Introduction

Transfer Calculations
Hohman Transfer
Free Return Trajectory
Spiral
Summary of Numerical Data

Trajectory
Launch Windows

The following section outlines the possible launch dates available for the mission.

Opportunity Number Launch from Earth Land on Mars Launch from Mars Land on Earth
1 2/9/02 9/23/02 10/6/03 6/22/04
2 3/31/04 11/2/04 11/25/05 8/11/06
3 5/20/06 12/22/06 1/14/08 10/30/08
4 7/9/08 2/10/09 3/5/10 11/19/10
5 8/28/10 4/1/11 4/24/12 1/8/13
6 10/17/12 5/21/13 6/13/14 2/27/15
7 12/6/14 7/10/15 8/2/16 4/8/17
8 1/25/17 8/29/17 9/21/18 6/7/19
9 3/16/19 10/18/19 11/10/20 7/27/21
10 5/5/21 12/7/21 12/30/22 9/15/3
11 6/24/23 1/26/24 2/18/25 11/24/25

These dates are only correct to within about a week because leap years were neglected and times were rounded in the calculations. However, this is an acceptable range of error for the purposes of long range planning since a launch any time within a couple of weeks of these dates would work. The trajectory could be slightly altered within that span so that the spacecraft still reached its destination.

Choice of Launch Window

When considering a launch date, there were several important factors. The most important was the alignment of the planets. Launch dates for which the orbit of the spacecraft intersects Mars' orbit when Mars is at that location occur about every two years (see table). Dates between the present and 2023 were considered because it seemed like a reasonable time frame for this mission. The propulsion system selected necessitates fifteen years of building time, so dates before 2015 were eliminated. Then the dates were compared to a graph of the solar activity and times of high dust storm probability on Mars versus time. It is important to avoid dust storms because they might destroy equipment, make navigation difficult, or cut off communications. However, these problems have been accounted for through engineering. A launch date during a time of low solar activity is perhaps more important because solar flares have the potential to hurt people quite badly when they are relatively unprotected in space, as well as cutting off communications. There were no launch windows within the time frame considered that avoided dust storms entirely, but a couple of them avoided landing or launching from the surface during a time of high dust storms. Fortunately, one of these times coincided with a time of minimum solar activity. This was the date ultimately chosen, January twenty-fifth, 2017. All dates generated are only accurate to within a week, since leap years were ignored and some rounding occurred in the calculations. Fortunately, this is okay because launch can occur within a couple weeks to either side of these dates if slightly more or less fuel is used and the trajectory is corrected a little.

References:
Kelppner, Daniel and Kolenkow, Robert J. An Introduction To Mechanics. McGraw Hill, Inc., Boston: 1973.