## How ‘Porkchop Plots’ Determine Earth-to-Mars Trajectories | #NASA

If you listened to Episode 1 of NASA’s newest podcast Rocket Ranch you might have heard the term ‘porkchop plot’ used a few times. This whitepaper co-authored by JPL Mars Advanced Studies and Program Architecture Office Manager Charles W. Whetsel describes what porkchop plots are and how they assist “ballistic trajectories between two [celestial] bodies.”

Plotting interplanetary trajectory parameters such as C3 and V∞ in launch-date/arrival-date space and tracing isometric lines are a valuable mission design tool that are used in optimizing the trajectories for most interplanetary missions. The most important energy parameters (C3 and V∞) typically create bi-lobed characteristic shapes which have earned these plots the colloquial nickname of “porkchop” plots. Porkchop plots aide early mission designers in selecting launch dates, in calculating launch energies and ΔV budgets, and visually optimizing trajectories. Launch periods are designed by applying constraints on some parameters (e.g. launch declination, arrival dates, launch period duration, entry speed, sun angles) while simultaneously minimizing others (e.g. launch energy, Mars orbit insertion (MOI) ΔV).1,2,3

Each opportunity (~26 months for Earth to Mars) a new porkchop plot is created with similar characteristics, but with different minima (on either side of the central ridge), minima locations, ridge width, and lobe shapes. In this paper we investigate how the orbital characteristics of Earth and Mars affect the nature of the porkchop plots and how they compare to ideal (circular, coplanar) and optimized (allowing launch, arrival, and transfer time to be free parameters) porkchop plots. We also explore what defines a “good” opportunity for Mars missions and to what extent certain characteristics repeat with Mars cycles (approximately 15 years or 7 opportunities) and super-cycles.

Lambert’s Theorem can be used to calculate the orbital parameters of the trajectory between any two points for a given time of flight (TOF). This means that for any launch date at Earth (which specifies location 1) and arrival date at Mars (which specifies location 2 and TOF), there exists a conic trajectory connecting the two. Plotting contours of the relevant parameters of the connecting trajectories against combinations of launch date and arrival date create a two-lobed chart known as a porkchop plot. While traditional porkchop plots often portray the specific departure energy and hyperbolic excess arrival energy individually (C3 and V∞ respectively), for the purposes of this investigation, the authors chose to focus on a combination of these parameters, termed the “total transfer ΔV”. Figure 1 shows total transfer ΔV (defined in Equation 1, below) for the 2018 Earth-to-Mars opportunity.

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