# Question about relativity and distance

1. Jul 13, 2016

### MelissaBlaze

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

2. Jul 13, 2016

### phyzguy

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.

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.

3. Jul 13, 2016

### Staff: Mentor

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.

4. Jul 14, 2016

### MelissaBlaze

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

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

5. Jul 14, 2016

### SammyS

Staff Emeritus
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.

6. Jul 15, 2016

### MelissaBlaze

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

7. Jul 15, 2016

### SammyS

Staff Emeritus
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.

8. Jul 15, 2016

### 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.

9. Jul 16, 2016

### 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.