Question about relativity and distance

[MelissaBlaze]

If someone left the Earth on a spacecraft traveling .99% the speed of light for a distance of one light year, and time slowed on the spacecraft relative to the earth, approximately how much time would the person on the spacecraft experience when arriving at the destination? (I'm leaving out acceleration to simplify the question.) Since observers from the Earth would see the spacecraft arrive one year after it left, and they would observe time running slower on the spacecraft through the entire trip, it seems that the people on the spacecraft would only experience a short amount of time when they arrive.
If the spacecraft was able to instantly stop and turn around, two years would have passed on the Earth when they arrived home. This would mean that only a short amount of time would have passed for the crew of the spacecraft .
I remember watching a science show a few years ago where they said if you could travel at the speed of light, you would be able to go anywhere in the universe instantaneously, from your own perspective, although your destination may no longer exist because of the amount of time that may have passed for the rest of the universe. If true, this should answer my question, but I'm not confident that my memory is correct.

 

[phyzguy]

If someone left the Earth on a spacecraft traveling .99% the speed of light for a distance of one light year, and time slowed on the spacecraft relative to the earth, approximately how much time would the person on the spacecraft experience when arriving at the destination? (I'm leaving out acceleration to simplify the question.)

The time dilation factor is \gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} . If v = 0.99 c, then γ = about 7. So they would experience about 1/7 of a year.

Since observers from the Earth would see the spacecraft arrive one year after it left, and they would observe time running slower on the spacecraft through the entire trip, it seems that the people on the spacecraft would only experience a short amount of time when they arrive.
If the spacecraft was able to instantly stop and turn around, two years would have passed on the Earth when they arrived home. This would mean that only a short amount of time would have passed for the crew of the spacecraft .

Correct. About 2/7 of a year, or about 3.5 months.

I remember watching a science show a few years ago where they said if you could travel at the speed of light, you would be able to go anywhere in the universe instantaneously, from your own perspective, although your destination may no longer exist because of the amount of time that may have passed for the rest of the universe. If true, this should answer my question, but I'm not confident that my memory is correct.

It's not possible for a massive object (like a human being) to travel at the speed of light. You can get arbitrarily close, but you can't attain the speed of light.

 

[Evo]

If someone left the Earth on a spacecraft traveling .99% the speed of light for a distance of one light year, and time slowed on the spacecraft relative to the earth, approximately how much time would the person on the spacecraft experience when arriving at the destination? (I'm leaving out acceleration to simplify the question.) Since observers from the Earth would see the spacecraft arrive one year after it left, and they would observe time running slower on the spacecraft through the entire trip, it seems that the people on the spacecraft would only experience a short amount of time when they arrive.
If the spacecraft was able to instantly stop and turn around, two years would have passed on the Earth when they arrived home. This would mean that only a short amount of time would have passed for the crew of the spacecraft .
I remember watching a science show a few years ago where they said if you could travel at the speed of light, you would be able to go anywhere in the universe instantaneously, from your own perspective, although your destination may no longer exist because of the amount of time that may have passed for the rest of the universe. If true, this should answer my question, but I'm not confident that my memory is correct.

Is this homework, or for that "story' you said you are writing? Because this is unacceptable for homework and in the wrong forum for help with story writing.

 

[MelissaBlaze]

Thank you for the confirmation phyzguy. This helps a lot.

Evo, sorry, I won't ask anymore questions here.

 

[SammyS]

If someone left the Earth on a spacecraft traveling .99% the speed of light ...

I believe you meant that this someone was traveling at 99% of the speed of light, i.e. 0.99c .

0.99% of the speed of light will not produce significant time dilation.

 

[MelissaBlaze]

You are correct. I was thinking 99.9% but I guess my brain had a disconnect with my fingers :)

 

[SammyS]

You are correct. I was thinking 99.9% but I guess my brain had a disconnect with my fingers :)

Following what @phyzguy said, 99.9% of c gives about 1/22 of a year, i.e. about 16 days.

Taking that further, 99.99% of c gives about 1/70 of a year, i.e. about 5 days.

 

[MelissaBlaze]

Wow, such a small difference in speed makes such a large difference in time. I know the power required for that difference in speed would not be small though.

 

[Kaura]

Following what @SammyS said, 99.999% of c gives about 1/224 of a year, i.e. about 1 day 15 hours.

Taking that further, 99.9999% of c gives about 1/707 of a year, i.e. about 12 hours 24 minutes.

Taking that even further, 99.99999% of c gives about 1/2236 of a year, i.e. about 3 hours 54 minutes.