Gravity and space travel

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According to relativity, gravitational fields cause time dilation effects, lets say for instance i have a 'magic' device that can generate gravitational fields

Is it possible that this can be used to slow down one's time so as to make the journey seem much shorter

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It is simpler than that. You don't need to use magic, just use time dilation due to your velocity.

If you travel to a star 400 light years away with an acceleration of 1g (which would give you a comfortable artificial gravity) then the journey would take 401 years from the point of view of Earth. But for you, only 12 years would pass.

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On the first missions to Mars will astronauts live and work, or at least sleep, in a centrifuge so they can have 1 G of gravity most of the time?

Can we build a centrifuge on Mars, or the Moon, so astronauts can at least sleep in 1 G ?

Edited by Airbrush
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It is simpler than that. You don't need to use magic, just use time dilation due to your velocity.

If you travel to a star 400 light years away with an acceleration of 1g (which would give you a comfortable artificial gravity) then the journey would take 401 years from the point of view of Earth. But for you, only 12 years would pass.

Does this take into account deceleration at midway point?

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Does this take into account deceleration at midway point?

Yes at midway the craft swivels 180 degrees and begins 1 G deceleration.

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Yes at midway the craft swivels 180 degrees and begins 1 G deceleration.

For a 400 light year trip taking into account the deceleration time of half the journey wouldn't it take considerably more than 400 years "earth" time to finish the voyage? Or are you thinking ftl?

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For a 400 light year trip taking into account the deceleration time of half the journey wouldn't it take considerably more than 400 years "earth" time to finish the voyage? Or are you thinking ftl?

Not much more (assuming the calculator is correct - I haven't checked). Because it only takes a relatively small time to get up to a significant fraction of c.

Off the top of my head, I thought it would be about 402 years ...

Edited by Strange
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For a 400 light year trip taking into account the deceleration time of half the journey wouldn't it take considerably more than 400 years "earth" time to finish the voyage? Or are you thinking ftl?

The formula is

$t= \sqrt { \left ( \frac{d}{c} \right )^2 + \frac{2d}{c}}$

with t and d measured in the Earth frame.

This works out to be ~201 years for the acceleration and deceleration legs, or a total time or ~402 years for the total trip.

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Doesnt it become harder and harder to maintain a 1 G acceleration as c is approached

assumig we have an intial velocity of 0 (whatever that is), there are 31557600 seconds in a year, multiply that by the acceleration, which is 9.80665m/s^2 and we get 309,264,480 ms-1, so we kept moving at g for 1 year we would be moving faster than light, which it seems regrettably is impossible, so can we really travel at g for 400+

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Doesnt it become harder and harder to maintain a 1 G acceleration as c is approached

It depends on what you mean by maintaining a 1 G acceleration. If you mean that the occupants would feel a constant "force" pushing them to the tail of the rocket, then no. If you mean that the occupants measure their speed relative to their departure point as increasing at a constant rate, then yes. (in fact it will prove to be impossible to do so.).

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It depends on what you mean by maintaining a 1 G acceleration. If you mean that the occupants would feel a constant "force" pushing them to the tail of the rocket, then no. If you mean that the occupants measure their speed relative to their departure point as increasing at a constant rate, then yes. (in fact it will prove to be impossible to do so.).

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If they speed increase, wont that translate into a force that pushes them to the tail

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If they speed increase, wont that translate into a force that pushes them to the tail

The relationship between the acceleration the occupants of the rocket feel and the relative velocity between the Earth and Rocket doesn't have the same simple relationship in Relativity as it does in Newtonian physics.

The occupants can feel a constant force, but the actual rate at which their velocity increases will decrease as they approach c. Someone on Earth measuring their progress will see their acceleration as decreasing.

And even though the occupants will feel like they are accelerating at a constant rate, if they measure their relative velocity with respect to the Earth, they will note that the rate at which this velocity increases falls off as time goes by.

This second observation can be illustrated in the following way:

Let's say your rocket has buoys that it can drop off as it travels. Each buoy maintains the velocity the rocket had at the time it was released. The rocket accelerates to 0.1 c with respect to the Earth and drops a buoy.

It now accelerates until it is moving at 0.1c relative to the buoy. How fast is it moving with respect to the Earth? In Newtonian physics one would say 0.1c+0.1c or 0.2c. However, in Relativity, velocities don't add up that way. Instead you would have to use

(0.1c+0.1c)/(1+0.1c(0.1c)/c^2)= 0.198c

If you now drop off another buoy and accelerate up to 0.1c relative to it, you will now be moving at (0.1c+0.198c)/(1+0.1c(0.198c)/c^2)= 0.292c ( not 0.3c or even 0.298c)

Keep up the process and you get this series of velocities with respect to Earth.

0.381c

0.463c

0.538c

0.606c

0.666c

0.718c

0.763c

Now remember, at each step the rocket has accelerated until it is moving at 0.1c relative to the last buoy it dropped off. And as far as the force it feels, it can't tell any difference between any of the steps.

It doesn't matter how large each step is either ( you could accelerate to 0.01c between buoy releases, or 0.001c, 0.0001c,...), the end result is the same. You will "feel" a constant acceleration, but the difference in velocity between you and the Earth will increase at a slower and slower rate.

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