • $\begingroup$ @barrycarter Your guess is wrong, except from the very specific point of view of an observer "hovering" above the event horizon. An observer from afar sees the speed increase and then asymptotically decrease to zero as the object approaches the event horizon. $\endgroup$ – Rob Jeffries Jan 18 '16 at 16:33
  • $\begingroup$ What about the view from the object itself? How would the object see the rest of the universe? $\endgroup$ – barrycarter Jan 18 '16 at 16:36
  • $\begingroup$ @barrycarter I had started to add that frame of reference, but it isn't straightforward. Whilst proper time is easy enough to define, a proper radial coordinate is not. $\endgroup$ – Rob Jeffries Jan 18 '16 at 19:57
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What is the maximum speed that can be achieved because of acceleration due to gravity?

The speed of light. But there's a catch.

In other words which is the strongest and largest gravitational field discovered in the universe till date.

That of a black hole. Sagittarius A* is thought to be the location of a supermassive black hole.

What is the maximum speed an object accelerating in these fields can gain?

The speed of light. See this list. The escape velocity for a black hole is the speed of light, and you can flip this around. If you drop an object from a great height, it's travelling at escape velocity when it reaches the gravitating body. But like I said, there's a catch. Take a look at this by Einstein:

enter image description here

See the second paragraph. The body falls down because the speed of light is spatially variable. If this continued unabated there would come a point where the body is falling faster than the speed of light at that location. But since matter can't faster than this the "coordinate" speed of light, the maximum speed it can fall is at the speed of light at that location. Which is circa half the speed of light at our location.

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It all depends on your frame of reference, but the biggest speeds caused by gravity will involve black holes or perhaps neutron stars.

From the point of view of a far external observer, an infalling object (from infinity) reaches a maximum inward speed of $0.385c$ (where $c$ is the speed of light) towards the black hole at 3 times the Schwarzschild radius. Thereafter, the object will appear to slow down and tend towards being stationary at the event horizon.

From the point of view of a "shell observer", that is somehow held stationary in the gravitational field of the black hole, the infalling object would have a speed that tended towards $c$ as the shell observer tended towards the event horizon at the Schwarzschild radius. It is meaningless to try to extend this inside the event horizon since (stationary) shell observers cannot exist inside the event horizon.

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  • $\begingroup$ will we experience a similar slowing of a falling object if it were to fall till the earth's magnetic core. $\endgroup$ – Anupam Rekha Jan 18 '16 at 12:17
  • $\begingroup$ @AnupamRekha - near the centre of the Earth there would be little or no gravity, because you would be surrounded on all sides by rock. (Think about it.) So falling down to the centre of the earth would add more velocity, but not an unlimited amount. $\endgroup$ – Andy Jan 18 '16 at 16:16
  • $\begingroup$ wondered if this is experimentally observed..as it is perhaps not as hard to verify. $\endgroup$ – Anupam Rekha Jan 18 '16 at 17:10
  • $\begingroup$ @AnupamRekha No black holes have been directly observed, so this is a theoretical calculation, but one built on a well understood and tested theory: General Relativity. $\endgroup$ – James K Jan 18 '16 at 22:12
  • $\begingroup$ thanks for your reply. I meant falling object to the earth's magnetic core is it experimentally observed. $\endgroup$ – Anupam Rekha Jan 19 '16 at 5:56

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