Moon shadow

[Genady]

During Solar eclipse the Moon shadow moves on the Earth surface. In which direction does it move, toward East or toward West?

[Janus]

 Generally, West to East.  However, there are occasions when the shadow is in upper latitudes, where the shadow has enough of a curved path over the surface, to start in one direction, and end going the other.

[Genady]

  On 5/20/2023 at 3:12 PM, Janus said:

 Generally, West to East.  However, there are occasions when the shadow is in upper latitudes, where the shadow has enough of a curved path over the surface, to start in one direction, and end going the other.

Expand  

Exactly correct. +1.

(May I ask you to hide your answer using Spoiler button next time as the question is in this forum?)

[TheVat]

  Reveal hidden contents

At lower latitudes, the visualization is easier, once you know that in terms of apparent motion the sun is overtaking the moon.  The moon's apparent motion is that it's going west across the sky more slowly since it is in fact orbiting Earth spinward, i.e. from west towards east.  So its shadow also goes generally that direction since its motion relative to the sun's apparent motion is eastward.   More so when sun and moon are angled so as to cast shadow at lower latitudes, IIRC.   At higher latitudes, you get into the complexity of greater oblique angles (the moon's orbit is closer to the ecliptic plane than the Earth's equatorial plane) and the shadow is fatter.  

 

[mistermack]

I'm missing something here, can anyone put me right? The Earth rotates 360 deg in 24 hours, whereas the Moon goes 360 deg round the Earth in one Lunar month, and yet the Moons orbit is apparently overriding  the rotation of the Earth, which would generally tend to cause the shadow to go East-West with the sunlight. 

I realise there's something I'm not seeing. 

[Genady]

  On 5/20/2023 at 4:04 PM, TheVat said:

  Reveal hidden contents

At lower latitudes, the visualization is easier, once you know that in terms of apparent motion the sun is overtaking the moon.  The moon's apparent motion is that it's going west across the sky more slowly since it is in fact orbiting Earth spinward, i.e. from west towards east.  So its shadow also goes generally that direction since its motion relative to the sun's apparent motion is eastward.   More so when sun and moon are angled so as to cast shadow at lower latitudes, IIRC.   At higher latitudes, you get into the complexity of greater oblique angles (the moon's orbit is closer to the ecliptic plane than the Earth's equatorial plane) and the shadow is fatter.  

 

Expand  

Yes, this is right. +1.

Around the equator, I have estimated it like this:

  Reveal hidden contents

The Earth spins from West to East making a full circle in 1 day. The Moon rotates around the Earth from West to East making a full circle in 30 days. OTOH, the radius of the Moon's circle is about 300000 km while the Earth's radius is about 6000 km. This makes the Moon's circle 50 times longer. The Moon makes 50 times longer way in 30 times longer time, i.e., it moves from West to East 50/30 times faster than the Earth surface. Thus, its shadow should move to the East faster than the Earth surface does, hence its shadow on the Earth surface moves to the East. 

 

  On 5/20/2023 at 6:08 PM, mistermack said:

I'm missing something here, can anyone put me right? The Earth rotates 360 deg in 24 hours, whereas the Moon goes 360 deg round the Earth in one Lunar month, and yet the Moons orbit is apparently overriding  the rotation of the Earth, which would generally tend to cause the shadow to go East-West with the sunlight. 

I realise there's something I'm not seeing. 

Expand  

I hope my reply above would clarify.

[mistermack]

  On 5/20/2023 at 6:18 PM, Genady said:

I hope my reply above would clarify.

Expand  

Yes, got it now thanks. 

[md65536]

  On 5/20/2023 at 4:04 PM, TheVat said:

  Reveal hidden contents

At lower latitudes, the visualization is easier, once you know that in terms of apparent motion the sun is overtaking the moon.  The moon's apparent motion is that it's going west across the sky more slowly since it is in fact orbiting Earth spinward, i.e. from west towards east.  So its shadow also goes generally that direction since its motion relative to the sun's apparent motion is eastward.

Expand  

I thought this might be incorrect reasoning, because you could change the east/west direction of the shadow simply by changing the rotation rate of the Earth, without affecting how the moon moves relative to the sun. But I think your reasoning must be right. It seems then that if the Earth were spinning much faster, then even though day-to-day the moon appears to have lagged behind the sun, during a single day the moon would appear to be overtaking the sun at lower latitudes. This would be due to parallax.

The animation at https://en.wikipedia.org/wiki/Solar_eclipse_of_August_23,_2044 shows how the shadow can go "backwards" at high latitudes. It seems that in this case, the sun and moon are "to the North", eg. during "night time" where there is midnight sun. The sun still appears to be overtaking the moon, but they're both moving in a west to east direction that late in the evening! This should happen anywhere at high latitudes when there is an eclipse in the evening after the sun has passed the westernmost point in the sky and begins moving eastward again before setting, or at dawn before the sun reaches the easternmost point.