Practical Understanding of Lunar Cyclers by@Parr

November 27th 2017 973 reads

In the book Artemis by Andy Weir, people are ferried between the Earth and moon aboard space liners that follow “cycler” trajectories. Weir puts lots of effort into worldbuilding research, and the lunar cycler is one example. On the scale of Artemis, the cycler would be a very scientifically attractive concept for passenger transport.

On one point, however, he was deeply wrong — that the cycler is easy to understand. The protagonist claims to be able to work out the details, and even do the math in her head. In my experience, the lunar cycler is a monumentally non-obvious concept.

Let me go into why it’s not easy.

I asked about various points of confusion in the cycler orbit, which involves a “backflip” here:

I found myself (along with other users) diving deep into subtle language in the original paper. This is the same paper that Weir references in his book.

At last, someone found a mention on page 10 of the paper, which clarifies how it is able to return to where it starts:

Earth-return trajectory that has a period of 1/2 month (or 1/3 month is some cases) in order to ensure return to the Moon after 2 (or 3) revolutions of the Cycler in its Earth-return orbit

This answered my main confusion, which was the most basic question of “how does it work?” I went on to develop even more confusion after I plugged in some numbers, and found that the 1/2 month option the paper mentions might be ill-conceived from the get-go, possibly an outright error, but that’s still up in the air.

You may already know, the moon orbits the Earth about once every month, roughly 28 days. However, the Lunar cycler is quoted by the paper to only offer bi-monthly transportation. Complexities don’t end there. It’s true that it would offer transportation to and from the moon once every 2 months, but its period is actually 3 months. Confused yet?

I tried to illustrate this with a very basic table:

+----------+----------+----------------------+-------------+

| | Time | Location | Handedness |

+----------+----------+----------------------+-------------+

| start | start | Earth perigee | (right) |

| | 7 days | Earth apogee | |

| | 14 days | Earth perigee | |

| | 21 days | Lunar outbound flyby | |

| 1 month | 28 days | mid-backflip | |

| | 35 days | Lunar inbound flyby | left |

| | 42 days | Earth perigee | |

| | 49 days | Earth apogee | |

| 2 months | 56 days | Earth perigee | |

| | 63 days | Lunar outbound flyby | |

| | 70 days | mid-backflip | |

| | 77 days | Lunar inbound flyby | right |

| 3 months | 84 days | Earth perigee | note repeat |

| | 91 days | Earth apogee | |

| | 98 days | Earth perigee | |

| | 105 days | Lunar outbound flyby | |

| 4 months | 112 days | mid-backflip | |

| | 119 days | Lunar inbound flyby | left |

| | | (continues) | |

+----------+----------+----------------------+-------------+

This is akin to a train schedule…. only in space.

Let’s break this down another time, in plain English. What is the spacecraft doing for the 3 month period? Basic time accounting:

- exactly 1 month is spent in the holding pattern orbit on the “right” side of the Earth
- another 1 month is spent in the holding pattern on the “left” side
- 1/2 month is spent transferring from the left to the right
- 1/2 month is spent transferring from the right to the left

Boy this is confusing!

It’s also confusing that the 2 holding pattern segments of 1 month length are further sub-divided into multiple passes. Thus, the controversy mentioned above about subdividing into 2 halves or 3 thirds is totally separate from the rhythm of the total pattern, which is the same either way. (note the table assumes the 2 halves case)

Still confused, huh? Let’s try a picture this time.

Okay, maybe not a picture, but a very busy and poorly drawn graph. I hope that this matches fully the tabular schedule above. I also hope it’s all correct (again, my thesis is that this is non-obvious). At least know that, if you are confused, you are “getting it”. If you’re not confused, you clearly don’t get it.

Graph components:

- Vertical axis (x) — One spatial dimension. Remember there are 3 total spatial dimensions, but budgetary constraints leave us with this. This axis is selected to be in the plane of the moon’s orbit, and also the axis that aligns with the direction of the space liner’s orbit in the holding pattern
- Horizontal axis — Time. It moves forward as you go to the right of the drawing. Note that time is sub-divided into parts of the orbit that correspond to the time table.
- Green line — Earth, it stays in the same place (its the center of our coordinate system)
- Blue line — The moon as it moves in its predictable orbit
- Red line — The space liner that is traveling in the cycler orbit

A few nuances are important to point out in all of this.

- I circled the points at which someone might board the liner going from the Earth to the moon or vice versa. You’re welcome.
- I starred the moments at which the space liner does a flyby of the moon, transitioning from the holding-pattern orbit to the backflip orbit. Note that not every flyby is a good time to board (but I guess you can go ahead and do it anyway if you’re looking to kill a few weeks)
- In the backflip phase, only this one particular axis aligns for the space liner and the moon. In the 2 other axises of space, they are quite far apart until the flyby.
- The hard part — what is going on with the orbits of the space liner???!

I drew the orbits in the holding pattern only going in 1 direction. This is because in actuality, it’s a highly elliptical orbit. When it goes by the Earth it is going super fast, and then slows down as it gets far away. This is why it looks like a fast bounce… it kind of is, at least in this axis.

Next, note that the space liner’s orbit is *higher* than the orbit of the moon. It needs a little bit of extra energy in order to balance the vectors in the flyby to match the orbit it needs within the viable range of orbital inclinations. But honestly, I’m okay if you’ve stopped reading by this point. You did good.

Finally, notice a weird period for the space liner. The elliptical orbit would actually need to be a teensy tiny bit slower than exactly 1/2 the moon’s orbital period in this scheme. The left hand holding orbit is a good way to visualize this. I think of it like a basketball dribble, where the moon is like the hand. The ball needs to have a little bit more energy that it would need to just rise up to the hand. That means that the bounce down and back up is a bit faster than a corresponding parabolic arc, starting at the same speed, going upward and allowed to fall back down to the ground. So the 7 days in the time table is kind of a lie, but you should have know better to expect accuracy with 1 significant figure.

So there you go.

Orbital mechanics are complicated. Even just a *qualitative* understanding of cycler/backflip trajectories is actually quite difficult, unless you’re a prick who likes to brag (*cough* Jazz). In that case, I guess you already knew all this.