Undergrad Energy contained in fuel in speed of light ship

[TeethWhitener]

The calculator got me 0.9999999999924827 for 5*10^5 light year. After that , rounding errors seems to kick in.
I'll do one myself using high precision library. I supposed you had some handy.

You're right. I must have messed up the calculation.

 

[mfb]

A constant 1 g acceleration for decades is beyond any feasibility with the universe as we know it, so that problem is purely theoretical.

A 100% antimatter/matter annihilation rocket with an I_sp of 3*10⁷ seconds (5 orders of magnitude higher than chemical rockets, 10 orders of magnitude in terms of energy density) would use about 2/3 of the ship mass as propellant per year to maintain this acceleration (as seen by the ship). Over 30 years, you need 10¹⁴ times the ship mass as propellant (likely more as you need multiple stages). A single kilogram as final ship mass would need 10¹⁴ kg of antimatter/matter, with an energy content of 10³¹ J, several billion times the global yearly energy consumption.

There is no known way to get 100% efficiency, however. In particular, some energy will be lost to neutrinos (assuming we have to use baryons). If just 50% of the energy contributes to thrust, we need 8/9 of the ship mass per year. Over 30 years, a single kilogram of ship mass will need 10²⁸ kg of matter/antimatter, or 10⁴⁵ J. That exceeds the energy released in a typical supernova by an order of magnitude and violates the rule that supernovae are always stronger.

You can scoop up matter on the way and use that as propellant - but that won't work beyond some critical (engineering-dependent) speed as scooping up the particles will slow the ship more than expelling it can accelerate it.