Celestial mechanics is the discipline that studies the motion of the celestial objects; this field played an important role in the history of science. CopernicusEbook On the revolutions of the Heavenly spheresE(1543) and Galileos observations of the Jovian moons (1610) are the foundation of the scientific revolution and of the scientific method. The word revolutionEitself comes from the latin revolvere, to revolve, as originally applied to the motion of the planets around the Sun. Newtons PrincipiaE(PhilosophiENaturalis Principia Mathematica) on the motion of massive bodies is arguably the most important work in the history of science. At the end of the XIX century, Poincares "New Methods of Celestial Mechanics" (1880) laid the foundation of chaos theory, while a few years later after, Einstein tested the theory of general relativity for the first time, by computing the perihelion precession of Mercury.
More recently, a new application of celestial mechanics emerged: orbital mechanics or mission design, which concerns with the motion of man-made spacecraft. An engineer by formation, the mission designer plans the trajectory of the spacecraft, maximizing the scientific return Ewith an eye to the costs and risks of the missions. Using disciplines from physics, mathematics and engineering, a mission designer explores possible geometries for the science orbit and provides a team of engineers and scientists with a selection of optimal paths to reach such orbit. Every space mission has different scientific objectives and constraints, requiring new creative solutions; for this reason, we mission designers like to think of ourselves as artists of some sort, although a more accurate job description would be that of travel agent (for space exploration).
It should not surprise then that there are special types of spacecraft trajectories called moon tours. During a moon tour, a spacecraft orbits a planet (primary), and has repeated close encounters (flybys) with its moons. Flybys not only provide an opportunity for scientific measurements: as the gravity of the moon bends the spacecraft trajectory in a predictable manner, flybys are used to change the spacecraft orbit around the primary at will, without the need of propellant. Planetary flybys are no new mechanism in orbital mechanics the Voyagers Grand Tours of the 70s and 80s included flybys at Jupiter, Saturn, Uranus, and Neptune; but their use is much more prominent in moon tours, where the shorter time scale [footnote: A typical period of revolution for a moon is a few days to a month; a typical period of revolution for a planet is a few months to centuries] allows tens of flybys to be implemented during the same missions. In this article I will show some examples of moon tours, and discuss their typical objectives and constraints - but first, lets step back and ask: why do we want to explore moon systems in the first place?
Over the last decades, the moons of the solar systems surged as some of the most interesting targets of space exploration. The spacecraft Galileo (NASA) and Cassini/Huygens (NASA/ESA/ASI) implemented the first moon tours, and returned groundbreaking discoveries on the moons of Jupiter and Saturn. Ios volcanoes eject charged particles that are accelerated by Jupiters magnetic field into a giant plasma torus. Rivers and seas of liquid methane populate the surface of Titan, and plumes of water vapor erupt from the surface Enceladus. Evidence of liquid water was found underneath the icy surfaces of Europa, Ganymede, Callisto, and Enceladus: if some primordial form of extraterrestrial life exists in our solar system, it is probably under the surface of an icy moon.