Transfer to Mars In 2022, SpaceX intends to land humans on Mars using its new rocket, BFR, and interplanetary spacecraft, BFS. To prepare for this mission, an uncrewed BFS will fly to Mars in 2020, validating the life support, EDL, and in-situ propellant production systems critical to the success of the 2022 crewed mission. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an Original Essay To simulate a worst-case life support requirement, BFS will be launched on a longer transfer duration trajectory than a typical crewed BFS mission. This longer trajectory, in addition to ensuring that BFS can withstand a longer-than-expected period of interplanetary flight, will also reduce delta-V requirements, saving more fuel for Mars EDL. Increasing fuel margins for the EDL helps ensure that experiments critical to the 2022 crewed mission, such as the Sabatier reactor that will produce liquid methane fuel for the BFS return to Earth, will reach the surface safely. To determine an optimal launch date in the 2020 transfer window, departures have been taken into account: arrivals starting April 1, 2020 and up to [date] and arrivals starting from September 28, 2020 and up to [date] . Furthermore, the trajectories were constrained to require no more than 500 and no less than 45 days of transfer time between Earth and Mars. From the resulting diagram, shown in Figure 1, a nominal human mission in the 2020 window would launch 100 days after April. 1, on July 10, 2020, and will arrive at Mars 90 days later on September 28, on December 27, 2020. These dates were selected to provide a nominal flight time of 170 days while minimizing the delta-V required for interplanetary transfer . Following the 2020 test launch, this trajectory will be changed to instead arrive 120 days after the start of the transfer window, on January 26, 2021. The July 10, 2020 launch date will not be changed from the nominal manned trajectory. This transfer will result in a hyperbolic excess velocity of 2.9012 km/s and a C3 of 13.7455 km2/s2. The flight time for this trajectory will be 200 days, which will allow testing of life support systems with an acceptable margin above a nominal trajectory. Table 1 shows these values ​​compared to those of a nominal crewed flight in 2020. The Lambert solver returns a tm of 1 for both the nominal crewed and uncrewed test trajectories, indicating that both are short transfers distance. J2 Perturbation The J2 perturbation is caused by the asphericity of the Earth. The Earth, like most rotating bodies, has a bulge around its equator that creates gravitational effects on orbiting satellites. This effect manifests itself in a gradual shift in the longitude of the ascending node and the subject of the periapsis of the orbit. This is shown in the attached Matlab plots, where you can see that the longitude of the ascending node of the A1 orbit decreases linearly over the course of four days. This is different from the two-body hypothesis, where the longitude of the ascending node would remain constant over time. The rates of change of both the longitude of the ascending node and the topic of the periapsis vary depending on the other orbital elements. Plots of both rates of change show that the apsidal and nodal regression rate approaches zero as the inclination approaches 90°. This is clear in the nodal regression plot but is obscured by a peak in the plot.