<p>We want it so that <span class="math-container">$1 \text{ year at the speed of x% of c} = \dfrac{10^{10}}{80} \text{ stationary years}$</span>. The Lorentz factor (in terms of c) is <span class="math-container">$\gamma=\dfrac{1}{\sqrt{1-v^2}}$</span>. Solving for <span class="math-container">$v$</span> with <span class="math-container">$\gamma =  \dfrac{10^{10}}{80},$</span> we get  <span class="math-container">$v=0.999999999999999968c = 299792457.999... \text{m}\cdot\text{s}^{-1}$</span>. This is definitely impossible, as the energy requirements are astronomically large: <span class="math-container">$$5572282108577709241 \text{J}\cdot c^{-2} \cdot 125000000 =696535263572213655125000000 \text{J} = 7.75 \cdot 10^9 \text{ kg of mass converted to energy}$$</span></p>
<p>This is definitely unrealistic, and is a probably impossible feat to complete. It would be better to study more and more stars instead of exploiting time dilation to view a single star for billions of years.</p>

CC BY-SA 4.0
2021-04-21T17:53:35.547Z
How do you travel that fast *and* stay anywhere near the star you want to study? Or if not staying near it, how do you study it given the redshift the speed implies.
ProfRob
CC BY-SA 4.0
2021-04-21T19:44:18.343Z
While the answer is right, the energy demands do not rule it out (one can in principle imagining an advanced civilization wasting massive resources on it). A better implausibility argument is that the blueshift of the CMB turns it into gamma rays, and they will brake the craft even if they do not fry it.
Anders Sandberg
CC BY-SA 4.0
2021-04-21T15:49:40.220Z
2021-04-21T15:49:40.220Z
WarpPrime
<p>Humans live for about 80 years. A star, however, lives from 1 million to trillions of years, depending on its mass. If humans want to have a detailed study of the life of a <span class="math-container">$1 M_\odot$</span> star, how fast would they have to travel, and would it be viable?</p>

<star><general-relativity><stellar-evolution><time-dilation>
How fast would an observer have to travel in order to be able to study an entire star's life in one human lifetime?
WarpPrime
# How fast would an observer have to travel in order to be able to study an entire star's life in one human lifetime?

(Asked by: username_0 on 2021-04-21)

Humans live for about 80 years. A star, however, lives from 1 million to trillions of years, depending on its mass. If humans want to have a detailed study of the life of a $1 M\_\odot$ star, how fast would they have to travel, and would it be viable?

**Tags:** star, general-relativity, stellar-evolution, time-dilation

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## 1 answers

### Answer by username_0 on 2021-04-21. Score: 1

We want it so that $1 \text{ year at the speed of x% of c} = \dfrac{10^{10}}{80} \text{ stationary years}$. The Lorentz factor (in terms of c) is $\gamma=\dfrac{1}{\sqrt{1-v^2}}$. Solving for $v$ with $\gamma = \dfrac{10^{10}}{80},$ we get $v=0.999999999999999968c = 299792457.999... \text{m}\cdot\text{s}^{-1}$. This is definitely impossible, as the energy requirements are astronomically large: $$5572282108577709241 \text{J}\cdot c^{-2} \cdot 125000000 =696535263572213655125000000 \text{J} = 7.75 \cdot 10^9 \text{ kg of mass converted to energy}$$

This is definitely unrealistic, and is a probably impossible feat to complete. It would be better to study more and more stars instead of exploiting time dilation to view a single star for billions of years.

> **Comments:**
> **username_1**: How do you travel that fast *and* stay anywhere near the star you want to study? Or if not staying near it, how do you study it given the redshift the speed implies.  
> **username_2**: While the answer is right, the energy demands do not rule it out (one can in principle imagining an advanced civilization wasting massive resources on it). A better implausibility argument is that the blueshift of the CMB turns it into gamma rays, and they will brake the craft even if they do not fry it.  

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