Mostly-Full or Slightly-Empty

Last night we were driving back from San Francisco (details forthcoming) when we spotted the moon a few degrees above the horizon. This was around 7:30, so it was still before sunset, and the moon was rising. We noticed that the moon was not quite full, with a little bite taken out of it at the bottom.

We wondered whether the moon was nearly full, or just past full.

I said, “There has to be a way to figure this out logically.”

My Dad said that this is an empirical problem, so he was doubtful we could reason our way out of it.

I said, “Well, we know that on average there’s more than one full moon per month, and so we ought to be able to figure out from that whether the moon rises a little earlier each day, or a little later. And if we know that then we should be able to figure out whether it’s nearly full or just past full.” I decided that since there’s more than one full moon per month, that meant that the moon was rising a little earlier each day, and that meant that that moon was not quite full.

About 20 minutes later I said, “The moon looks a little more full to me now, so I think I’m right.” Much laughter ensued.

I think my reasoning was a little off, mainly because what I really need to know is whether the moon rises more than once per day, and using “full moons per month” as a proxy for that is not right, because they’re not the same thing. Indeed, since our months are somewhat based on the lunar cycle, “full moons per month” is a circular argument. Well, sort of.

But it turns out I was right anyway, since the full moon is tomorrow.

Which goes to show once again that it’s better to be lucky than good.

2 thoughts on “Mostly-Full or Slightly-Empty”

  1. The easy way to tell is by which side of the moon the shadow is on. If the right side of the moon is bright, then it’s waxing, otherwise, it’s waning.

    You can work it out from the geometry, of course, but then you’d have to sit down with a pencil and paper and draw it out. Or at least I would. The moon actually rises a little bit LATER every day.

  2. Heh. After your comment, I realized that the moon would need to rise a little later each day, not earlier, for it to be nearly full. The principle I was applying was that the moon would be full when it’s at its farthest point from the sun relative to the Earth, and since both sun and moon were in the sky, it wasn’t quite there yet.

    Complicated. Your heuristic is simpler. But of course, I didn’t know the heuristic!

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