James L. Cooley
What does a math major do at NASA surrounded by engineers, physicists, and astronomers? Mathematicians provide excellent background to model physical systems. The physical systems can be related to a spacecraft (an attitude system, a propulsion system, etcetera), a spacecraft support system (such as a ground or space tracking system), or a system in nature (such as the earth's gravity field or atmosphere). Mathematics provides excellent background to model data (such as noisy or biased data taken from an attitude system or a tracking system) and determine the optimal information from the data. Mathematics also provides excellent background to understand geometric relationships and deal with changing relationships over different time scales (predicting ahead, in real-time, and after the fact).
After graduating from Pennsylvania State University and adding an additional year of graduate study in mathematics at the University of Maryland, I joined the Goddard Space Flight Center in 1963. Immediately there was the challenging problem of modeling the tracking system for the Apollo program. There continued to be many challenging problems in the area of flight dynamics: the area encompassing orbits and orbit maneuvers, attitude systems and attitude maneuvers, and spacecraft tracking. Other challenges involved modeling tracking from spacecraft (the tracking and data relay system) instead of from ground antennas, controlling spacecraft dipping low into the atmosphere, and controlling spacecraft around a mathematical point (the sun-earth calibration point). There continue to be challenges in designing future missions: tracking and controlling four spacecraft in tetrahedron formation, for example, and designing missions allowing correlation of scientific data from two or more spacecraft. Mathematics and mathematical approaches are used a great deal in modeling physical systems and designing NASA missions.
Any spacecraft mission is a team effort involving engineers, physicists, astronomers, and mathematicians. One rapidly realizes it is necessary to have a background in and learn the language of engineering, physics, and astronomy. Computer and computer science knowledge is also indispensable. Thus I always recommend some minor courses in these fields for a mathematics undergraduate or graduate student.
NASA Goddard Space Flight Center in Greenbelt, Maryland, has formed a mathematics support group to enhance mathematics and mathematics education. The group supports common areas of concern such as chaos theory (chaos theory may provide an exciting breakthrough in modeling and predicting sunspots and solar activity). This group also promotes the concept that a mathematics major who is familiar with physical sciences is as good as, if not better than, an engineer, physicist, or astronomer who is familiar with mathematics.