# Full Mission Analysis elements?

I am trying to complete a full trajectory design and analysis for a low thrust interplanetary mission to Mars. Right now, computing optimal trajectories from Earth to Mars for a number of dates and other such parameters is complete. I can compile these into a low-thrust "porkchop" plot easy enough. My question is, what other elements do I need to consider for the trajectory design in order for this to be considered a "full" analysis? For example, off the top of my head I can think of, launch c3's, arrival c3's, time of flight constraints, power constraints. Out from those is there any crucial elements I am missing?

Edit I thought of another. I am currently approximating the 2-D case, so obviously for a "full" analysis, I will need to increase the case to 3-D.

• You might consider adding a "duty cycle" parameter to the low-thrust system. If you compute a trajectory assuming the system is thrusting 100% of the time, then any interrupton of thrusting, no matter how temporary, causes falling off of that trajectory. Trajectories used by NASA low-thrust missions so far, such as Dawn (see dawn-mission.org/mission/Dawn_overview.pdf), always include mission margin to allow for unexpected loss of on-thrust time, and an additional duty cycle (~95%) to allow a few hrs/week for such things as telecom sessions. – Tom Spilker Jul 28 '18 at 18:04
• Could you tell what exacltly phases of your mission use low-thrust propulsion? (Earth-depart acceleration, trans-martian acceleration, Mars orbit insertion, Mars orbit lowering) – Heopps Jul 30 '18 at 12:41
• Right now I am considering all phases, though if the project gets unwieldy as a result I'll more than likely change that – Harvey Rael Jul 30 '18 at 12:53

You've taken on a daunting—but not impossible!—task. There are a lot of aspects and issues to be addressed before a mission analyst would look at your work and say, "Yes, this trajectory is actually flyable."

There are a couple of good reference books available, such as Jim Wertz's Space Mission Analysis and Design, and David Vallado's Fundamentals of Astrodynamics and Applications. The most recent editions of these books are really expensive (hundreds of US dollars—bleah!) but older editions can cost a lot less and would probably be fine for your purposes.

Since you're working in the inner solar system I will assume that the low-thrust propulsion system you're using is a solar electric propulsion (SEP) system. One characteristic of low-thrust trajectories is that the trajectory design and the spacecraft design are joined at the hip: relatively minor increases in spacecraft mass can make a trajectory unflyable without changes in the SEP system design.

You've already identified the 3-D aspect of the problem. Doing it 2-D, it might appear that you could launch from Earth to, say, Venus, at any time, and arrive ~1/2 orbit later, with a launch C3 that varies a little but not hugely. But once you go to the full 3-D treatment you quickly see that Venus's orbit inclination with respect to the ecliptic makes a huge difference in the timing, duration, and C3 of launch windows. The same is true for Mars and the other planets.

Other seemingly minor aspects of solar system dynamics can wind up having big effects on an interplanetary trajectory. One important example is small forces, which come in a variety of flavors, including solar light pressure, radiation pressure from hot components like RTGs or the backs of solar arrays, reaction forces due to asymmetrical outgassing of spacecraft components or propellant/pressurant leaks, and gravitational accelerations due to other massive solar system bodies, like the moon, Jupiter, Venus and Saturn (I assume you're already handling the sun, Earth, and Mars!).

Solar light pressure is truly significant. If your spacecraft is similar to the Dawn spacecraft, running 90 mN of thrust on ~1,000 kg mass, its propulsive acceleration is ~$9\times {10^{-5}} m/{s^{2}}$ (of course varying as remaining propellant mass decreases). At 1 AU, solar light pressure on an area of one square meter, assuming no reflection at all, is ~$4.5\times {10^{-6}}$ N (~$4.5 \mu$N). Dawn's 36.4 $m^{2}$ of solar arrays would produce ~160 $\mu$N of force if perfectly absorbing, which they're not. That 160 $\mu$N is about 0.2% of the SEP system's propulsive force, and that is significant. Partially reflective arrays will produce even greater force. And as if that isn't headache enough, if the arrays aren't pointed exactly at the sun the reflection will produce a component of force not aligned with the direction from the sun. A full mission analysis must include light pressure effects!

When the spacecraft isn't near the moon, Earth, or Mars, after the sun Jupiter is the Big Dog of the solar system in terms of gravitational effects. When Venus is as close to Earth as it can get, its gravitational acceleration at Earth is still only ~2/3 that of Jupiter at its closest, and most of the time it's much less than that. Saturn's maximum is ~1/10 of Venus's maximum, Uranus's is ~4% of Saturn's, and Neptune's is ~half of Uranus's. At its nearest to Earth, Jupiter's gravitational acceleration at Earth is ~$3\times {10^{-10}} m/{s^{2}}$, a factor of ~1/300,000 of the propulsive acceleration — small, but for long flight times it becomes important.

There are multiple SEP-related issues.

For a SEP system heliocentric distance becomes an issue. Sunlight intensity falls off as 1/$r^{2}$ so the output of solar arrays falls off as well. If you design the power system to supply full power to the SEP thruster at 1 AU, decreasing as heliocentric distance increases, the thrust produced will decrease too, and the specific impulse will probably decrease as well. The thruster's power table would give those power/thrust/specific-impulse curves.

This brings up another point: hardware-specific SEP mission designs. Real SEP hardware has characteristics such as the power table just mentioned. If you assume a theoretical thruster with an Isp that doesn't vary with power you might be in for some criticism: "No real SEP system behaves like that."

One way around that is to design the system such that the thruster runs at full power even at the largest heliocentric distance. But this means that the arrays will be larger and heavier, and at 1 AU you'll be way over-designed, so you'll either need the added mass of shunt radiators to dump the excess power, or let the arrays heat up. Going to Mars it might be worth it. Going to Jupiter? Almost certainly not.

Mission designs always include margins for everything performance-related. Margins on the amount of electric power required and produced. Margins on the mass of propellant required. Margins on the thrust produced. To echo my comment from a few days ago: "You might consider adding a "duty cycle" parameter to the low-thrust system. If you compute a trajectory assuming the system is thrusting 100% of the time, then any interrupton of thrusting, no matter how temporary, causes falling off of that trajectory. Trajectories used by NASA low-thrust missions so far, such as Dawn (see dawn-mission.org/mission/Dawn_overview.pdf), always include mission margin to allow for unexpected loss of on-thrust time, and an additional duty cycle (~95%) to allow a few hrs/week for such things as telecom sessions."

I can't claim that this answer is complete. That would take a book! (Like the references I gave above) I haven't discussed the secondary propulsion system (an RCS/attitude-control system) and trajectory perturbations it can cause, the interplanetary magnetic field and its effects requiring use of the secondary propulsion system, propellant requirements (and margins!) for that system, just to name a few. But this should give you a feel for the task, and the references (or other references other folks might recommend) can fill in the holes.

If you get this to work, I can only begin to imagine the sense of satisfaction and accomplishment you'll get from it! They pay people at JPL big bucks to do this kind of work. Good luck!

• This was an excellent answer Tom! I understand the nature of the question was vaguer than is usually liked on Stack, so I understand there's a limit to the info you can provide, but given that, you have done more than exceeds expectations! I knew the trajectory was a major focus, but I wanted a feel for the other things that go into a "Mission Analysis". Again, thank you for the answer that is absolutely what I was looking for, and I will let you know how I get on! – Harvey Rael Jul 30 '18 at 12:10