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A MATLAB Script for Creating Pork Chop Plots of
Ballistic Earth-to-Mars Trajectories
This document describes a MATLAB script called porkchop that can be used to create and plot
interplanetary “pork chop” plots for Type I and Type II Earth-to-Mars trajectories. These plots illustrate
the behavior of launch energy (C3L), right ascension (RLA) and declination (DLA) of the departure
hyperbola, time-of-flight, and arrival v-infinity, DLA and RLA, and total heliocentric scalar delta-v for a
range of user-defined launch and arrival calendar dates.
The data required for these contour plots is created by solving the heliocentric, two-body “patched-
conic” Lambert problem. A patched-conic trajectory ignores the gravitational effect of both the launch
and arrivals planets on the heliocentric trajectory. Type I trajectories are characterized by heliocentric
Earth-to-Mars transfer angles which are less than 180 degrees while Type II trajectories have transfer
angles greater than 180 degrees. Pork chop plots are typically used for preliminary mission analysis.
The angular coordinates of the launch hyperbola (DLA and RLA) are provided in the Earth mean
equator and equinox of J2000 (EME2000) coordinate system. The angular coordinates of the arrival
hyperbola (DLA and RLA) are provided in the Mars mean equator and IAU node of epoch coordinate
system. The total delta-v is the sum of the heliocentric departure and arrival scalar delta-v values. The
porkchop script can be easily modified for other departure and arrival planets.
Typical user interaction
The following is typical user interaction with this MATLAB application. This example creates typical
data and plots for the Phoenix 2007 mission. In the following discussion the user inputs are in bold
courier font and all explanations are in times italic font.
program porkchop
< interplanetary pork chop plots >
The first user input is the nominal launch calendar date in the order month, day, and year. Please be
sure to include all four digits of the calendar year.
nominal launch date
please input the calendar date
(1 <= month <= 12, 1 <= day <= 31, year = all digits!)
? 9,25,2007
The next user input is the calendar date of the nominal arrival at Mars.
nominal arrival date
please input the calendar date
(1 <= month <= 12, 1 <= day <= 31, year = all digits!)
? 8,15,2008
The next input is the analysis “span” centered about the nominal launch date. This number should be
input in days. The software will create data over the range (nominal – span) and (nominal + span).
please input the launch date span in days
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