#### Time and distance

It gets complicated, because you're working in a gravity field, and that modifies the basic speed/time/distance/acceleration equations taught at school. Let's make it easy and assume a trip distance of 100 million kilometres and a time of 4 million seconds.

A constant-acceleration trip, ignoring the sun's gravity, would have a turn-round at the half-way mark, accelerating and decelerating under power, all the way. So 50 million kilometres in 2 million seconds.

distance = acceleration * time-squared / 2

Re-arrange: acceleration = 2 * distance / time-squared

1E11 / (4E12) = 1/40 = 2.5 cm/sec/sec

Average speed is 25 km / sec for the whole trip, and must be the same for each half, which gives a maximum speed of 50 km / sec. Aerobraking is so fast that the time taken can be ignored for our purposes, and the same for a chemical booster. We'd need a heat shield that could stand to an aerobraking speed some five times faster than Apollo.

Yes, I know the reality is more complicated. Not only there is the gravity of the sun, there is the difference in the orbital speed of Earth and Mars. If you want more rigorous math, and pretty pictures, I recommend http://www.projectrho.com/rocket/

I'll wait for the torchship.