Subject: So what's a full moon?
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Posted on: 2020-02-24 14:22:42 UTC

I'm assuming from the tweet that we're treating Collins as being directly affected by the light of the full moon: that is, if he stays out of direct moonlight, he's fine, regardless of whether it's full moon tonight or not.

But that doesn't actually establish the mechanism for his change. I can come up with three hypotheses:

1) The 'full moon' has to be the illumination of the entire Lunar nearside. You could split this into various sub-reasons (perhaps it's due to a wolf-goddess only possessing her chosen at full moon, or perhaps it's actually a calendar thing, with any light reflected from lunar rock at the right time prompting the transformation), but the result is the same: Michael Collins transforms if he's in a moonlit area during the full moon on Earth.

Which means it's good news for Apollo 11: their mission ran 16-24 July 1969, but the full moon that month was 29th July. By that time, the astronauts had splashed down and been taken to JSC, where they were safely inside the Lunar Receiving Laboratory. Provided no-one bounces light off any of their samples at Collins on the 29th, he should be fine.

2) The 'full moon' is any sight of a fully illuminated lunar disc, nearside or farside, it doesn't matter. This, again, can be split into two sub-hypotheses:

2a) Collins has to be able to see the entire illuminated area. This keeps him safe while he's actually orbiting over the moon: at only 100 km up, the moon would easily overflow his field of vision.

The human field of vision can contain the entirety of a circle spanning 150 degrees of arc. With the moon roughly 1800 km across, you can draw a triangle with Collins at the apex and the moon at the base; chopping it in half and plugging in some trig, we get sin(75) = 900/[distance], and ultimately [distance] = ~930 km. Once Collins is inside that range of the Lunar surface, he's safe.

So, did he see a 'full moon' at any point beyond that distance? That would take a lot of maths to figure out for sure, but I'll give it an estimate.

-On approach, I think no: the new moon was on the 14th, and Apollo 11 began its lunar insertion burn on July 19th, only just past it. At that point they were directly 'behind' the moon, and only 80 nautical miles from it; my intuition is that, whichever side they came in on, they would have been too close for Mike to 'see' the disc by the time it was visible.

-On departure, things might be a little dicier. Apollo 11 left lunar orbit on the 22nd, the night of the first quarter moon. Did they come out around the lit side? Could their 150-second burn mean they pulled away fast enough to hit that magic 930km before they passed safely back into partial darkness? I think they're probably still safe, but would want to play around with Celestia to check.

2b) Okay, but what if Collins only needs to be able to see part of the full moon? Perhaps it's just that the 'full moon' needs to be able to see him (makes about as much sense as anything else). In that scenario, he goes furry the first time Apollo 11 crosses onto the 'full moon' side - which is just before or after the translunar injection burn.

Which? Well, the diagrams of the orbit are fairly consistent in showing Apollo 11 orbiting clockwise around the moon. The first quarter moon illuminates the right-hand side (as seen from the northern hemisphere); the moon was progressing towards first quarter as Apollo 11 entered orbit, which I think means Collins would have come in from the left, and only hit the 'full moon' after the injection burn.

Which, uh, means that a very confused werewolf manifested in a confined space, with two other people, in an elliptical orbit over the moon. I... don't think that would end well. Assuming it does, he's going to transform again, once every orbit, which he made once every two hours. For three days. That's a lot of shed fur.

Moving on!

3) What if, instead of any of this 'full moon' nonsense, it's actually the light intensity causing the change? In this hypothesis, Collins transforms any time the amount of moonlight hitting him equals the amount that would hit him during a clear full-moon night. That means that, at some point approaching the crescent moon, he'll hit that threshold and morph.

How much light does he need? Moonlight is about 0.1 lux. I... don't really understand units of luminance, so let's fudge this:

Two lightbulbs hit me with twice as much light as one light bulb. Therefore, every square degree of arc that is illuminated will hit me with roughly the same amount of moonlight, whether that illumination is at 100 km or 100,000 km.

On this picture, the full moon (day 15) occupies 42,000 pixels. The day 5 crescent occupies only 8000. 42/8 = 5.25, therefore each pixel on the quarter needs to look roughly 5 times larger to hit me with the same amount of light.

Going back to trigonometry, a 1 km object will cover 1 degree of arc at 57km, and expand to 5 degrees of arc at 11km. So I need to be five times closer to get the same light from an object five times smaller (makes sense!). The moon is about 385,000 km from the Earth, which means Michael Collins hits the danger zone at 77,000 km up.

... which was well after the mid-course correction (which took place around halfway to the moon, some 180,000 km up), meaning that even if he goes crazy and kills his fellow astronauts, the ship will still follow its free-return path and fly back to Earth orbit without any further crew intervention. I think Ground Control would then be able to land the command capsule, and drag a likely-traumatised Collins out of there.

Heaven only knows what they'd do with him.

hS

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