# Could Earth-lunar flybys be repeated consecutively without the use of propellant?

Ever since a recent orbital mechanics question, lunar flybys have been nagging me in the sense that there is obviously energy available in the system. I'm interested if you could get a repeatable process that is energy-positive and could be done at the same cost as an ordinary NASA mission. This requirement limits the possible approaches to a spacecraft trajectory, along with the familiar toolset.

There is precedent that deep space probes get gravity assists from the Moon. Accumulated over time, these are demonstrated to be useful for helping to get probes out of Earth's gravity well. However, that's a 1-way process, so it has no obligation to preserve angular momentum, and it's non-trivial whether it could be tailored to make a repeatable orbit or not.

Lunar flybys are certainly tunable to some degree - in that you can hit a bullseye on Earth after the flyby. You could graze LEO instead, and you're off into another elliptical orbit. The problem is that the Moon has left you behind in that time, and you won't come close to it at next apogee.

But the system is rife with orbital energy! More than likely, the lunar flyby itself gave the probe kinetic energy. With extra juice to spend, why not spend some of that in an aero-brake with Earth, allowing you to tune your orbital parameters for the next pass? Something like:

Now, I'm asking this question because there's something obviously ill-conceived about the above scheme. I definitely can't get the energetic arguments to work. Notice that I used East-West (retrograde) orbits above. That's because angular momentum arguments seem to rule out West-East orbits. The tidal evolution of the Earth-Moon system is that Earth's rotational energy is transferred to the Moon, so if this scheme is energy-positive, I expect it to slow down Earth's rotation (marginal amounts).

My arguments in favor of the scheme are so-far highly suspicious. While the Earth's rotation contains energy, it seems unlikely that skimming it at 11 km/s could ever possibly extract energy from that rotation. From the probe's perspective, the Earth could probably be taken to not be rotating at all. That logic ties me in knots, because it suggests that energy could be extracted from the Moon by slowing it down, which we know to be totally wrong. Energy can only be extracted from the Moon by speeding it up. Something is obviously wrong with that simplification.

Of course "simple" aerobraking won't work. That would only lower apogee, which isn't what we want. However, if NASA outfits it with some purpose-built movable flaps, it could do something like "feathering" to do controlled aerobraking before perigee, affecting the other orbital parameters. You could even possibly use lift during the pass to "aim" for the Moon's new position.

But all of those arguments are useless, unless the energy and momentum transfer can be clearly articulated. If possible, it could be proven beyond a doubt in an orbital simulator. If not possible, I expect that orbital physics arguments could falsify it.

To add more detail, I'm asking if a system is possible that uses:

• A trajectory-based approach
• converts Earth-Moon kinetic energy into some other form of energy
• Doesn't rely on Earth's quadrupole moment (you could say tidal power does this now)
• Doesn't require direct force transference on "space elevator" scales

That last point is the killer here. If you could get around that, you could do this with something the size of a cubesat. But that might also kill the entire idea.

What you are referring to is a Free Return Trajectory. It references a paper called Trajectories in the Earth-Moon Space with Symmetrical Free Return Properties, which states that the right path can lead to flying between the Earth and Moon with no further fuel required. But you won't gain any momentum from that.

• That took me some time to digest, but I see now how a zero-energy trajectory can be repeatable in theory. The angular momentum of the probe returns to its initial value, haven obtained a negative contribution from the moon and a positive contribution from Earth, resulting in no physics violation. There is no way for rotation of either body to factor in (aside from quadrature, which I excluded), because there are no physical means for that to happen. – AlanSE Oct 22 '13 at 2:46

I don't know if there was propellant used in between, but I know of at least one mission that had a spacecraft use two lunar assists: STEREO.

If you look at the first video on their web page explaining the orbits, you'll see that B (STEREO-Behind) gets a second gravity assist from the moon.

(Disclaimer: I work for the STEREO Science Center)

• Actually, in watching the phasing orbits movie again ... I suspect that there were three gravity assists for B, two for A. (the orbit gets bumped out a little in the pass before A gets flung away) – Joe Mar 27 '14 at 13:13
• Excellent videos! Are these available as a YouTube link? – uhoh Aug 18 '16 at 6:14
• @uhoh : not that I know of – Joe Aug 18 '16 at 18:41
• OK thanks - I've constructed a GIF from it so it can be seen in stackexchange - it's only about 110 frames long so it still looks reasonably similar, and it's now easier to view than downloading the video. – uhoh Aug 21 '16 at 15:19