How long does it take to travel 500 light years?

Mar 18, 2016

$242 , 718.447$ years (3dp)

Explanation:

This depends on what is doing the traveling, obviously if it was light travelling, then 500 years! But I'm guessing you want some sort of spacecraft.

To escape the sun's gravity, a rocket has to exceed 618 km per second, so let's take this as the speed of out rocket.

The speed of light is about 300,000 km (or $300 , 000 , 000$ m) per second, so in a year, light travels $300 , 000 \times 3 , 600$ (seconds in an hour) $\times 24$ (hours in a day) $\times 365$ (days in a year)
Which gives us 9460800000000 (or $9.4608 \times {10}^{12}$)

So then multiply this by $500$
$9.4608 \times {10}^{12} \times 500 = 4730400000000000$ ( or $4.7304 \times {10}^{15}$)

So that is how far we have travelled.
When $t = t i m e$, $d = \mathrm{di} s \tan c e$ and $s = s p e e d$,
$t = \frac{d}{s}$

So, we need to carry out the following calculation:
$4730400000000000$ km $/ 618$ km/s$= 7654368932038.835$ seconds (3dp)

Divide this by seconds in a hour, hours in a day and days in a year
$\frac{7654368932038.835}{3 , 600 \times 24 \times 365} = 242718.447$ years (3dp)

Hope this helps; let me know if I can do anything else:)
A big thank you to AO8 for helping me with this!