Due to the curvature of the earth, and the way the moon interacts with the atmosphere (especially close to the horizon), is there a known function that describes the speed of the moon relative to its angle in the sky?

For bonus points, imagine that you are at altitude in a plane, and for some reason want to descend at a rate that would keep the total % of the moon illuminated constant. Is there a function for that?

Thank you in advance, this is not for an assignment, just for my own curiosity as I watched moonrise tonight. I have tried googling these questions, to no avail.

  • $\begingroup$ This is an interesting question! I think there will be answers with equations that closely approximate how the apparent speed slows down near the horizon due to refraction, but they won't be very simple. It may be easier to answer if the question is about the speed relative to the horizon, rather than "relative to a fixed point on the ground" (title) or "relative to its angle in the sky" (body of question). $\endgroup$
    – uhoh
    Jul 18 '19 at 3:12
  • $\begingroup$ I wouldn't like to travel on your aeroplane! While descending for a night landing, the pilot's attention should not be focussed on the moon but solely on locating the runway and how he is going to make a safe landing. Perhaps the situation you describe has led to several avoidable accidents. $\endgroup$ Jul 18 '19 at 10:27
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    $\begingroup$ @MichaelWalsby chillax! This is a gedanken experiment. If it helps, let the plane be a pilotless drone. $\endgroup$ Jul 18 '19 at 17:17
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    $\begingroup$ @MichaelWalsby - This is just a thought experiment. No doubt this would pose risks in flight. $\endgroup$ Jul 18 '19 at 17:53
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    $\begingroup$ @uhoh - The equation has to be differential of some sort, but I agree. It would be rather complex. $\endgroup$ Jul 18 '19 at 17:54

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