This was done in preparation for the feasibility studies above. Below is an excerpt from this book. There are many ways of going to Mars. Each and every one of these ways has it's own advantages and disadvantages. These different ways are called trajectories.
Trajectories are the flight paths of objects.
In this case, objects in space. One of the possible missions to Mars is called a sprint mission. Sprinting to Mars is going to Mars and coming back to Earth as fast as you can. On the sprint mission you stay in space the shortest amount of time and the risk of equipment malfunctioning is minimized. However, the disadvantage to this mission is the cost of the fuel and the weight.