at 1 G, how fast would you be going in a year?

[bwanaaa]

yes i know that V=a*t and if a is 9.8m/s then in a year you'd be close to the speed of light,c, from the frame of reference of the observer where you started. But it's been awhile since i set up a differential equation and i'd like to graph the actual velocity over time.

 

[KIAman]

I got around 9,000c

 

[firewolfsm]

So a better question would be: how do I convert all that kinetic energy into mass?

Don't ask me though.

 

[KIAman]

Btw, g = 9.8m/s^2

 

[Markbnj]

This is fun to play with...

http://home.att.net/~srschmitt/script_starship.html

 

[bwanaaa]

the point is that c cannot be exceeded. we begin with a constant force (say an ion engine) to give constant acceleration.what are the possible outcomes?

1) our mass increases as we approach c and despite a constant force, acceleration decreases OR
2)as velocity approaches c spaces enlarges=>acceleration continues but actual velocity decreases

what do the occupant and observer measure?

how do i interpret SR to deduce the correct scenario? can a differential equation using SR be set up to reveal the right scenario?

 

[bwanaaa]

so tell me if i am on the right track:
the ion sail applies a constant force F

the acceleration you sense is F/mr

where mr is the relativistic mass

so your velocity at any given time is

V=f/mr * t

but mr is a function of velocity thusly:

mr=m /sqrt(1 - v2/c2)

substituting and 'simplifying'

V=Ftc / sqrt [ c2m2+f2t2]

 

[PowerEngineer]

Look here.

I think you'll find this site helpful.

 

[f95toli]

Originally posted by: bwanaaa
how do i interpret SR to deduce the correct scenario? can a differential equation using SR be set up to reveal the right scenario?

With difficulty. Or to be more specific, it is possible to handle accelerating frames in SR but you have to beyond the "usual" equations and you also need to be very careful about which frame you are working in (I suspect you need some tensor algebra).
You basically end up with curved worldlines.
As far as I remember the result for a constant acceleration is something along the line of the velocity as a function of proper time being a function of a tanh function (mening v goes to c as T goes to infinity, as it should).
In the general case I suspect you need GR.


Edit: Look at
http://math.ucr.edu/home/baez/...ativity/SR/rocket.html

 

[DrPizza]

Wow, that's something I never thought of (from one of the links): my feet are aging faster than my head. My head is farther from the center of the earth, and thus is moving at a higher speed.

Someone bored enough to want to do this calculation:

Assuming a person is standing somewhere on the equator, and that person is exactly 2 meters tall, lives for 80 years, and stands the entire time...
What is the relative to the bottom of the feet, how much less time has elapsed for the top of the head? (He was born 2 meters tall, to keep it simple)

 

[manowar821]

Wow wow wow. At 1G for a million light years, it would effectively feel like 26-27 years for the crew, but obviously 1000002 (rounded) years on earth. WOW.

This is a fun little calculator..

 

[Nathelion]

I think there was a sci-fi novel written about this. A few test crewmen get stuck on a prototype spaceship with a constant acceleration and find out they can't turn it off. They end up witnessing the death of the universe as the last star goes out and stuff like that. Arthur C Clarke maybe?

 

[thebeyonder]

think of it as 9.8 "meters per second" per second. that makes it much easier. every second, add another 9.8 m/s faster.

you want to make a graph of the speed over 1 year? easy. boring. straight line. it's linear acceleration.

anyways, 1 year = 365 days = 8760 hours = 31,536,000 seconds.

after 1 year you would be going 9.8*31,536,000=309,052,800 m/s.

the speed of light is 299,792,458 m/s, so before a year is up, you would get to the point where a stationary observer would still see you accelerating, but not as fast as you were before. when you get closer to the speed of light, the energy that is put into acceleration would be translated into increasing your mass.

from your point of view you would keep on accelerating just like before, and wouldn't feel anything different.

it's all relative.

 

[SonicIce]

Originally posted by: DrPizza
Wow, that's something I never thought of (from one of the links): my feet are aging faster than my head. My head is farther from the center of the earth, and thus is moving at a higher speed.

Someone bored enough to want to do this calculation:

Assuming a person is standing somewhere on the equator, and that person is exactly 2 meters tall, lives for 80 years, and stands the entire time...
What is the relative to the bottom of the feet, how much less time has elapsed for the top of the head? (He was born 2 meters tall, to keep it simple)

probly like a couple seconds at most. same with people who fly in airplanes alot.