Which programs are used to calculate delta V and launch dates to get to other objects?

Question

I have noticed that many people here have used different programs to calculate the launch dates and delta V to get to other planets.

For example:

• https://space.stackexchange.com/a/59585/44505
• https://space.stackexchange.com/a/57738/44505
• etc...

Which programs are being used to calculate the delta V and launch dates?

Answer 1

Both linked examples use the same "program" (mine), they just show different representations & interpretations of the output data.

My "program" is a messy collection of MATLAB scripts & functions that I have developed over the past 3 or so years into a somewhat general interplanetary trajectory tool. One day I hope to clean it up enough and post it on Github to share with others.

In short, my "program" takes the following inputs:

• departure and destination planets (i.e., from Earth to Mars)
• departure dates and times-of-flight (i.e., 30-Jul-2020 & 203 days, but typically a large set of dates and TOFs)
  • from this information & using JPL NAIF's SPICE Toolkit along with a JPL developmental ephemeris (DE) you can get the state vector (position and velocity) of the planets on those dates

Performs some calculations:

• solves Lambert's problem
• patches heliocentric conic to departure and arrival planets' hyperbolic conics (patched conic approximation)
• filters out values based on user defined limits ($\Delta V$, $C3$, entry velocity, etc.)

And arrives at the following output data:

• 2 matrices of planeto-centric $v_{\infty}$ vectors, one for the departure planet and one for the arrival planet (the matrices are 2D: one dimension is departure dates, the other is arrival dates, each date combination produces a unique trajectory)
  • these are typically transposed to something more "useful" like orbital insertion $\Delta V$, entry velocity, launch C3, etc.

I wrote another answer here describing this process in few more words and also touched upon gravity assist trajectories, which my "program" also handles.

Crucially, the two "independent" variables of departure and arrival date enable the data to be represented in a contour plot, more affectionately known as a porkchop plot:

(Personal work, from another answer of mine)

I pick launch dates "visually" by looking at the low energy (low $\Delta V$) regions in the porkchop plot.

In gravity assist trajectories the filtering is more involved so I end up with a 1D set of viable trajectories so the plots look like clusters of blue dots (see here, here, here, and here).