> I am very curious what the selected family of orbits is ...
There's not much leeway, it's going to be something close to a Hohmann transfer, with the aphelion ahead of and above Mars to get to a hyperbolic capture orbit with the periareion deep in the atmosphere for (almost) direct re-entry.
This kind of orbits can be solved for arbitrary departure date and time of flight using a Lambert's problem solver and numerical optimization. Not a particularly difficult problem by modern standards.
Pure Hohmann transfer to another planet will result in inevitable collision due to relative velocity, but it's useful for lower bound estimates.
Another alternative for recurring Mars intercept is is the "Aldrin cycler" (after Buzz Aldrin) which is a free return trajectory but that is difficult when the goal is to land and take off again.
There are lots of possibilities for lower energy transfers but most of them are out of question when life support is required for humans on board.
There's not much leeway, it's going to be something close to a Hohmann transfer, with the aphelion ahead of and above Mars to get to a hyperbolic capture orbit with the periareion deep in the atmosphere for (almost) direct re-entry.
This kind of orbits can be solved for arbitrary departure date and time of flight using a Lambert's problem solver and numerical optimization. Not a particularly difficult problem by modern standards.
Pure Hohmann transfer to another planet will result in inevitable collision due to relative velocity, but it's useful for lower bound estimates.
Another alternative for recurring Mars intercept is is the "Aldrin cycler" (after Buzz Aldrin) which is a free return trajectory but that is difficult when the goal is to land and take off again.
There are lots of possibilities for lower energy transfers but most of them are out of question when life support is required for humans on board.