Jolly Roger wrote:

The maximum speed of the ship is not limited by the exhaust velocity as the action is relative… The speed limitation is mainly one of fuel, the ship will keep accelerating forever with infinite fuel and time, however as you approach the speed of light the net acceleration drops significantly as the relative mass increases.

My Bad! Thank you. I stand corrected. I was assuming that the equation for final velocity was:

Vf = Ve,

where Vf is the final velocity and Ve is the exhaust velocity.

The correct equation is:

Vf = Ve * ln(Mi/Mf)

where ln is the natural log, Mi is the initial mass of the ship, and Mf is the final mass.

I will do some calculations with various mass ratios and post my results later.

I kicked around a few numbers. With multiple stages, the ratio can get quite high. Then it turns out that the low acceleration becomes the limiting factor. Even at an almost respectable 0.6 m/sec^2, it would take almost 6 months to get out to my brown dwarf.