<p>You're actually describing the <a href="https://en.wikipedia.org/wiki/Twin_paradox" rel="nofollow">twin paradox</a>.
That's a little beyond <a href="https://en.wikipedia.org/wiki/Special_relativity" rel="nofollow">Special Relativity</a>, since the astronaut accelerates, and deaccelerates. Since Special Relativity treats only <a href="https://en.wikipedia.org/wiki/Inertial_frame_of_reference" rel="nofollow">inertial frames of reference</a>, accurate treatment would require some extension towards <a href="https://en.wikipedia.org/wiki/General_relativity" rel="nofollow">General Relativity</a>.
But you may consider two astronauts, one travelling with constant velocity towards Earth, the other one with the same (by amount) velocity away from the Earth, and then apply the formula for <a href="https://en.wikipedia.org/wiki/Time_dilation" rel="nofollow">time dilation</a> of Special Relativity to both astronauts, as an approximation, and to avoid the twin paradox.
Then you get the almost ubiquitous factor $\sqrt{1-\beta^2}$ of Special Relativity, with $b=v/c$ the ratio of the relative velocity to the speed of light. For $\beta=0.1$, hence 10% the speed of light, we get a factor of</p>

<p>$\sqrt{1-\beta^2}=\sqrt{1-0.1^2}=\sqrt{1-0.01}=\sqrt{0.99}\approx 0.9949874371$.</p>

<p>Divide 10 years by 0.9949874371, and you get 10 years plus 18.4 days on Earth.</p>

<p>For $\beta=1$ this division would fail, implying a break-down of the formulas of Special Relativity. That's why travelling with the speed of light doesn't work for astronauts respecting Special Relativity.</p>

CC BY-SA 3.0
2015-12-11T14:44:35.597Z
2015-12-11T14:44:35.597Z
Gerald
<p>So I read that if an astronaut travels at the speed of light and goes to a nearby star system , when he or she returns, he or she will have aged 10 years but 1000 years will have gone by on Earth. Travel at the speed of light is not achievable ,so I was wondering if the spacecraft was traveling at an achievable speed of 10% the speed of light , how much will the astronaut have aged and how much time has elapsed here on Earth upon the return of the astronaut ?</p>

CC BY-SA 3.0
2015-12-09T20:15:44.997Z
Relevant: https://en.wikipedia.org/wiki/Twin_paradox#Specific_example
tmwilson26
CC BY-SA 3.0
2015-12-09T21:01:28.487Z
As you suggest, nobody can travel at the speed of light, that requires infinite energy for a body with mass (that is if we assume, as all the evidence suggests, that relativity is correct). The time dilation function is here: https://en.wikipedia.org/wiki/Time_dilation#Overview_of_formulae
adrianmcmenamin
CC BY-SA 3.0
2015-12-09T22:03:24.733Z
For those too lazy to do the math:   http://www.1728.org/reltivty.htm   At 10% of the speed of light, the time dilation is about 0.5%, enough to make the clocks not match, but 6 months over 100 years.   Not much at all.   Traveling fast enough for significant time dilation would require technology that we don't currently even have a good design for.   It's very difficult.
userLTK
CC BY-SA 3.0
2015-12-10T07:54:00.660Z
This is basic special relativity. You can find the calculation all over the internet. The source you read that said "if an astronaut travels at the speed of light" is nonsense. Only massless particles can do so, and suffer infinite time dilation. No time passed in a photon's frame of reference. The effect of moving at 0.1c is small.
ProfRob
CC BY-SA 3.0
2015-12-14T19:26:22.140Z
I'm voting to close this question as off-topic because it would fit better with physics or space exploration, instead of astronomy.
James K
<space-travel>
Space Travel and length of time
Peter U
# Space Travel and length of time

(Asked by: username_0 on 2015-12-09)

So I read that if an astronaut travels at the speed of light and goes to a nearby star system , when he or she returns, he or she will have aged 10 years but 1000 years will have gone by on Earth. Travel at the speed of light is not achievable ,so I was wondering if the spacecraft was traveling at an achievable speed of 10% the speed of light , how much will the astronaut have aged and how much time has elapsed here on Earth upon the return of the astronaut ?

**Tags:** space-travel

> **Comments:**
> **username_1**: Relevant: https://en.wikipedia.org/wiki/Twin_paradox#Specific_example  
> **username_2**: As you suggest, nobody can travel at the speed of light, that requires infinite energy for a body with mass (that is if we assume, as all the evidence suggests, that relativity is correct). The time dilation function is here: https://en.wikipedia.org/wiki/Time_dilation#Overview_of_formulae  
> **username_3**: For those too lazy to do the math:   http://www.1728.org/reltivty.htm   At 10% of the speed of light, the time dilation is about 0.5%, enough to make the clocks not match, but 6 months over 100 years.   Not much at all.   Traveling fast enough for significant time dilation would require technology that we don't currently even have a good design for.   It's very difficult.  
> **username_4**: This is basic special relativity. You can find the calculation all over the internet. The source you read that said "if an astronaut travels at the speed of light" is nonsense. Only massless particles can do so, and suffer infinite time dilation. No time passed in a photon's frame of reference. The effect of moving at 0.1c is small.  
> **username_5**: I'm voting to close this question as off-topic because it would fit better with physics or space exploration, instead of astronomy.  

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## 1 answers

### Answer by username_6 on 2015-12-11. Score: 2

You're actually describing the [twin paradox](https://en.wikipedia.org/wiki/Twin_paradox).
That's a little beyond [Special Relativity](https://en.wikipedia.org/wiki/Special_relativity), since the astronaut accelerates, and deaccelerates. Since Special Relativity treats only [inertial frames of reference](https://en.wikipedia.org/wiki/Inertial_frame_of_reference), accurate treatment would require some extension towards [General Relativity](https://en.wikipedia.org/wiki/General_relativity).
But you may consider two astronauts, one travelling with constant velocity towards Earth, the other one with the same (by amount) velocity away from the Earth, and then apply the formula for [time dilation](https://en.wikipedia.org/wiki/Time_dilation) of Special Relativity to both astronauts, as an approximation, and to avoid the twin paradox.
Then you get the almost ubiquitous factor $\sqrt{1-\beta^2}$ of Special Relativity, with $b=v/c$ the ratio of the relative velocity to the speed of light. For $\beta=0.1$, hence 10% the speed of light, we get a factor of

$\sqrt{1-\beta^2}=\sqrt{1-0.1^2}=\sqrt{1-0.01}=\sqrt{0.99}\approx 0.9949874371$.

Divide 10 years by 0.9949874371, and you get 10 years plus 18.4 days on Earth.

For $\beta=1$ this division would fail, implying a break-down of the formulas of Special Relativity. That's why travelling with the speed of light doesn't work for astronauts respecting Special Relativity.


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