Cislunar Aerocycler Basics

Let me tell you of a special orbit that generates its own energy.

Abstract:

A spacecraft that generates lift in planetary flybys attains a sustained orbit within the Earth-moon system, and remains co-planar with the moon’s orbit through the entire cycle. In the climbing stage, it departs Earth in a highly elliptical orbit that places its apogee (furthest point from Earth) approximately where the moon is. In the redirect stage, it passes in a hyperbolic orbit around the moon, redirecting it into a more highly energetic orbit around Earth (but with the same perigee altitude). Finally, as it passes by Earth, the spacecraft produces downward lift, causing its departure angle to, once again, point toward the moon, losing some energy in the process. The amount of energy lost by drag is equal to the energy gained by the lunar redirect.

First, let’s deconstruct the title of “cislunar aerocycler”. This consists of two words that both combine two concepts and could be written with hyphens as cis-lunar aero-cycler. The first word is a common concept which simply means “takes place between the Earth and The Moon”. The second word is where all the novelty is. Firstly, I use the word “aero” in reference to use of the atmosphere, and specifically within orbital mechanics. The common similar use of this prefix is the Aerogravity assist:

In fact, this one component of the concept (the part where it generates lift in the Earth flyby) is an aerogravity assist.

The second part of the second word refers to orbits that cycle between two astronomical bodies at regular intervals — which have been proposed by Buzz Aldrin and others as helping to facilitate transit between the two bodies.

My argument here is that the orbit is more than academically “interesting”. I argue that it would likely be economically useful in a cislunar economy. Once you consider all the activity and movement which would happen in that space if we have propellant depots and substantial habitats, it seems downright implausible that we would not use the tidal mechanism as a means of locomotion, provided that it is in some way possible.

Here, I’m just laying out the most simple concept in which it would be plausible.

Technical Design Details

I’m going to break the concept description down into 3 main parts which I’ll illustrate here.

  • Moon aiming problem
  • Downwards lift to solve the aiming problem
  • Lunar redirect change of coordinates & energy gain

To state the obvious, the moon orbits around the Earth in a roughly spherical orbit. To “shoot at” the moon, you would do the first burn of a Hohmann Transfer, raising your apogee to the moon’s distance from Earth, but if you contained on this trajectory without passing close to the moon, you would continue in an elliptical orbit with a period shorter than that of the moon’s orbit by a factor of 2 raised to the 3/2 (for reasons I won’t get into here), or about 2.8, meaning the orbit completes slightly less than 3 orbits per one orbit of the moon.

In a normal pass past perigee, you return almost 180 degrees opposite of the velocity you came in with. This is characteristic of highly elliptical orbits. In our case, we desire to “bend the curve” to get substantial greater angular deflection in order to make up for the roughly 127 degrees that the moon has moved. The full picture of this looks something like the following:

Slingshot, Banked Turn, New Direction, Repeat… sort of the idea

Next, we should consider what methods we have to do to “bend the curve” as I referenced. Counter-intuitively, you would fly like an upside-down plane, generating lift downward toward Earth. This can temporarily hold the spacecraft in an altitude that it would otherwise have been moving too fast to maintain.

Not actually getting into complications of hypersonic lift here, this is just force balancing

Next, I want to show that the lunar flyby can both restart the process over again, as well as adding additional energy to the system. For this, we consider the satellite’s incoming and exiting velocity vector as it enters and exists the moon’s gravity well. This is considered for both the moon and the Earth systems.

As the satellite reaches it apogee, it essentially has no vertical momentum, with only a teeny tiny residual amount of sideways motion left. The frame-change vector of the moon’s velocity reverses this velocity and leaves us with a velocity much higher and going towards the moon. Basically, the moon overtakes the satellite.

Actually, the exit vector here should probably be even more horizontal

Then, from the moon’s perspective, it just does a passive flyby. In the Earth’s reference frame, however, its orbit apparently gains energy in this process. Ultimately, this should contribute to quickening the process to tidal locking of the Earth and the moon, but the question of sustainability is far from our minds still at this point.

Technical Challenges Generating Lift

I would prefer to address this as a separate subject and I have a bit of an in-progress Medium series on that subject on its own. In short, hypersonic aerofoils can generate very substantial lift (although much lower than atmospheric planes), although this alone might be iffy for the hard 120 degree redirect in this scheme. On the other hand, I’m extremely optimistic about magnetic ion deflection as a means of generating extraordinarily high lift-to-drag ratios, making this design easily viable.

Variant with only Aerobraking?

Within cislunar space, lots of cycler designs are possible, and in the past, people have generally only considered fully ballistic trajectories. The problem comes down to matching the moon’s angle. The solution is to do something particular awkward in the lunar “backflip”.

The Aldrin design for Lunar Backflip cycler

Once you allow yourself to consider designs with atmospheric interaction, it doesn’t take much creativity to imagine adjustments to this design that would involve atmosphere grazing. But let me cover a key point.

Naturally, an object in a moon-grazing trajectory would match the moons orbit roughly in a 3–1 ratio, but actually a little bit more, say 3.2–1 for sake of argument. Aldrin, in his design, slows down the orbit by raising perigee somewhat. This works for the design there, but precludes atmospheric grazing. To fix this, you can make a trivial switch from temporal-matching to angular-matching, where you allow the lift to alter the orbit ever-so-slightly so that it makes its time window in the 3–1 ratio. This would present extremely modest technical challenges relative to the design I presented.

So basically, the overall scheme is infinitely tune-able. If your aerofoils aren’t very good, then you can just use an orbit that is easier to manage (although slower).

Applications

One of the uses I have in mind is as a proving ground for applying aerogravity assist technologies for deeper space interplanetary missions, like Mars missions. The designs could be tested repeatedly on a sub-monthly time schedule before embarking on multi-year journeys with the designs.

Use as Energy Generators

This design could be combined with an Atmospheric Scoop, which is an idea that siphons off gases from the top of the atmosphere. Studies have consistently shown that the deal-breaker for that idea is the drag from the large solar panels necessary to accelerate a station-keeping ion stream out the back. Not so in this design, because the energy comes from tidal energy.

Slightly increasing drag doesn’t pose any serious problems for the design outlined here. You would just go about adjusting the lunar flyby angle a little bit. It is true that time spent in the atmosphere would be small compared to the total, but since it’s not necessarily energy-intensive, a gas capture mechanism could still conceivably be highly efficient, although this would constitute a major new research area in itself.

Speculative use as LEO Station Keeping

I am intensely intrigued by this concept as micro-satellites. The trajectory might be “dangerous” in a certain way with risks of the atmospheric flight going wrong, or missing the lunar rendezvous, and tiny drones would be ideal to carry out the maturation of this technology. But what other uses would micro-sats in these orbits have?

Well, since there is a surplus of momentum due to getting energy from tidal forces, it’s not out of the question that they could somehow apply direct force to boost other craft in an LEO orbit. However, the problem with this scheme is that the moon is in a rather awkward inclination, and the LEO orbit would have to match this exactly in order to have regular meets with the micro-sats. Even so, you could only pass once for each orbit of the micro-sat. On a systems-level design, this is still entirely workable, but it’s possible that the utility isn’t worth picking that particular orbit… or at least it might only apply to a dedicated lunar supply transportation network.

Obligatory analytical writing, online participation account for Medium. Engineering, software, books, space, constant daydreaming.