B Travel 7 Light Years at 50000km/s - How Long?

[Spockishere]

TL;DR

I'm intrigued to hear your answers on this one.

let's say i would like to drop by one of my pals on a certain planet, 7ly away. I got to 42 years but it doesn't really sound correct.

 

[Spockishere]

Just tried an other formula and got 1 year, I'm lost haha.

 

[berkeman]

Welcome to PF.

Can you show us your calculation that got you to 42 years? Did you assume any acceleration/deceleration times, or just simplified it to that speed for the whole trip?

 

[PeroK]

Summary: I'm intrigued to hear your answers on this one.

let's say i would like to drop by one of my pals on a certain planet, 7ly away. I got to 42 years but it doesn't really sound correct.

That speed is about $\frac c 6$. So, yes, about $42$ years. Although a little less.

 

[Bandersnatch]

You're going at 1/6th the speed of light w/r to the target. At that velocity, the relativistic corrections are on the order of 1%. They're pretty much irrelevant. So the answer actually is just about six times seven = 42 years. Minus maybe half a year.

 

[Spockishere]

Thanks for the answers guys.

 

[Spockishere]

Welcome to PF.

Can you show us your calculation that got you to 42 years? Did you assume any acceleration/deceleration times, or just simplified it to that speed for the whole trip?

Thanks for the warm welcome! I used this formula ( 1/(sqrt(1-v^2/c^2)). And i just simplified it to one constant speed for the whole trip.

 

[PeroK]

Thanks for the warm welcome! I used this formula ( 1/(sqrt(1-v^2/c^2)). And i just simplified it to one constant speed for the whole trip.

That's the one! It's the gamma factor. But, for $v = \frac c 6$, we have:
$$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} = \frac{1}{\sqrt{\frac{35}{36}}} \approx 1.014$$Which is not very significantly different from $1$ and implies only a $1.4 \%$ difference between Earth time and spaceship time for the journey.

 

[Grinkle]

Summary: I'm intrigued to hear your answers on this one.

but it doesn't really sound correct.

Out of curiosity, why were you doubting the results? IMO, actually doing some math before posting a question puts you in pretty exclusive club. ;-)

 

[Spockishere]

Out of curiosity, why were you doubting the results? IMO, actually doing some math before posting a question puts you in pretty exclusive club. ;-)

I wasn't really doubting the results, i just hoped they were wrong. I was curious as to how a space voyage would feel like at those distances. 42 years is a lot haha. And thanks.

 

[PeroK]

I wasn't really doubting the results, i just hoped they were wrong. I was curious as to how a space voyage would feel like at those distances. 42 years is a lot haha. And thanks.

Even at $0.5c$ the gamma factor is only about $1.15$. That's still not very significant. You need to get up to $0.8c$ where the gamma factor is $1.67$ to make a real difference.

Interstellar space travel is never going to be easy.

 

[Sagittarius A-Star]

I wasn't really doubting the results, i just hoped they were wrong. I was curious as to how a space voyage would feel like at those distances. 42 years is a lot haha. And thanks.

But you are better than Apollo 12 and Apollo 13. They even needed $0.5 ms$ more from relativistic effects, mainly gravitational time-dilation.

Source:
https://ntrs.nasa.gov/citations/19720022040

 

[BWV]

However at constant 1G acceleration then decelleration you could make the 7 LY trip in a little over 4 years ship time, but would hit a top speed of 0.97c

there are a number of calculators online for this