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As the team responsible for the trajectory of the Mission from Earth to Mars, we considered many options for the transfer. We thought about the number of flights to send, the time required to complete the transfer, the power needed to accomplish the transfer (measured in delta V), and the costs involved. First, looking as a whole at all of the factors involved in an interplanetary flight, we came to the conclusion that attempting to send the human crew, all of their survival gear, and all of the scientific equipment in one flight would require vast quantities of power. As the amount of fuel needed as well as the cost of the mission are directly proportional to the delta V needed to accomplish the mission, we decided to search for a more feasible option. In our research, we learned of several kinds of possible transfers from Earth to Mars. Transfers based on conic sections were the most common type of transfer we read about. A bi-elliptic transfer is one in which two ellipses, both with the sun as one focus, are drawn, one tangent to Earth's orbit, and one tangent to Mars' orbit. At the point where the two ellipses intersect, the vehicle's rockets are fired, changing the vehicle's course from one elliptical orbit to the other. A variation on this transfer is the bi-parabolic transfer, in which the radius of the ellipse goes to infinity. This requires little to no delta V, but is only a theoretical trajectory, as the time of transfer is infinity. A transfer modeled on a single ellipse that intersects both earth and Mars orbits can also be used. A single ellipse transfer that is tangent to both earth and Mars' orbits is known as a Hohman transfer. We also considered planetary flyby transfers. In this kind of transfer, the vehicle is launched from earth to either Venus or the Moon. The vehicle then flies around Venus or the Moon, "borrowing" energy from the other mass's gravitational field. A final type of transfer is the spiral transfer. A low thrust ion propulsion engine applies continuous thrust to the ship, causing it to spiral slowly from low earth orbit until it reaches escape velocity. Once escape velocity is attained, the vehicle travels from Earth to Mars, and slowly spirals into Mars' gravity well. We then defined what characteristics we needed in each transfer. For the first transfer we need only to minimize the delta V to the lowest reasonable value. For the second transfer, the human transfer, we again wanted to decrease delta V, but we also recognized the need for a quicker time of transfer. In addition, we wanted to choose a free-return trajectory, one that, should the vehicle fail to enter Mars, would be capable of returning to the Earth with the crew. With these criteria in mind, we first eliminated the flyby transfers. A flyby past the moon gave no appreciable decrease in delta V. A flyby past Venus increased the time of transfer greatly, and also brought the vehicle too close to the sun for our safety standards. A Venus flyby would subject delicate scientific equipment and human crewmembers to unreasonable extremes of heat and other radiation, and also increased the likelihood that a solar flare would disturb the trajectory of the vehicle. We then examined the spiral transfer. According to our reading, a spiral transfer required little delta V, but had a time of transit that was longer than anything we felt was acceptable for a human flight. We decided that the savings in delta V were worth the time trade-off for the non-human flight. We then looked at the possible elliptical transfer for human flight. The bi-parabolic we immediately eliminated, because although the delta V was close to zero, the time of transit approached infinity, and this was unacceptable for both manned and unmanned flights. The bi-elliptical we also ruled out, because its delta V was lower than a single-ellipse transfer only when the radius of orbit for the outer planet was more than 15.58 times the radius of orbit for the inner planet. The ratio of Mars' radius of orbit to that of the Earth is approximately 1.5. Also, the bi-elliptical transfer gave us no time benefit. Of the single elliptical transfer, a Hohman transfer is the lowest energy transfer, but a larger ellipse would provide a free return trajectory. We calculated the delta V for both kinds of transfers and consulted the team responsible for vehicle design and propulsion. We finally came to the conclusion that although a free return trajectory was desirable, the large increase in delta V that it caused was not feasible. If a mishap occurs and the vehicle does not enter Mars on the Hohman transfer, there are still large quantities of fuel aboard the ship. The crew would be able to divert the fuel intended for landing on Mars, lift-off, and flight home to the purpose of correcting the ship's orbit such that it would return to the Earth. In doing our calculations we made several assumptions. First, on the advice of an MIT professor, we made the assumption that while in Earth's gravity well, the gravitational attraction of the other planets was negligible. We made the same assumption for when the vehicle is in Mars' gravity well. We assumed that while between Earth and Mars, the force exerted by the sun is much greater than forces exerted by other planets, thus gravity due to the planets could be ignored. We also assumed that the difference in the plane of orbit for earth and Mars was negligible. Finally, we assumed that since the space vehicle is much smaller than either Earth or Mars, we could treat it as a point mass in our calculations. Refs: Case for Mars. Robert Zubrin. Hohmann Transfer.