# Terminal velocity in a vacuum?

• kubaanglin
In summary: OP stated and you seem to be agreeing with. See my post above. Relativity does not really factor into the value of terminal velocity, unless you want to consider a very massive object onto which the object is dropped, and where the velocity of the object could become relativistic.
kubaanglin
If an object is dropped in a hypothetical infinitely long vacuum tube, will it reach a terminal velocity? I assume that it must because according to Einstein, no object that has mass can travel at the speed of light. My guess would be that the terminal velocity of an object in a vacuum would depend on its mass. I suggest this because I imagine some parabolic graph to denote the effect of mass on terminal velocity within a vacuum; not just a simple "does it have mass or not". I am just a junior in high school and have no great knowledge of relativity, but I post this to simply gain knowledge that I was unable to acquire from my school as my physics teacher disregarded my question as "too advanced for the class to comprehend".

paulb203
That's actually true. Some people would say its because the object's mass increases as its speed increases and so it becomes harder and harder to accelerate it until a point that for any force, the acceleration is zero and there it stops increasing speed and so doesn't reach the speed of light.
But I don't like relativistic mass(and I'm not alone in that), so I prefer to say that in special relativity, Newton's second law of motion is changed somehow that as the speed approaches the speed of light, the acceleration, for any force, approaches zero.
These explanations are equivalent and it depends on you which one to accept.

paulb203
kubaanglin said:
If an object is dropped in a hypothetical infinitely long vacuum tube, will it reach a terminal velocity? I assume that it must because according to Einstein, no object that has mass can travel at the speed of light. My guess would be that the terminal velocity of an object in a vacuum would depend on its mass. I suggest this because I imagine some parabolic graph to denote the effect of mass on terminal velocity within a vacuum; not just a simple "does it have mass or not". I am just a junior in high school and have no great knowledge of relativity, but I post this to simply gain knowledge that I was unable to acquire from my school as my physics teacher disregarded my question as "too advanced for the class to comprehend".

What makes an object travel faster and faster is a force applied to it. In the concept of "terminal velocity" we are talking about the force of gravity. It doesn't matter. Force is force. (Let's ignore for the moment the GR description of gravity as spacetime curvature since in this case, it has the same effect).

Forces applied to one object to make it move faster relative to another object (and all motion is relative) are subject to, and you can Google this, "relativistic velocity addition", which is what keeps things with mass from going as fast as c.

Shyan said:
That's actually true. Some people would say its because the object's mass increases as its speed increases and so it becomes harder and harder to accelerate it until a point that for any force, the acceleration is zero and there it stops increasing speed and so doesn't reach the speed of light.
But I don't like relativistic mass(and I'm not alone in that), so I prefer to say that in special relativity, Newton's second law of motion is changed somehow that as the speed approaches the speed of light, the acceleration, for any force, approaches zero.
These explanations are equivalent and it depends on you which one to accept.

Uh ... no, it's not due to the object's mass, as the OP stated and you seem to be agreeing with. See my post above.

Relativity does not really factor into the value of terminal velocity, unless you want to consider a very massive object onto which the object is dropped, and where the velocity of the object could become relativistic.

An object "dropped" onto the Earth would be able to achieve a calculable terminal velocity ( at impact with the Earth the velocity would be maximum through a tube of vacuum ) no matter how far the object is placed from the earth. Drop the object onto the sun, or other larger masses, and the terminal velocity would be greater. Consider that space is mostly vacuum anyways, we really do not need a tube of vacuum, even if the sun or Earth has an atmosphere surrounding it, as most of the increase in velocity will be accomplished in space if the object is sufficiently far away.

phinds said:
Forces applied to one object to make it move faster relative to another object (and all motion is relative) are subject to, and you can Google this, "relativistic velocity addition", which is what keeps things with mass from going as fast as c.
I don't get it. Could you explain more clearly?

phinds said:
Uh ... no, it's not due to the object's mass, as the OP stated and you seem to be agreeing with. See my post above.
Why not? How is it different from any other situations where we try to explain why things can't go at c or faster?
And notice I said I don't accept relativistic mass and so don't use it for explaining what OP asked. I just mentioned it so that the OP knows about different views.

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phinds said:
Let's ignore for the moment the GR description of gravity as spacetime curvature since in this case, it has the same effect.
That doesn't make any sense. If the OP asks about relativistic limits of free fall under gravity, you have to use GR. SR is not compatible with Newtonian gravity.

ComplexVar89
A.T. said:
That doesn't make any sense. If the OP asks about relativistic limits of free fall under gravity, you have to use GR. SR is not compatible with Newtonian gravity.

