You are behind the times on physics advancements buddy! Thanks to the recently discovered concept of relativistic time dilation, a 5000 light year trip at the speed of light will take literally 0 seconds of your lifespan. More practically, travelling in a starship that accelerates at 1G to the halfway point, turns around and decelerates to the destination, you can reach ridiculous distances within a single human lifetime:
shipboard time | distance | earth time |
---|---|---|
1 year | .263 LY | 1.05 Y |
2 years | 1.13 LY | 2.37 Y |
3 years | 2.82 LY | 4.35 Y |
4 years | 5.80 LY | 7.50 Y |
5 years | 10.9 LY | 12.7 Y |
10 years | 166 LY | 168 Y |
15 years | 2199 LY | 2201 Y |
20 years | 28.8 kLY | 28.8 kY |
25 years | 380 kLY | 380 kY |
50 years | 149 GLy | 149 GY |
100 years | 22.8 ZLy | 22.8 ZY |
This is the formula to calculate the distance and time:
x(τ) = c**2/a [cosh(τ a/c) - 1]
t(τ) = c/a sinh(τ a/c)
a = 9.8 m/s
c = 3e8 m/s
The formula is hyperbolic, which is why travel distance is not a linear relation of travel time. E.g. given τ = 10 years:
x = 3e8**2/9.8 * (cosh(60*60*24*365*10/2 * 9.8/3e8) - 1) * 2 / (3e8 * 60*60*24*365)
= 166 light years
t = 3e8/9.8 * sinh(60*60*24*365*10/2 * 9.8/3e8) * 2 / (60*60*24*365)
= 168 years