How long will it take me to get to Mars?

I am a spaceship travelling from Jupiter under constant acceleration of 1g (9.8meters/sec2) provided by fusion drive to Mars. I departed at exactly the same time as an identical ship, travelling the same route but at 0.3g

How long will it take each of us to arrive at Mars? We are both aiming to stop at low-Earth orbit and transfer to surface (not just fly by).

Looking for answers with shortest and longest travel times determined by maximum and minimum possible distances between the two planets.

• Are you stopping there or just powering on through? "Arrive" is ambiguous. – Organic Marble Nov 13 '18 at 18:04
• Where and when are Jupiter and Mars in their orbits? Their relative positions may change the answer significantly, especially in the 0.3g case. – Jack Nov 13 '18 at 22:14
• @Jack Considering the constant acceleration, tricky Hohman transfer and other orbits don't count. Practically a linear acceleration (and later deceleration) could be calculated. – peterh Nov 14 '18 at 1:02
• these accelerations from your fusion drive are 1000x bigger than the Sun's gravitational acceleration, even at 1 AU, so solutions to this problem could be closely approximated with $x=\frac{1}{2}at^2$ to about three decimal places. For example, with 1 g acceleration for ~3 days you get to 1% the speed of light, ~3 more days decelerating an you are near Mars. The Sun's gravity almost doesn't matter. By "stop at low-Earth orbit" do you mean low-Mars orbit instead? – uhoh Nov 14 '18 at 1:45
• @Chairman Yang See the discussion in Heinlein's "Have Spacesuit, Will Travel" for how to do simple constant-boost calculations. – Organic Marble Nov 14 '18 at 13:53