The Solar System’s moons are intriguing objects for exploration. Especially moons like Europa and Enceladus. Their subsurface oceans make them primary targets in the search for life.

But why not send one spacecraft to visit several moons? NASA’s about to launch its Lucy mission which will visit 8 separate asteroids. Could the same be done for a mission to multiple moons?

For a spacecraft to do that, it would have to do a little dance with the notorious three-body problem, which makes a stubborn partner. A new study presents a possible way to do that.

Missions like Galileo and Cassini were able to gather some data on the moons of Jupiter and Saturn. But they performed distant flybys; they never orbited the moons. It’s tricky sending a spacecraft to visit and orbit different moons around the same planet because of all the gravitational forces involved. A spacecraft with unlimited propellant could use brute force to enter and exit orbits. But that’s not how space travel works. Everything is launched from Earth on rockets, at great expense, and fuel must be carefully husbanded.

A new study looks at a method to move a spacecraft between lunar orbits without using mission-busting quantities of fuel. The title of the paper is “Transfer design between neighbourhoods of planetary moons in the circular restricted three-body problem: The Moon-to-Moon Analytical Transfer Method.” The lead author of the paper is David Canales from the School of Aeronautics and Astronautics, Purdue University.

The “circular restricted three-body problem” is one of those vexing aspects of space travel in need of a stronger solution. In the case of transferring a spacecraft between different moons. the planet, the moons, and the spacecraft create a complicated gravitational situation that’s difficult to navigate. Especially when the moons are travelling at different velocities, and on different orbital planes.

For a better understanding of the three-body problem, watch this video.

Their solution is called the Moon-to-Moon Analytical Transfer (MMAT) Method. MMAT is a general methodology for transferring spacecraft between moons “…within the context of the circular restricted three-body problem..” the authors write.

“A simplified model enables analytical constraints to efficiently determine the feasibility of a transfer between two different moons moving in the vicinity of a common planet. In particular, connections between the periodic orbits of such two different moons are achieved,” they write. In their paper, they present two case studies: one for the Jovian system and one for the Uranian system.

The authors explain that other researchers have come up with solutions to the three-body problem. But they say that these solutions are unsatisfactory for different reasons. For example, some solutions assume that the moons are on coplanar orbits, which may not be true. Some solutions require too much fuel and restrict mission design. And some modelled solutions don’t hold true when modelled at higher resolutions. They write that solutions must be “…sometimes adjusted on a case-by-case basis.”

Their MMAT method is more effective. They describe it as “…an alternative general methodology for transfer design between moons applicable to any given system;”

This figure from the study illustrates the circular rotating three-body problem (CR3BP.) Ls one through five are equilibrium points. Image Credit: Canales et al 2021.
This figure from the study illustrates the circular rotating three-body problem (CR3BP.) Ls one through five are equilibrium points. Image Credit: Canales et al 2021.

The specific math behind the MMAT method is beyond this article’s scope. Interested readers can explore the paper for themselves. For the rest of us, the paper’s conclusion explains it best.

In their conclusion, the authors drive home the point that transfers from moon to moon are extraordinarily complex maneuvers. “Trajectory design for transfers between different moons moving in the vicinity of a common planet is a balance between diverse constraints, priorities and requirements to enable trajectory design for successful missions.” The solution involves the use of libration points in the system. “The analysis supports transfers between libration point
orbits near different moons,” they write.

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