# Terminal Velocity in a bottomless vacuum

Anttech
How would you calculate the terminal velocity of a massive object falling through a bottomless vacuum?

As nothing can go faster than the speed of light the object must have a terminal velocity also due to E=mc^2, and A=F/M...

I am just wondering if you can calculate the terminal velocity from the objects static mass.

## Answers and Replies

Anttech
sorry I should have added, with a constant force acting on the object, like g on earth...

Science Advisor
Homework Helper
Well, gravity isn't constant on the surface of earth, just close to constant.

In Newtonian mechanics, the object goes faster and faster forever.

In Special Relativity, if the force is constant, the mass that the object gains through kinetic energy will decrease the acceleration preventing it from ever getting to c.

In General Relativity (which I'm not familiar with) it might be possible to demonstrate that a constant acceleration (not constant force) path like that leads into a black hole.

For more information, you should look into information on particle accelerators.

Anttech
Thanks, Yep I understand special relativty, however I was wondering if there was a formula for calculating what the terminal velocity would be, If you know the constant force accelerating the object and the static mass of the object...

Here is the scenario I have conjered up:

An object of know mass, has a solar powered engine of knowen mass attached to it and has a thrust of know quantity applied to the system when knowing the total mass of the system could you calculate the terminal velocity in a vacuum...

:)

Science Advisor
Homework Helper
There is no terminal velocity in the sense of a velocity which the object reaches after a finite time.

The objects velocity approaches c as a limit.

If you wanted to calculate the velocity as a function of time, you would have to specify the force as a function of time.

Anttech
Force as a function of time, is this not power... or am I missing the point...

Anttech
Originally posted by HallsofIvy
There is no terminal velocity in the sense of a velocity which the object reaches after a finite time.

The objects velocity approaches c as a limit.

If you wanted to calculate the velocity as a function of time, you would have to specify the force as a function of time.

Sorry I am not with you 100%... How can the velocity approach C if the mass increase as the KE increases, surely there must be a point where the mass approaches infinite and therefore the acceleration becomes 0 if you are applying a constant force (a=f/m)...

can you explain what you said with a little more depth?

thx

Last edited by a moderator:
Mentor
Originally posted by Anttech
Force as a function of time, is this not power... or am I missing the point...
Yes, I think you missed the point - Hurkyl gave you the answer: C.

And power is force times distance times time.

Science Advisor
Gold Member
What Hall of Ivy means is that you have to specify f(t) = F, though looking at your first post you have specified F = k, where k is a constant.

From your point of view you would just keep on accelrating under this force, as after all it is a constant force, but if we take an observer who was in your rest frame when the force was applied he would view your velocity appraoching c as time approaches infinity.

Anttech
by K you mean Kinetic energy, well if my velocity increase how can K be constant...

Forgive me if I am coming over as stupid :)

Science Advisor
Originally posted by russ_watters
Yes, I think you missed the point - Hurkyl gave you the answer: C.

And power is force times distance times time.

Russ: Power is force times distance over time, or Force times velocity.

Science Advisor
Gold Member
Originally posted by Anttech
by K you mean Kinetic energy, well if my velocity increase how can K be constant...

Forgive me if I am coming over as stupid :)

I just used k as a generic constant, i.e. the force is always constant and always equal to some fixed value k

Anttech
ok let me rephraze my initial post, I was looking for a solution to a riddle which I thought you could do this way but obviously not exactly (I am sure by approximizing you could) The initial Riddle I was asked was,

"How would you "weight" a plane without scales?" If you can think of any other way you could do this I would be much obliged...

thx

sigSEGV
I do know that the terminal velocity would not be c. The object would continue to accelerate until the downward acceleration force balanced out with the increase in mass due to special relativity (I might not have phrased that clearly, but hopefully someone will understand). I don't have the skills to do the math, but I'm sure someone on this site does.

Science Advisor
Homework Helper
Originally posted by Anttech
"How would you "weight" a plane without scales?" If you can think of any other way you could do this I would be much obliged...

How about mass spectrometry?

Mentor
Originally posted by krab
Russ: Power is force times distance over time, or Force times velocity.
Oops. I do that sometimes.

Anttech
Originally posted by NateTG
How about mass spectrometry?

Good idea! :)

Science Advisor
Without probing the plane with gravity (eg a scale or some sort) you would have to use EM forces to probe the exact mass.

Eg count all the constituent particles, go ot the rest frame, add up the energies presto mass.

You can do it with gravity too, for instance, measure the curvature of space that the plane induces on the metric. Eg, measure light deviation the plane causes.