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russ_watters

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That's one long and incoherent sentence but maybe this helps: an object can never reach the speed of light but as long as you keep applying a force it will keep accelerating. There is no terminal velocity like you are describing.

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and how could it not reach a terminal velocity.

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our terminal velocity is the speed of light

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DaveC426913

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OK, let's clear a few things up:

1] Acceleration due to gravity and acceleration due to propulsion are synonymous. Whether you accelerate by using your engines or you accelerate by falling in to a black hole has no effect on how close to the speed of light you can get. All I'm trying to say here is: the BH does not add a complication to accelerating to c.

2] Velocities do not add linearly at relativistic speeds. If you are travelling at .9c and you (either turn on your engines or fall into a BH), you will not "hit" 1.0c. What happens is your velocity goes**from .9c to .99c**. If you continue to accelerate, your velocity will reach .999c. You can accelerate until you grow old, and your velocity will reach .999999999c.

The formula is [tex]v = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex]

So, c is not a terminal; it is an**asymptote**.

1] Acceleration due to gravity and acceleration due to propulsion are synonymous. Whether you accelerate by using your engines or you accelerate by falling in to a black hole has no effect on how close to the speed of light you can get. All I'm trying to say here is: the BH does not add a complication to accelerating to c.

2] Velocities do not add linearly at relativistic speeds. If you are travelling at .9c and you (either turn on your engines or fall into a BH), you will not "hit" 1.0c. What happens is your velocity goes

The formula is [tex]v = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex]

So, c is not a terminal; it is an

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LURCH

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Suppose you are travelling atr very nearly the speed of light; only 2kph slower. You can apply an acceleration force, and cover 1/2 the difference. Now, you are just 1kph slower than

and how could it not reach a terminal velocity.

you continue to accelerate, but never reach

Or, y'know... what Dave said.

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Bob S

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Suppose you are travelling atr very nearly the speed of light; only 2kph slower. You can apply an acceleration force, and cover 1/2 the difference. Now, you are just 1kph slower thanc. Apply more acceleration, and oyu make up half the difference again; you are now travellingc[/ki]-.5kph. You can keep accelerating throughc-1/4, 1/8,etc...

you continue to accelerate, but never reachc. And so, no lightspeed and no terminal velocity.

Forgive me if I'm misunderstanding, but I'm not sure this is quite right. The above is a statement of Zeno's paradox. It's the classic paradox involving a man standing near a wall. To reach the wall he must first cross half the distance, and then half that distance, ad infinitum. Thus he can never reach the wall. The fallacy can only be exposed by the mathematical notion of functional continuity; motion is continuous, and shouldn't be discretized as the paradox describes.

Here we're dealing with velocities, but the idea is the same. Velocity is continuous, so discretized increases in speed isn't the reason we can't reach light speed. The reason is because the relativistic energy is proportional to the gamma factor, and as speed increases, the gamma factor goes to infinity. Thus it would require infinite energy to accelerate any massive object to

Again, sorry if I'm misunderstanding what you said.

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"You" would never get anywhere in the vicinity of c, though what is left of you after gravity has ripped you to pieces will be accelerated to greater speeds for greater mass black holes. Exactly what speed you reach at a certain radial distance from the BH depends on where you started from.

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Nabeshin

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To be fair, a terminal velocity as created by air resistance is also an asymptote.So, c is not a terminal; it is anasymptote.

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DaveC426913

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Yes, I didn't mean to imply it wasn't. I was trying to disabuse the OP of the notion that, wrt reaching c, acceleration increased until some point, as then justTo be fair, a terminal velocity as created by air resistance is also an asymptote.

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DaveC426913

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With a large enough black hole, the gradient is small enough that gravity will not pull you apart....what is left of you after gravity has ripped you to pieces...

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Nabeshin

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I did an elaboration on the speeds of infalling observers from infinity which might be useful for this discussion in a thread not too long ago. I might think about an analysis for observers infalling from a given radius later, or someone else could do that:"You" would never get anywhere in the vicinity of c, though what is left of you after gravity has ripped you to pieces will be accelerated to greater speeds for greater mass black holes. Exactly what speed you reach at a certain radial distance from the BH depends on where you started from.

https://www.physicsforums.com/showpost.php?p=2476880&postcount=6

https://www.physicsforums.com/showpost.php?p=2477762&postcount=12

(First post included because the second isn't very self-contained).

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thanks for your answers guys , you put a lot of effort into them.

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