I understand that fuel mass is a major consideration of total vehicle mass and mission cost. Considering that earth passes Mars,I was wondering; If a trajectory optimization to Mars, similar to that of the moon landing's trajectory optimization of a figure 8,was initiated at some point ahead of Mars to use both the launch to Mars' trajectory velocity and the planet's(Mars')trajectory velocity together and control the decent velocity to the planet's surface from space would optimize fuel mass, over all mission cost and transit time to Mars?


The figure-8 is probably not the most efficient way to get to Mars, but it's likely how we're going to go. As an example of a mission that didn't use it, India's MOM (Mars Orbiter Mission) spent a lot of time in earth orbit, slowly raising its orbit every time it passed perigee. This allowed, for example, a smaller rocket engine.

There is a concept called a Mars Cycler that has some interesting applications in low-fuel missions. The idea is you put a big spacecraft on an Earth-Mars trajectory that cycles between the two planets repeatedly. This larger spacecraft only needs to be launched on this trajectory once, and could be used for multiple missions. You then need to accelerate only a smaller spacecraft to rendezvous with the larger craft and eventually enter Mars orbit. This reduces the need for large spacecraft every time a crew goes to Mars, thus reducing fuel use substantially. Read more here.

The figure-8 itself was part of the free-return trajectory. It minimized fuel to return if something went wrong. Practically, all Apollo missions were on an almost-free return trajectory where only a small push would put them back onto one. A Mars free-return is possible (check out here). There were discussions of a private, two-person spacecraft doing a Mars free-return, which would essentially be a Mars flyby with people on board who need to come back home.

Trajectory optimization is complicated. You will need to make sure you use both a fuel and time optimal trajectory, which are usually competing goals! For example, there is a nearly energy-free way to get from Earth-Sun Lagrange points to Mars. Getting to those Lagrange points is lower energy than getting to Mars. Unfortunately, actually getting to Mars following this trajectory would take thousands of years. Read more here. They're really cool. So at the end of the day, fuel-optimality is not the be-all and end-all and many more constraints are needed. For that reason, it is highly likely that time-optimality giving spacecraft delta-V and thrust constraints is far more important than fuel-optimality, at least for crew missions.


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