Do to the size and complexity of a manned mission to Mars the Odysseus mission will consists of two parts. Odysseus I is a cargo mission that launches from low Earth orbit (LEO) and arrives at the surface of Mars, it's design to support Odysseus II a manned Mars mission. Odysseus II will also launch from LEO and arrive to an orbit about Mars. While Odysseus II orbits Mars, a Mars lander departs form Odysseus II and lands on the surface of Mars near Odysseus I, thus making the essential supplies and equipment accessible to the astronauts.

In planning any space mission one of the most important steps is determining the trajectory of the spacecraft. The success and feasibility of the mission relies upon the best-designed trajectory.

There are two essential design parameters that influence a trajectory design. The overall mission time and the energy requirements needed for transit and orbit change. The problem in trajectory design is to optimize the two parameters resulting in the best trajectory for the mission.

The overall mission time has paramount affects on the overall mission: human factors, equipment reliability and cost for the mission. Human factors consist of psychological effects, medical supplies, basic supplies for survival, and long term exposure to a zero or low gravity environment. Equipment reliability is effected by the length of time in use causing redundancy in equipment design. While cost is drastically effected by mission duration due to amount of essential supplies, equipment redundancy and long term mission operation.

The energy requirements for transit and orbit change effects the size of the spacecraft (mainly the propulsion system) and the cost of its design. By using time and energy consumption as the major constraints of the mission several trajectories have been run in order to find the best trajectories possible.

In determining a trajectory to Mars it is necessary to consider the influence of other celestial bodies that will have an effect on the spacecraft during transit and if possible use these influences to the missions advantage. In the Odysseus mission the primary influencing bodies are Earth, Mars, and the Sun. Since many different trajectories come in close proximity of Venus it to can be considered as an influencing body (which we use to our advantage in the Odysseus II trajectory).

Through the use of a trajectory optimization program obtained by Science Applications International Corporation the trajectories for Odysseus I and Odysseus II were determined. The LEO and initial elliptical orbit about Mars of both missions are described in table 1 below.

Since Odysseus I is a supply spacecraft it is imperative that it arrives on the surface of Mars before the launch of Odysseus II. The reason this is important is if there are any detrimental problems in the transit, orbiting or landing of Odysseus I, the Odysseus II mission can be aborted as to not endanger the lives of the astronauts.

The trajectory for Odysseus I leaving LEO and arriving in orbit about Mars is outlined below in table 2.

Odysseus I enters in an elliptical orbit about Mars (as described in table 1) on December 29, 2003 and will deploy communication satellites to be used throughout the entire Odysseus mission. After completing satellite deployment Odysseus I performs one last burn to enter into the landing trajectory to the Martian surface (details in table 3).

After Odysseus I touches down on the Martian surface and communications has been established Odysseus II will be ready to launch around 6 months after touch down.

Odysseus II will also be starting in low Earth orbit of 200 kilometers above the Earth's surface. Since Odysseus II launches during the year 2004 and this is not a prime launch year for a Mars trajectory, an indirect rout is considered. Through the use of other influencing celestial bodies in this case Venus the optimum trajectory for the year 2004 is described in table 4 below.

By Odysseus II performing a gravity assist swing-by at Venus results in a lower energy expenditure at departure from Earth and a low outbound time to Mars. The gravity assist swing-by causes a slingshot effect; the spacecraft is accelerated without burning fuel. Upon arriving at Mars, Odysseus II enters an elliptical orbit listed in table 1, then performs another burn to inject itself into a low Mars orbit of 100 kilometers above the surface. Once in the low Mars orbit the Mars lander will depart from the main spacecraft and land on the surface near Odysseus I.

Using the Hohmann transfer ellipse approximates the Odysseus Lander Module's energy consumption for landing on Mars's surface and launching from Mars's surface. These values are listed in table 5 below.

D V₁ is the first velocity change removing the module from low Mars orbit and into a landing ellipse. The second velocity change occurs as the landing module arrives at the Martian surface. For the launch of the lander module the D V₁ occurs at lift off from the surface and D V₂ is used to change from the ellipse orbit into the circular orbit rendezvous with Odysseus II.

A major concern is in the case of an emergency and the Odysseus II mission needs to be aborted after the start of the mission is the safe return of the astronauts. Table 1 outlines option 1 abort and return mission of Odysseus II. The assumption is the spacecraft will perform the first Earth to Mars burn before the mission is aborted. There are still two required burns in order for the spacecraft to return to Earth parking orbit. The first is during the fly-by at Mars the second is during the insertion of the Earth parking orbit.

Option 2 differs from option 1 in that a gravity assist swing-by is performed not only at Venus but also at Mars. Thus resulting in a small-required burn at Venus but no required burn at Mars. From observing tables 1 and 2, the total energy consumption for option 2 is significantly less than option 1, which if the mission is aborted after the first outbound burn then option 2 would be the best abort and return mission. If the mission needs to be aborted after the Venus swing-by then option 1 would best outline the mission characteristics.

One important observation to notice from table 1 and 2 is the length of time the total return missions take. In option 1 the total time is 570 days and option 2 is 650 days. Depending upon the reason for mission abortion these mission times may be unreasonably long. Also other accommodations will need to be made for the survival of the astronauts (such as food and supplies) for such length times in space flight.

Constants and Parameters

m Å = 3.98601E5 km³/s² Earths Gravitational Parameter

m = 1.32715E11 km³/s² Suns Gravitational Parameter

m X = 4.2845E4 km³/s² Mars Gravitational Parameter

TÅ = 86164.09 sec. Period of Earth

TX = 88642.44 sec Period of Mars