Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed, to include representations, asymptotic methods, variational methods, and numerical analysis); and applied probability. These areas of mathematics related directly to the development of Newtonian physics, and in fact, the distinction between mathematicians and physicists was not sharply drawn before the mid-19th century. This history left a pedagogical legacy in the United States: until the early 20th century, subjects such as classical mechanics were often taught in applied mathematics departments at American universities rather than in physics departments, and fluid mechanics may still be taught in applied mathematics departments. Quantitative finance is now taught in mathematics departments across universities and mathematical finance is considered a full branch of applied mathematics. Engineering and computer science departments have traditionally made use of applied mathematics.

Simply put, resistance to the creation of a space frontier originates with the insecurities of Western leaders. First, it is clear that everything changes with the emergence of a frontier. Established power structures are usually shaken, not reinforced. (If this is not clear, try reading Walter Prescott Webb's The Great Frontier, particularly the last chapter, and Divided We Stand: The Crisis of a Frontierless Democracy, by the same author.) Dr. Porco further believes that Enceladus's orbit could have been much more eccentric in the past. The greater the eccentricity, the greater the tidal squeezing, and the resulting structural variations produce heat. In this case, the heat would have been saved inside the icy moon, melting some of the ice to replenish the liquid water sea. Dr. Porco continued to explain that "(T)he tidal flexing occurring now is not enough to account for all the heat presently coming out of Enceladus. One way out of this dilemma is to assume that some of the heat observed today was generated and stored internally in the past... (N)ow that the orbit's eccentricity has lessened, the heat emanating from the interior is a combination of heat produced today and in the past." Ganymede is larger than Mercury, which is the innermost--and smallest--major planet in our Solar System. The surface area of Ganymede is more than half that of the land area of Earth, and it provides scientists with a wealth of data concerning a great variety of surface features.