# Calculating hyperbolic orbit elements for interplanetary intercepts

As part of a final year project at university I'm currently trying to simulate an interplanetary transfer between Earth and Mars for a manned mission. The ultimate aim is to use NASA's GMAT to simulate the mission and calculate the detailed orbital elements at each point of the mission as well as $\Delta v$ requirements etc...

We've narrowed down our departure window to 26 Jun 2035, taken from the Trajectory Browser webpage, also by NASA. The issue I've now come across is that to simulate the orbit within GMAT we need a lot more detail than the Trajectory Browser provides.

Other than GMAT, is there any software which I can input my current parameters (departure date, parking orbit, transfer time, dV) and get out the hyperbolic elements of that transfer? For simulation in GMAT I need either SMA/RAAN/INC/ECC/AOP/TA or $\Delta v$ in VNB components. If not, is it possible to calculate them by hand?

I have asked a similar question on the GMAT forum, but that seems to have died a bit of a death recently.

• That sounds very interesting, are the results going to be published somewhere? – mike Apr 24 '17 at 13:39

How much do you know about programming? If you're willing to get your hands somewhat dirty by looking at a few examples and coding up your own script, biased-me would recommend you use the software I developed and validated last year for my thesis: space mission design (or smd). I have used it successfully to design literally dozens (if not hundreds) of interplanetary trajectories between the Earth and Mars (and back), but also to design a trajectory to Neptune using resonant orbits and several gravity assist maneuvers.

Concerning your specific project though, if I may, I would recommend doing an initial analysis using a tool like mine to find the cheapest $\Delta v$ trajectory from Earth to Mars, and then plugging in the returned values as $C_3$, right ascension and declination of launch into GMAT, and using GMAT to iterate and optimize these values. Also note that you don't need the delta-V expressed in the VNC frame: the C3, DLA and RLA values are enough if you assume that you spacecraft will be sent on an interplanetary trajectory by the launch vehicle.

I suspect this sounds complicated at first sight: there should be a GMAT tutorial on most of this, and the rest should be covered by lab assignments of the University of Colorado at Boulder "Space Mission Design" 6008 class of 2017. I'm pretty sure these assignments are available for free online.

A great piece of software is called Orbiter, and can help educate in a very hands-on manner the exact procedures for such a mission.

• this is not an answer to this question. – JCRM Nov 28 '17 at 11:10