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Neil Russell
2016-Aug-19, 08:25 AM
M y maths is not up to this!

We have a space craft which can accelerate at a steady one gravity. ( ignore for now the how!) how fast will it be going after 24 hours? after a week? and finally how long to reach light speed?

lemming
2016-Aug-19, 09:40 AM
M y maths is not up to this!

We have a space craft which can accelerate at a steady one gravity. ( ignore for now the how!) how fast will it be going after 24 hours?

Assuming I didn't stuff it up, about 0.28% of the speed of light.

after a week?

About 1.9% of the speed of light.

and finally how long to reach light speed?

If your constant 1G acceleration were from the perspective of someone left behind, a little bit less than a year. That ignores the slight technical difficulty that the amount of energy required is infinite, but you did say to ignore the "how".

Again, that's all assuming I didn't stuff it up.

John Mendenhall
2016-Aug-19, 10:00 AM
Ye, very handy. Means anywhere is about two comoving frame years away.

Cougar
2016-Aug-19, 11:40 AM
M y maths is not up to this!

We have a space craft which can accelerate at a steady one gravity. ( ignore for now the how!) how fast will it be going after 24 hours? after a week? and finally how long to reach light speed?

Um, say the spacecraft is sitting motionless on the surface of the earth. According to the equivalence principle, this is equivalent to accelerating "at a steady one gravity." After a week, it will still be motionless.

With relativity, you always have to specify motion relative to something else.

George
2016-Aug-19, 02:38 PM
The math is simple for the 24 hour and even the one week time frame since Newton's v=gt is all you need. Relativity has little relative effect (sorry :)).

Here (http://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html) is a site showing the relativistic equations, including fuel expenditures.

Neil Russell
2016-Aug-19, 09:28 PM
Thankyou Lemming just what I needed. Now all we have to do is find that infinite power source!!

Neil Russell
2016-Aug-19, 09:40 PM
George great site thank you.

Strange
2016-Aug-19, 10:48 PM
There are a whole bunch of sites that let you plug in the numbers and get a result. I can't vouch for the accuracy (or usefulness) of any of these but for example:
http://convertalot.com/relativistic_star_ship_calculator.html
http://nathangeffen.webfactional.com/spacetravel/spacetravel.php
http://gregsspacecalculations.blogspot.co.uk/2014/11/relativistic-rocket-calculator.html
http://gregsspacecalculations.blogspot.co.uk/p/blog-page.html
http://www.relativitycalculator.com/relativistic_photon_rocket.shtml
http://www.cthreepo.com/lab/math1/

Jens
2016-Aug-20, 04:02 AM
Assuming I didn't stuff it up, about 0.28% of the speed of light.

About 1.9% of the speed of light.

If your constant 1G acceleration were from the perspective of someone left behind, a little bit less than a year. That ignores the slight technical difficulty that the amount of energy required is infinite, but you did say to ignore the "how".

I'm under the impression that even if you accelerated at one g for a thousand years, you would not reach c for any observer, but would only get closer and closer to it.

Solfe
2016-Aug-20, 04:13 AM
I'm under the impression that even if you accelerated at one g for a thousand years, you would not reach c for any observer, but would only get closer and closer to it.

Yes, but mathematically, you can go up to any arbitrarily high number. In the real world, that doesn't work out.

Jens
2016-Aug-20, 04:19 AM
Yes, but mathematically, you can go up to any arbitrarily high number. In the real world, that doesn't work out.

Doesn't that depend on what mathematical equations you use? If you use Newtonian ones, then yes, but if you use relativistic ones, it shouldn't work.

Jens
2016-Aug-20, 04:23 AM
If your constant 1G acceleration were from the perspective of someone left behind, a little bit less than a year. That ignores the slight technical difficulty that the amount of energy required is infinite, but you did say to ignore the "how".

But you don't need infinite energy to accelerate at 1 g for a year. It's a lot of energy, but not infinite.

lemming
2016-Aug-20, 04:50 AM
But you don't need infinite energy to accelerate at 1 g for a year. It's a lot of energy, but not infinite.

It depends on how you interpret constant acceleration at 1g, which is why I added the phrase about the perspective of a person left behind.