OK, I agree, but are you going to contend that an object travels faster that c? The point I was making was that Einstein Velocity Addition applies. I didn't want to get into a discussion of whether or not gravity is a force or a curvature of spacetime since the end result is the same.

phinds said:
OK, I agree, but are you going to contend that an object travels faster that c?
Not in a local inertial frame.

phinds said:
The point I was making was that Einstein Velocity Addition applies.
How exactly?

A.T. said:
Not in a local inertial frame.How exactly?

I guess I don't know, I'm just confident that you can't exceed c.

I do know that the acceleration due to gravity at the EH of a BH is c, which is why even light can't escape, so it would seem that the acceleration inside the EH would be even more, but what I have read is that inside the EH, things become time-like instead of space-like so that seems to be the difference. Still, I don't think that applies here.

I thought about this after logging off last night and realized that the whole discussion is moot anyway. "Terminal velocity" in the sense being discussed here is a ballistic velocity. Take an airless huge planet, oven a solar mass planet (but not a black hole) and shoot a gun directly away from the center of mass of the object. The terminal velocity of any object falling back is the same as the escape velocity of the bullet, even if that velocity is an appreciable fraction of c (that is, a "relativistic velocity") but it is not possible for a bullet to reach c, so it is not possible for a free falling object to reach c (again, ignoring black holes)

EDIT: OOPS .. I didn't see 256bits post. He beat me to it.

kubaanglin said:
If an object is dropped in a hypothetical infinitely long vacuum tube, will it reach a terminal velocity?

Infinitely long means anything that could affect the object is infinitely far away from it, thus exerting no influence on the object, hence the object's velocity won't change at all.

If you still want the object to be subject to something affecting its velocity in the infinitely long tube, you will need to specify exactly what influence it is.

ComplexVar89
It is a bit disappointing that no one gave the correct answer, but instead people got distracted by the possibility of Relativity playing a role. Relativity doesn't apply here except if the object falling toward is really massive and dense (like a black hole).

The object falling accelerates until impact, reaching a specific speed: escape speed (velocity).

russ_watters said:
instead people got distracted by the possibility of Relativity playing a role.

russ_watters said:
The object falling accelerates until impact, reaching a specific speed: escape speed (velocity).
And what is the maximally possible escape speed, according to Newton?

A.T. said:
Yes; that was his guess at an answer. It wasn't going down the right path.
And what is the maximally possible escape speed, according to Newton?
Depends: are we talking about real objects(among other framing issues)? I think we should be. But either way, "escape speed" is the core issue here, not relativity's limit on escape speed.

A.T. said:
And what is the maximally possible escape speed, according to Newton?
russ_watters said:
Depends: are we talking about real objects(among other framing issues)?
All objects consistent with Newtonian mechanics. Also note that nothing in the OP states that the fall ends at the surface of a spherical mass.

Then there is an additional potentional framing issue with the op in that s/he may be trying to say the object falls for an infinite distance. But eventually you have to hit what you are falling toward.

Fixing the framing (implied or not) of the question is an important part of answering it.

An infinitely long tube has as much mass in front as behind and no net gravitational attraction. OP mistakes the size of infinite.

russ_watters said:
But eventually you have to hit what you are falling toward.
Not if it has a hole. So is there anything in Newtonian mechanics, that restricts escape speeds to a finite value?

A.T. said:
Not if it has a hole.
That's enough with the games, A.T.

This is the OP's thread and regardless of where he wants to go with it AFTER learning how escape speed works, the point is that none of those other potential alternate scenarios can be discussed until AFTER escape velocity is introduced.

At this point it would be best if we allow the OP to catch up and see where he wants to go.

russ_watters said:
It is a bit disappointing that no one gave the correct answer, but instead people got distracted by the possibility of Relativity playing a role. Relativity doesn't apply here except if the object falling toward is really massive and dense (like a black hole).

The object falling accelerates until impact, reaching a specific speed: escape speed (velocity).

I guess you missed post #11, yes?

There is no terminal velocity for an object in a vacuum.

When an object which is falling under the influence of gravity or subject to some other constant driving force is subject to a resistance or drag force which increases with velocity, it will ultimately reach a maximum velocity where the drag force equals the driving force. This final, constant velocity of motion is called a "terminal velocity"

http://hyperphysics.phy-astr.gsu.edu/hbase/airfri2.html

During the fall, there is no point at which the velocity is constant.

I don't think we get to redefine what terminal velocity means.

TumblingDice
Jimmy said:
There is no terminal velocity for an object in a vacuum.

http://hyperphysics.phy-astr.gsu.edu/hbase/airfri2.html

During the fall, there is no point at which the velocity is constant.

I don't think we get to redefine what terminal velocity means.

You are right about the velocity constantly changing but you are missing the point. The terminal velocity is the FINAL velocity in this case and it is the "escape velocity". Do you not agree w/ my post #11 ?

