Terminal Velocity in a Vacuum

[Asphyxi8]

If it is true that an gravity will not cause objects to exceed the speed of light (which I believe entirely), then is there a terminal velocity for 1 G in a bottomeless vacuum? Or will it just accellerate at 9.8 meters per second per second until it theoretically hits the light barrier and does something that we can't figure out or doesn't make sense?

[dextercioby]

What's "bottomless (sic) vacuum"...?On normal basis,if the body is accelerated,then its velocity will increase,but it will never reach "c"...

Daniel.

P.S.It will asymptotically tend to "c"...

[Asphyxi8]

I'm sorry, but that makes no sense to me. What is "(sic)" representing? I assume that "c" is the constant speed of light, but the question seems to be unanswered. I already believe that "c" will not be reached, so you do not have to convince me of this. My original question was relating to the terminal velocity, not to the speed of light.

And a "bottomless vacuum" is an area with no particles in it to create friction that an object could theoretically move through without encountering resistance for an infinite amount of time.

[pervect]

If you are in a rocket ship accelerating at 1g, there are a number of odd and non-intuitive things that will happen.

I suppose the best short summary is that rather than a terminal velocity, there is a maximum distance "below you" that an object can be in a 1g field, and anything further below you than that critical distance disappears beyond an event horizon, called the Rindler Horizon.


If the 1-g field is not due to the accleleration of a rocket, but is due to the gravitation of an actual physical body, similar remarks apply, except that the event horizon one sees is the more familiar event horizon of a black hole, rather than the Rindler horizon due to accelerated motion.

You might want to look up the "Rindler Horzion" for more details about the accelerated motion case.

There's a little bit of popular level discussion in an old sci.physics.research thread that Google found

http://olympus.het.brown.edu/pipermail/spr/Week-of-Mon-20020422/000874.html

but I'm not sure how well it stands alone, it appears like some of the more interesting parts of the thread didn't remain in storage.

[Asphyxi8]

Okay, I figured it out. The answer is:

NOBODY KNOWS!

Apparently, the accelleration would continue and the only limit would be Einstein's theory of relativity, at which it might stop or do something absolutely unheard of.

[pervect]

Actually I just gave you an answer - while it didn't have a lot of detail, neither did your original question. The details depends on how you are trying to set up your "consant 1-g field".

(I'm guessing that you did read my answer before your latest response, though it's possible that the timing was such that you were composing your response while I was composing mine).

[KingNothing]

If it is true that an gravity will not cause objects to exceed the speed of light (which I believe entirely), then is there a terminal velocity for 1 G in a bottomeless vacuum? Or will it just accellerate at 9.8 meters per second per second until it theoretically hits the light barrier and does something that we can't figure out or doesn't make sense?

Why would it accelerate at 9.8 M/s^2 if it's in a vacuum without objects? There would be no gravity in that case. 9.8 m/s^2 just happens to be the average acceleration at sea level on planet earth. It's not like that in a vacuum. Anyway, if we assume that the object has a positive acceleration, the speed will increase what appears to be linearly but isn't.

Normally we just consider such a small speed that we can't measure with enough detail to see the relationship isn't linear. If we look at such a time interval such that the speed gets very close to c, we would see that it's a curve.

[Mk]

If it is true that an gravity will not cause objects to exceed the speed of light (which I believe entirely), then is there a terminal velocity for 1 G in a bottomeless vacuum? Or will it just accellerate at 9.8 meters per second per second until it theoretically hits the light barrier and does something that we can't figure out or doesn't make sense?
It seems you may have a few misconsceptions or haven't phrased a question well.

Roughly 9.8 m/s2 know as g, is the gravitational constant for the earth.

Its not gravity that keeps the speed of light as a sort of a speed barrier, its mass itself.

In a perfect vacuum there is no terminal velocity

A mass cannot hit the light barrier really, it can come infinantly close, but not even touch it.

:smile: Glad to help,
Mk :smile:

[FrogPad]

And for future reference "(sic)" is used when someone quotes another, but achnowleges that the person they are quoting has made a spelling mistake.

For example, if I was to quote what I just said above:
“And for future reference "(sic)" is used when someone quotes another, but achnowleges (sic) that the person they are quoting has made a spelling mistake.”

Since “achnowleges” is actually spelled acknowledge, then you place a “(sic)” there to show that you did that intentionally.

Since you made a spelling mistake (actually two), dextercioby placed a “(sic)” there to show that he changed your spelling mistake.

“If it is true that an gravity will not cause objects to exceed the speed of light (which I believe entirely), then is there a terminal velocity for 1 G in a bottomeless vacuum? Or will it just accellerate at 9.8 meters per second per second until it theoretically hits the light barrier and does something that we can't figure out or doesn't make sense?”

[HallsofIvy]

It depends upon your "point of view".

[b]IS there a frame of reference in which the acceleration is constant?

The person, A, constantly accelerating will observe himself to be stationary (of course) but feel a force.

A person in a non-accelerating frame of reference would observe the acceleration decreasing as A's speed increases. Such a person would observe the "terminal velocity" as c (of course, he would see A's speed approaching c but never reaching it).

[Dazaga]

Ok, here's what I've discovered by deriving formulas and equations from my list of formulas my AP Physics teacher gave me (and I'm only a 17 year old physics enthusiast so don't trust me completely here)...

I derived the following formula for the final velocity of an object just before impact due to the acceleration of gravity (in a vacuum and unaffected by any other forces):

v=sqr(((initial v)*2)+2x(integral((6.673x(10*23))x(m)x(x*(-2)),x,r,(r+d))))

I think I typed that out right...it should read "velocity equals the square root of the quantity of the initial velocity squared plus 2 times the integral of the quantity of the gravitational constant (6.673 times 10 to the 23rd power) times the mass of the planet (or whatever object your are using as the frame of reference for which your target object is being pulled towards by gravity) times the quantity x to the negative second power all in respect to the variable x over the interval r (the radius of the planet) to the quantity r plus d (the radius of the planet plus the distance the object is from the planet's surface since that is where it will impact).

