# The Naked Scientists Forum

### Author Topic: How long does it take to reach C at a constant rate of 1 G?  (Read 5382 times)

#### AllenG

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##### How long does it take to reach C at a constant rate of 1 G?
« on: 13/10/2009 06:04:58 »
I was an art student because math makes my brain hurt.

If one were to build a spaceship that could constantly accelerate at one gravity, how long would it take for said interstellar caravan to reach .999 C?

#### RD

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##### How long does it take to reach C at a constant rate of 1 G?
« Reply #1 on: 13/10/2009 10:41:01 »
c = 3x108 meters per second,
1g = 9.8 meters per second per second
Divide the first by the second gives ...

3.06 x 107 seconds = 354 days

Obtaining the energy to do it is the difficult bit ...

Quote
As an object approaches the speed of light, more and more energy is needed to accelerate it further.
To reach the speed of light an infinite amount of energy would be required.
http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html
« Last Edit: 13/10/2009 10:54:36 by RD »

#### graham.d

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##### How long does it take to reach C at a constant rate of 1 G?
« Reply #2 on: 13/10/2009 13:19:17 »
The answer according to the equations on the website you posted, RD, is as follows (I put them in excel):

Time to get to 0.999c

As experienced by the travellers: 1331 days
As observed in the "rest" frame: 7604 days

I didn't check their equations but I think I typed them in properly. I think the answer you gave is based on Newton's theory rather than Relativity.

#### syhprum

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##### How long does it take to reach C at a constant rate of 1 G?
« Reply #3 on: 13/10/2009 13:33:59 »
While your astronauts are belting along at 0.999c presumably they will encounter the CMBR blue shifted to about 2700°K that might be a problem.

#### RD

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##### How long does it take to reach C at a constant rate of 1 G?
« Reply #4 on: 13/10/2009 13:53:40 »
Correction  [:I] ...

http://www.projectrho.com/rocket/rocket3aj.html#relativity

The amount of energy required to maintain 1g acceleration would increase exponentially as the speed of the craft approached c.
« Last Edit: 13/10/2009 14:01:17 by RD »

#### graham.d

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##### How long does it take to reach C at a constant rate of 1 G?
« Reply #5 on: 13/10/2009 15:45:00 »
Something that often gets forgotten about is that, from the point of view of the traveller, the universe gets Lorentz contracted in the direction of travel. So it works out that travelling great distances is not such a huge problem as it first appears. It is still a huge problem nonetheless.

#### Soul Surfer

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##### How long does it take to reach C at a constant rate of 1 G?
« Reply #6 on: 13/10/2009 16:22:48 »
It is interesting to note what this looks like from the perceived time of the traveller.  Apparently if someone accelerates continuously at a perceived rate of 1g continuously and then decelerates continuously at 1g to reach the destination it is theoretically possible for a person to reach the edge of the visible universe and return in one human lifetime of perceived time.

#### syhprum

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##### How long does it take to reach C at a constant rate of 1 G?
« Reply #7 on: 14/10/2009 08:05:30 »
I am interested in the relationship between time dilation and power, how many joules are required to make 1 kg one second younger ?

#### Soul Surfer

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##### How long does it take to reach C at a constant rate of 1 G?
« Reply #8 on: 14/10/2009 09:09:57 »
It can't make anything younger only less old relative to something else that did not accelerate and you bneed to specify the time over which this age difference will even occur even assuming you require an out and back trip.
« Last Edit: 14/10/2009 09:13:24 by Soul Surfer »

#### syhprum

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##### How long does it take to reach C at a constant rate of 1 G?
« Reply #9 on: 14/10/2009 14:01:58 »
I phased it rather poorly, What I had in mind was for our astronaut or particle to travel out, loop round a massive object and return finding he had aged 1 sec less than his compatriots.
and of course the power required depends on how long he takes to accomplish this task, lets us assume he does it in a liesurely fashion taking 1,000,000 seconds.
Of course when he returns he will have almost the same amount of energy (Kinetic) as was required to launch him on his journey, presumably the small difference will have gone into producing the the age difference.

#### yor_on

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##### How long does it take to reach C at a constant rate of 1 G?
« Reply #10 on: 17/10/2009 02:02:45 »
I phased it rather poorly, What I had in mind was for our astronaut or particle to travel out, loop round a massive object and return finding he had aged 1 sec less than his compatriots.
and of course the power required depends on how long he takes to accomplish this task, lets us assume he does it in a liesurely fashion taking 1,000,000 seconds.
-----

Of course when he returns he will have almost the same amount of energy (Kinetic) as was required to launch him on his journey, presumably the small difference will have gone into producing the the age difference.
You're losing me there? the only energy spent I would presume to be the rockets?
I'm not sure if you expect him to somehow contribute to the effect?
The time dilation is a result of different frames even though they leave and join the same frame as I see it?

#### The Naked Scientists Forum

##### How long does it take to reach C at a constant rate of 1 G?
« Reply #10 on: 17/10/2009 02:02:45 »