This is somewhat a matter of terminology. In one sense you are right that there is no "terminal velocity" with the situation being that the object falls further at that velocity (which IS the normal definition of terminal velocity)

I agree with Jimmy. Terminal velocity is typically used to refer to the limiting velocity when drag and accelerating force cancel exactly. If an object is falling faster it will slow down, if it is falling slower it will speed up. This is not the case with escape velocity, if I give the object an initial velocity it will have a velocity which is larger than the escape velocity when (and if) it hits the surface.

phinds said:
You are right about the velocity constantly changing but you are missing the point. The terminal velocity is the FINAL velocity in this case and it is the "escape velocity".
But that isn't terminal velocity. If we get to redefine standard physics terms then we can pretty much say anything we want.

OP:
Terminal velocity doesn't necessarily need to be about the force of gravity and drag.

Consider a rocket that is under constant acceleration in the vacuum of space. There is no point in time the rocket will ever reach a terminal velocity. Even if you take relativity into account the velocity of the rocket will always increase but never reach c.

Jimmy said:
Consider a rocket that is under constant acceleration in the vacuum of space. There is no point in time the rocket will ever reach a terminal velocity. Even if you take relativity into account the velocity of the rocket will always increase but never reach c.

This is exactly what happens with the terminal velocity in the "usual" case. It is never reached, if the body starts with any other velocity.

russ_watters said:
those other potential alternate scenarios...
Alternate to what? The OP didn't specify what kind of object creates the gravitation under which the object falls.

russ_watters said:
... can be discussed until AFTER escape velocity is introduced.
Since escape velocity has been already introduced, can you now explain how Newtonian physics limits the maximally possible escape velocity?

phinds said:
I guess you missed post #11, yes?
I did indeed. Apologies.

A.T. said:
Alternate to what? The OP didn't specify what kind of object creates the gravitation under which the object falls.

Since escape velocity has been already introduced, can you now explain how Newtonian physics limits the maximally possible escape velocity?
Right: until we get further clarification from the op on his scenario or you on yours, it can't be answered. And I'm not really inclined to go down your rabbit hole either way. Asking how Newtonian physics would describe this is a booby-trap because we have to decide how to mix and match Newtonian and non-Newtonian constraints with reality. Worse, Newtonian physics was never fully developed for some of the scenarios that may arise from this. It may be interesting to you to discuss that, but not here/now.

russ_watters said:
until we get further clarification from the op on his scenario or you on yours,
There is no "my scenario". I'm asking about the OP's scenario as stated, without added constraints that the OP doesn't state.

russ_watters said:
Worse, Newtonian physics was never fully developed for some of the scenarios that may arise from this. It may be interesting to you to discuss that, but not here/now.
So we should neither use Relativity (despite the OP explicitly asking about it) nor Newtonian physics?

A.T. said:
There is no "my scenario". I'm asking about the OP's scenario as stated, without added constraints that the OP doesn't state.So we should neither use Relativity (despite the OP explicitly asking about it) nor Newtonian physics?
That's not what I said. Enough.

I now understand that there is no truly confirmed answer to my question as the scenario I described is completely hypothetical and will never exist in the real world to be observed and analysed. I definitely have a better understanding of the rules and possibilities concerning my question, but understand that an evidence-based answer is impossible.

And just to clarify my scenario, the gravitational force reacting upon the accelerating object is constant throughout the entire tube.

kubaanglin said:
And just to clarify my scenario, the gravitational force reacting upon the accelerating object is constant throughout the entire tube.

Huh? That's going to be a good trick. Gravity certainly doesn't work that way. Not sure what you might mean by that.

If we the force comes from a central object, then the maximal velocity is the escape velocity of this object (a bit more if we dig into the object) - or the speed of light for black holes.

If the force comes from something else (no one ever said we have gravity, right?) and is constant over the tube, then we still get the speed of light as the limit. This is basically realized in particle accelerators. Electrons in LEP reached a speed of 299792.457996 km/s where the speed of light is exactly 299792.458 km/s. They were slower by just 4mm/s (about 350m/day).

The only hard limit is the speed of light. That doesn't mean that objects will reach the velocity of light. As long as gravity is the force, mass changes will not change it's acceleration. Gravity works on every unit of mass, so the force grows as the mass grows, and the acceleration is not changed by the total mass. An object extremely far from Earth (nearly infinite distance) will keep accelerating toward earth. But that process will just be the time reverse of the same object escaping the Earth's gravitational field. It takes the escape velocity of about 6.96 mi/s to totally leave the Earth's gravity and go out to infinity. An object falling to Earth from an initial velocity of 0 will be the time reverse of the escaping object and will never exceed 6.96 mi/s no matter how far away it starts.

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