There's no stupid questions, only stupid answers.

There are, however, questions that do not show any research effort @DiegoSánchez - space is not about going high, it's about going fast and "stopping" isn't going fast.

You should play Kerbal Space Program.

What do you mean by "stop"? Do you mean remain stationary relative to the Sun or do you simply mean to stop thrusting?

@DiegoSánchez. There are many stupid questions: everything can be stupid. This question just isn't one.

You have to match both position and velocity, so you want to get there right when Mars does and be going roughly the same velocity. The length of the trip will, of course, be different for different departure times...you want to leave Earth at a time when Mars will be closer to your departure point when you arrive. It's a 3-way tradeoff, usually optimized for fuel consumption more than other factors. (A faster and safer way would be to cruise at 1G most of the way, just changing the thrust direction, but that's a LOT of fuel.)

@JCRM "questions that do not show any research effort" and those are stupid questions.

Minus the nonsense about stopping (because there is no such thing as absolute position in space thus no such thing as absolute stop) this is basically SpaceX's plan of going to Mars - schedule rocket launches so that we launch when intercepting Mars uses the least amount of energy

@CristobolPolychronopolis: re "cruise at 1G most of the way", how does the thrust-related apparent gravity change over the course of a typical Mars trajectory? and what are the human-factors implications of that?

@smci It doesn't. You can do a constant-acceleration trip for any value of acceleration, for wildly different fuel usage and transit times. This is called a Brachistochrone ("lowest time") transfer. If you can do constant 1G thrust, the optimal trip to Mars would take about 3000 km/s dV and take about four days. Needless to say, this is in a completely different ballpark than the 3 km/s dV and 9 months or so for the Hohmann transfer :)

@Luaan: I'm obviously asking how thrust-related apparent gravity changes over the course of a typical (Hohmann) Mars trajectory, not the totally uneconomical constant-1G-acceleration... I'm simply wondering whether they make any human-factors tradeoffs in the acceleration profile (other than never exceeding some maximum acceleration).

@smci It's still extremely simple. A Hohmann transfer spends the vast majority of time in free fall (the thrust is only active for a few minutes, and the whole trip takes about nine months). A brachistochrone spends the whole time under constant acceleration.

@Luaan: so, 9 months' muscle and brain degradation for the crew. Then 0.38 Earth gravity for a couple of years. Then 9 months back. I expect they would add a spinning-wheel section for human factors, then.

@smci there's some evidence that people can spend that long in free-fall without long term ill effects. I can't see it being much fun, though. Radiation shielding would seem to be more important for long term health than a centrifuge.

@smci Yup. That's exactly why Aldrin cyclers sound like such a good idea - you can afford much more comfortable quarters for the nine month trip, and you only have to pay for them once. If you actually do a trip on every cycle, the cost of the cycler itself quickly becomes negligible.

@Luaan: Ahh. Aldrin cycler: outbound Earth-Mars in 4.8 months, 16 months later, 4.8 months back. And that only takes 4.8 months, compared to 9 months for Hohmann transfer. And we could have a nice radiation-shielded spinning-wheel for sleeping and exercise.

@RonJohn Just playing Devil's Advocate here... no where in either tour or help center does this Exchange require "showing research effort" - Perhaps one or both should be updated to fully explain expectations?

@CGCampbell that should probably be aimed at JCRM.

@user253751 I have sometimes wondered if reading a disclaimer about KSP should be required to use the orbital-mechanics tag.