<blockquote>
  <p>What is the maximum speed that can be achieved because of acceleration due to gravity?</p>
</blockquote>

<p>The speed of light. But there's a catch.  </p>

<blockquote>
  <p>In other words which is the strongest and largest gravitational field discovered in the universe till date. </p>
</blockquote>

<p>That of a black hole. <a href="https://en.wikipedia.org/wiki/Sagittarius_A*" rel="nofollow noreferrer">Sagittarius A*</a> is thought to be the location of a supermassive black hole. </p>

<blockquote>
  <p>What is the maximum speed an object accelerating in these fields can gain?</p>
</blockquote>

<p>The speed of light. See <a href="https://en.wikipedia.org/wiki/Escape_velocity#List_of_escape_velocities" rel="nofollow noreferrer">this list</a>. 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 <a href="http://einsteinpapers.press.princeton.edu/" rel="nofollow noreferrer">Einstein</a>: </p>

<p><img src="https://i.sstatic.net/8KXbI.jpg" alt="enter image description here"></p>

<p>See the second paragraph. The body falls down <em>because</em> 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 <em>can</em> fall is at the speed of light at that location. Which is circa half the speed of light at our location.   </p>

CC BY-SA 3.0
2016-01-18T20:07:24.797Z
2016-01-18T20:07:24.797Z
John Duffield
<p>It all depends on your frame of reference, but the biggest speeds caused by gravity will involve black holes or perhaps neutron stars.</p>

<p>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 <em>appear</em> to slow down and tend towards being stationary at the event horizon.</p>

<p>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.</p>

CC BY-SA 3.0
2016-01-18T12:17:30.483Z
will we experience a similar slowing of a falling object if it were to fall till the earth's magnetic core.
Anupam Rekha
CC BY-SA 3.0
2016-01-18T16:16:05.433Z
@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.
Andy
CC BY-SA 3.0
2016-01-18T17:10:07.567Z
wondered if this is experimentally observed..as it is perhaps not as hard to verify.
Anupam Rekha
CC BY-SA 3.0
2016-01-18T22:12:16.707Z
@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.
James K
CC BY-SA 3.0
2016-01-19T05:56:53.433Z
thanks for your reply. I meant falling object to the earth's magnetic core is it experimentally observed.
Anupam Rekha
CC BY-SA 3.0
2016-01-19T20:59:25.230Z
If a body was released from a location that was some multiple of the Schwarzschild radius from the event horizon, all observers will agree that the body is falling into the black hole. If that body had some initial velocity towards the black hole, all observers will agree that its speed increases as it falls in. All observers agree that falling bodies fall _faster_. Not slower.
John Duffield
CC BY-SA 3.0
2016-01-18T09:46:34.683Z
2016-01-18T09:46:34.683Z
ProfRob
<p>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. </p>

<p>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?</p>

CC BY-SA 3.0
2016-01-18T06:49:09.143Z
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.
Anupam Rekha
CC BY-SA 3.0
2016-01-18T16:33:04.900Z
@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.
ProfRob
CC BY-SA 3.0
2016-01-18T19:57:23.103Z
@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.
ProfRob
CC BY-SA 3.0
2016-01-18T21:51:06.510Z
@RobJeffries Wouldn't Gullstrand-Painleve chart suffice? At an instant of infallee time, spatial geometry is Euclidean, so there shouldn't be a mismatch between lengths of freefalling ideal physical rods and coordinate differences.
Stan Liou
CC BY-SA 3.0
2016-01-18T23:11:40.723Z
@StanLiou Perhaps you could add that; I'd be interested. $dr/d\tau$ appears to exceed $c$  for a free-falling frame when $r <r_s$.
ProfRob
<gravity><speed>
What is the Maximum Speed that can be acheived Because of Acceleration Due to Gravity?
Anupam Rekha
# What is the Maximum Speed that can be acheived Because of Acceleration Due to Gravity?

(Asked by: username_0 on 2016-01-18)

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?

**Tags:** gravity, speed
> **Comments:**
> **username_0**: 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.  
> **username_1**: @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.  
> **username_1**: @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.  
> **username_2**: @RobJeffries Wouldn't Gullstrand-Painleve chart suffice? At an instant of infallee time, spatial geometry is Euclidean, so there shouldn't be a mismatch between lengths of freefalling ideal physical rods and coordinate differences.  
> **username_1**: @StanLiou Perhaps you could add that; I'd be interested. $dr/d\tau$ appears to exceed $c$  for a free-falling frame when $r <r_s$.  

---

## 2 answers

### Answer by username_3 on 2016-01-18. Score: 1 | Accepted answer

> 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\*](https://en.wikipedia.org/wiki/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](https://en.wikipedia.org/wiki/Escape_velocity#List_of_escape_velocities). 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](http://einsteinpapers.press.princeton.edu/):

![enter image description here](https://i.sstatic.net/8KXbI.jpg)

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.


---

### Answer by username_1 on 2016-01-18. Score: 7

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.

> **Comments:**
> **username_0**: will we experience a similar slowing of a falling object if it were to fall till the earth's magnetic core.  
> **username_4**: @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.  
> **username_0**: wondered if this is experimentally observed..as it is perhaps not as hard to verify.  
> **username_5**: @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.  
> **username_0**: thanks for your reply. I meant falling object to the earth's magnetic core is it experimentally observed.  
> **username_3**: If a body was released from a location that was some multiple of the Schwarzschild radius from the event horizon, all observers will agree that the body is falling into the black hole. If that body had some initial velocity towards the black hole, all observers will agree that its speed increases as it falls in. All observers agree that falling bodies fall _faster_. Not slower.  

---