Sorry, I couldn't find all the proper characters on the character map to type it out properly so I had to do it that way...good luck deciphering that...

Anyway, using that formula (which I believe to be true since I tested it out with small calulations using Earth's radius, mass, etc [and it worked out] - though I only used objects starting from rest...so I guess I'm not sure about the initial v being squared and within the radical since it always dropped out...any help on checking that out would be appreciated), I found only 2 "possible" scenarios where it would cross the "light speed barrier"...

Scenario #1: With d approaching infinity, r=0, and m>0, v approaches infinity which means it would obviously cross the finite light barrier velocity...

Catch #1: Well, you can't set an object an infinite distance from a planet...plus...it would take an infinite amount of time for it to impact the planet if you could...which you can't...also, you can't have a planet with a radius of 0 and mass greater than 0...(I don't think...but even if you can the other two snags stop this from occurring - not to mention this requires no other forces in the entire universe affecting either the object or the planet...)

Catch #2: According to Einstein's Theory of Relativity, an object approaching the speed of light has a relativistic mass approaching 0 (if I understand it correctly...I'm not into this stuff yet so don't trust me here)...if it's relativistic mass approaches 0...the acceleration due to gravity would approach 0 thus forcing an asymptotic approach to the speed of light...

Scenario #2: initial velocity ~ speed of light (in other words it is ALMOST at the speed of light to begin with and heading towards the planet)...then any acceleration due to gravity would theoretically bring it over that threshold...

Catch: (same as Catch #2 of last scenario)...it's relativistic mass would already be near zero and approaching zero...thus...it would also have an asymptotic approach to the speed of light...

[Dazaga]

Again, in all that typing I may have made a mistake...plus I am uneducated in Einstein's Theory of Relativity so please correct me if I am mistaken anywhere...but I believe what I posted is correct and I hope it is helpful if anyone still cares about this nearly 3-year-old thread (I'm new so I had to post what I think I know on the topic :) ).

[mtbear]

Good analogy. So. We all know about the light beam though the bubble in the aquarium. My question: what does that photon see, traveling at C, when light around it is traveling at .75 C?

m.t.bear, who sez,
Two things a man has to have;
a waterproof light meter and
duct tape.

[mtbear]

If you are in a rocket ship accelerating at 1g, there are a number of odd and non-intuitive things that will happen.

.As good an explanation as any I've read. And what would be your view on a photon's view, said photon traveling through a bubble in an aquarium at C while all fellow photon's are (outside the bubble) dragging around at .75 C?

m.t.bear

[Hootenanny]

Good analogy. So. We all know about the light beam though the bubble in the aquarium. My question: what does that photon see, traveling at C, when light around it is traveling at .75 C?

m.t.bear, who sez,
Two things a man has to have;
a waterproof light meter and
duct tape.

As good an explanation as any I've read. And what would be your view on a photon's view, said photon traveling through a bubble in an aquarium at C while all fellow photon's are (outside the bubble) dragging around at .75 C?

m.t.bear
Although the group velocity of light may be less than C, a photon always travels at C, irrespective of any medium. See here (http://www.physicsforums.com/showpost.php?p=899393&postcount=4) for more information.

[mtbear]

Although the group velocity of light may be less than C, a photon always travels at C, irrespective of any medium. See here (http://www.physicsforums.com/showpost.php?p=899393&postcount=4) for more information.

Thank you, Hootenaany, especially for the reference. I'll be muddling through that for a nonce. Then I'll get to your Latin quote.

In the mean time, you accented "always" and I'm curious to know why. As for my original question, let me rephrase and ask what the light "group" might witness on this aquatic tour? Or am I yet again stubbing, or stepping on, quantum toes? Seems like a lot of yakking has been done about observant twins, one traveling at C while the other stays home and looks after the old folk. What if... Tweedle Dumb is traveling at C and Tweedle Dope ((who thinks he is traveling at C (but we know he's only loping along at .75 C)) and each makes a rude gesture at the other? What will Dumb see? What will Dope see? Who will be offended first?

And while I'm at it, say the universe is the aquarium and the bubble is that phenomenon that Portuguese (Brazilian/) scientists is on about vis a vis Variable C?

Anyway, thanks for your attention to this matter.

m.t.bear, who sez,
Only two things a man needs:
an impossible idea and
duct tape.

[maverick_starstrider]

Okay, I figured it out. The answer is:

NOBODY KNOWS!

Apparently, the accelleration would continue and the only limit would be Einstein's theory of relativity, at which it might stop or do something absolutely unheard of.

Actually the answer is "SPECIAL RELATIVITY IS VERY WELL UNDERSTOOD AND IS SEEN EVERY DAY IN PARTICLE ACCELERATORS AND SUCH (AND HAS BEEN KNOWN FOR OVER A 100 YEARS)". Just look up Special Relativity. The crux is that relative to a 'stationary' frame of reference your velocity would only increase relative to the relativistic equation for velocity addition and when you think your velocity is infinity a 'stationary' observer will see you going at exactly the speed of light.

P.S. Pretty much every experiment done in a particle accelerator is done at speeds that are about 99.999% the speed of light and the temporal distortions (i.e. known decay times becoming longer relative to the lab frame) predicted by special relativity is just part of what you have to consider when planning these experiments (as opposed to 'oh my god we don't know what is going to happen, we're in new territory here')