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I was trying to solve this little task:

An Australian astronomer at the latitude of Melbourne (-38 °) observed a series of unusual events. First, he watched the setting of the sun and the rising of the moon. In the middle of the astronomical night, a penumbral lunar eclipse was observed. The astronomer then watched the moon set and the sun rise at the same time. Which edge of the lunar disk was submerged deeper in the Earth's shadow?

So the Moon is in the phase of full moon since we observed the eclipse. As Moon goes to the East in the sky it's left edge first reaches the shadow and then it's right edge (in North hemisphere). So we have two options to answer the question: bottom edge or top edge. But I can't think of what changes when we examine this or that case. So it seems like both variants are possible. But the answer is only one. What is it?

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    $\begingroup$ Oooooo this is nice! I think the key is "at the same time" for the set/rise and rise/set events. Since the Sun and Moon were at opposition (so to speak) in the middle of the night, half way between these two events, the point is that they were not at the beginning or the end. And yet they rose/set or set/rose simultaneously. Recall that the Moon moves "backwards" in that it sets nearly an hour later each 24 hours (or half-hour each 12!) on average, this lag, coupled with rising/setting either further South or North than the Sun is the magic that lets them rise/set & set/rise simultaneously $\endgroup$
    – uhoh
    Commented Nov 22, 2021 at 9:00
  • $\begingroup$ So it must be the top edge because the Moon moves slower than the Sun for us in the sky and it's trajectory should be shorter. $\endgroup$
    – ALiCe P.
    Commented Nov 22, 2021 at 11:53

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