After the launch of Galileo and Cassini, the American, European, and Japanese space agencies studied a variety of options to return to the moons and further explore their geology, chemistry, composition, and more generally, their habitability. One of the most ambitious programs was the Europa Jupiter System Missions, which included contributions from ESA (Ganymede orbiter), NASA (Europa orbiter) and JAXA (Magnetospheric Orbiter). The NASA and JAXA spacecraft were later cancelled for budgetary constraints, but the European contribution reincarnated into the JUICE mission, which will be launched in the 2020s.
From the early Europa Orbiter study (NASA, 1999) to the recently approved JUICE, all the proposed scenarios start with the spacecraft launched on an interplanetary journey to a giant planet. At arrival, the main engine performs an orbit insertion burn which is large enough to trap the spacecraft into the gravitational sphere of influence of the planet - but not much larger: the first orbit of the spacecraft around the primary can last 8 months. Then a moon flyby reduces the orbital period, and the time interval between the following flybys. From this moment on, moon tours take different paths to satisfy the specific mission goals and constraints.
A representative example of a moon tour is the Neptune Orbiter trajectory shown in Figure 1. The tour was part of a JAXA lead white paper (supported by 150 scientists worldwide) about the scientific themes a mission to Neptune would address. [FOOTNOTE: While an orbiter mission to Neptune cannot be implemented in the near future for cost and technological constraints, these studies identify high-priority science themes for the following decade of space explorations, focusing the research and technology development on the fewest areas.]. Neptunes largest moon Triton is not only an important scientific target (probably a captured Kuiper belt object, with an ocean of liquid water bellow the surface), but it is also an effective tour engineE we used to attain a wide range of Neptune orbits and Triton flyby geometries. Typical examples of desired orbits are: (1) high-inclination orbits, for remote observations of the pole regions of primary Neptune, and to measure the magnetic field and its interaction with the solar wind at different latitudes ;(2) orbits at all solar local times (longitude measured from midnight, which is the Sun-Neptune direction), to measure the magnetic field at different locations, and to target Sun occultation by any moon or Neptune;(3) flybys of Triton at different points of its orbit around Neptune, for gravity measurements of the tidal effects; (4) flybys over different location of Triton, for global gravity and magnetic field measurements, remote sensing of the surface and sub-surface features, and for imaging (over the lit side); (5) low-altitude flyby passages for in-situ measurements of the atmosphere. The Neptune orbiter tour in figure 1 attains all these geometries in three distinct phases (magenta, green, and yellow orbits) using 55 Triton flybys over the course of two years.
To plan the tour, we picked the optimal values of the design parameters so to maximize the science return and satisfy the mission constraints. Graphs like the one in figure 2, although apparently very complicated, are a simplified representation of the spacecraft trajectory and are used to design long sequences of flybys. The graph shows the pump and crank angles, which define the direction of the velocity of the spacecraft after a flyby. If other design parameters are fixed, each point of the graph identifies one orbit around Neptune. The moon tour in figure 1 is then represented by a discrete set of dots (magenta, green, and yellow dots, depending on the phase), connected by Triton flybys. Contour lines aid the design process: the shaded areas should be avoided, since they correspond to orbits that impact Neptune or its rings; the points on the closed curves represent the orbits that can be reached with a minimum-altitude flyby; the points on the vertical lines corresponds to resonant orbits (orbit with period commensurable to the period of Triton around Neptune), which are uses to connect consecutive flybys; and the dash contours shows the inclination of the orbit on Neptune equatorial plane.