Acceleration is frame-invariant in a Newtonian universe, but not in a relativistic universe. If the 1g constant acceleration is as measured by a person who was left behind when the acceleration began (the same person who is going to judge the speed of the thing that is accelerating), then my statement stands. If you manage to achieve the impossible, and accelerate at 1g for about one year from the perspective of the person you left behind, you would indeed achieve light speed. But the reason it is impossible is because it does require infinite energy.

You could also consider the constant 1g acceleration to be from the perspective of your own frame (assuming you are the person doing the accelerating). This would mean, as you are flying through space, if you look out your rocket window and notice a person in another rocket coasting right along side you at the same speed and in the same direction, but with their engine off, they would notice you accelerating at 1g, at that particular point in time. The person who stayed behind when you boarded your rocket to begin this epic journey would initially perceive you to be accelerating at 1g, but then would note that you start to accelerate more and more slowly, approaching, but never quite reaching, the speed of light. This is constant 1g acceleration from the perspective of the person on the rocket, not from the perspective of the person left behind.

So it depends on what "constant 1g acceleration" means. This wasn't specified in the original post.

Solfe
2016-Aug-20, 04:56 AM
Doesn't that depend on what mathematical equations you use? If you use Newtonian ones, then yes, but if you use relativistic ones, it shouldn't work.

Yes, that is true. I mean, it has unity built right in, so over 1 c is a no go. I guess you could do something goofy like jam in an irrational number for v and get goofy answers.*

*Edit - Actually, you are better off not doing that at all. For some reason I switched formulas and was working the difference in ship time verse Earth time instead of acceleration. I guess I am pretty tired. I couldn't figure out where the v^2 came from after I hit post.

Jaaanosik
2016-Aug-20, 04:06 PM
It depends on how you interpret constant acceleration at 1g, which is why I added the phrase about the perspective of a person left behind.

Acceleration is frame-invariant in a Newtonian universe, but not in a relativistic universe. If the 1g constant acceleration is as measured by a person who was left behind when the acceleration began (the same person who is going to judge the speed of the thing that is accelerating), then my statement stands. If you manage to achieve the impossible, and accelerate at 1g for about one year from the perspective of the person you left behind, you would indeed achieve light speed. But the reason it is impossible is because it does require infinite energy.

You could also consider the constant 1g acceleration to be from the perspective of your own frame (assuming you are the person doing the accelerating). This would mean, as you are flying through space, if you look out your rocket window and notice a person in another rocket coasting right along side you at the same speed and in the same direction, but with their engine off, they would notice you accelerating at 1g, at that particular point in time. The person who stayed behind when you boarded your rocket to begin this epic journey would initially perceive you to be accelerating at 1g, but then would note that you start to accelerate more and more slowly, approaching, but never quite reaching, the speed of light. This is constant 1g acceleration from the perspective of the person on the rocket, not from the perspective of the person left behind.

So it depends on what "constant 1g acceleration" means. This wasn't specified in the original post.
How much energy is required to accelerate towards a black hole?

2016-Aug-21, 05:32 PM
Thankyou Lemming just what I needed. Now all we have to do is find that infinite power source!!

I happen to know that gaseous waste from rabbits is potentially inexhaustible...pardon the pun.

schlaugh
2016-Aug-21, 06:30 PM
How much energy is required to accelerate towards a black hole?

Only just enough to accelerate into the BH's gravity well. The energy required for such acceleration would depend on distance from the BH, current velocity, motion and direction. You can get there in a slow walk or at near light speed.

Sent from my iPhone using Tapatalk

Jens
2016-Aug-22, 12:19 AM
It depends on how you interpret constant acceleration at 1g, which is why I added the phrase about the perspective of a person left behind.

Thanks, I see what you mean. I was assuming the original post was asking about 1g in the reference frame of the astronauts, since I presumed they meant to ask about an acceleration that would be comfortable for the astronauts. And so I was imagining precisely what you wrote here:

The person who stayed behind when you boarded your rocket to begin this epic journey would initially perceive you to be accelerating at 1g, but then would note that you start to accelerate more and more slowly, approaching, but never quite reaching, the speed of light. This is constant 1g acceleration from the perspective of the person on the rocket, not from the perspective of the person left behind.