<p>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?</p>

<p>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?</p>

<p>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. </p>

CC BY-SA 4.0
2019-07-18T03:12:08.323Z
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).
uhoh
CC BY-SA 4.0
2019-07-18T10:27:11.067Z
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.
Michael Walsby
CC BY-SA 4.0
2019-07-18T17:17:05.550Z
Just pointing out that this is essentially identical to speed of sunrise for the same latitude of the sun or moon's rising.
Carl Witthoft
CC BY-SA 4.0
2019-07-18T17:17:46.433Z
@MichaelWalsby  chillax! This is a gedanken experiment.  If it helps, let the plane be a pilotless drone.
Carl Witthoft
CC BY-SA 4.0
2019-07-18T17:52:20.447Z
@CarlWitthoft - I was thinking the same about the speed being relative to sunrise. Especially since the sun's apparent speed is the same close to the horizon.
nick_halden
CC BY-SA 4.0
2019-07-18T17:53:09.800Z
@MichaelWalsby - This is just a thought experiment. No doubt this would pose risks in flight.
nick_halden
CC BY-SA 4.0
2019-07-18T17:54:16.483Z
@uhoh - The equation has to be differential of some sort, but I agree. It would be rather complex.
nick_halden
<the-moon><natural-satellites><orbital-mechanics><mathematics>
Speed of Moonrise relative to fixed point on ground
nick_halden
# Speed of Moonrise relative to fixed point on ground

(Asked by: username_0 on 2019-07-18)

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.

**Tags:** the-moon, natural-satellites, orbital-mechanics, mathematics
> **Comments:**
> **username_1**: 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).  
> **username_2**: 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.  
> **username_3**: Just pointing out that this is essentially identical to speed of sunrise for the same latitude of the sun or moon's rising.  
> **username_3**: @MichaelWalsby  chillax! This is a gedanken experiment.  If it helps, let the plane be a pilotless drone.  
> **username_0**: @CarlWitthoft - I was thinking the same about the speed being relative to sunrise. Especially since the sun's apparent speed is the same close to the horizon.  
> **username_0**: @MichaelWalsby - This is just a thought experiment. No doubt this would pose risks in flight.  
> **username_0**: @uhoh - The equation has to be differential of some sort, but I agree. It would be rather complex.  

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