Terminator Line Observations

[lewyt]

A couple weeks ago Randall asked a guest to explain a phenomenon with the terminator line of the earth.
If I recall the scenario was that the visible line on a mountain and nearby terrain was moving much slower than the calculated speed the terminator should be moving.
The guest (Chris Rutkowski) provided a short explanation but it seemed to me that didn't fully satisfy @Randall
I'm new to the forums but have been listening for years and I thought maybe I could help explain this apparent weirdness.
As Chris mentioned it has everything to do with the unevenness of the earths surfaces.
The fact that Randal first noticed the phenomenon while viewing a mountain is significant.
to make sure I understand exactly what was seen I will try to recreate it in words here.

Randal was looking westward toward a mountain with the sun rising in the east behind him at dawn.
the sun first struck the top of the mountain and a distinct shadow line traveled down the mountain and across the level landscape toward Randall
It travelled much slower than the 600 mi/h that Randal calculated as the speed of the terminator.

One way to think of it is that this was not the terminator but rather a shadow of another mountain further east from Randall's location.
Another way to think of it is that it was indeed the terminator but that the terminator is not a straight line.
It undulates across the landscape on average at the calculated speed if you consider the earth as a whole but locally it can go much slower or faster.
If I understand the scenario correctly the line Randall witnessed was travelling eastward toward the sun, not westward with the sun.
the un-straight-terminator theorem would indicate that sections of the terminator would jump far ahead of the rest of it to kiss a mountain top breaking off into a loop.
the small loops would then grow back eastward to rejoin the rest of the approaching terminator as the sun rises further over distant ridges.

does that make sense?
I could draw pictures if that helps but I don't have time this morning.

thanks for taking the time to read this long post

 

[Randall]

A couple weeks ago Randall asked a guest to explain a phenomenon with the terminator line of the earth.
If I recall the scenario was that the visible line on a mountain and nearby terrain was moving much slower than the calculated speed the terminator should be moving.
The guest (Chris Rutkowski) provided a short explanation but it seemed to me that didn't fully satisfy @Randall
I'm new to the forums but have been listening for years and I thought maybe I could help explain this apparent weirdness.
As Chris mentioned it has everything to do with the unevenness of the earths surfaces.
The fact that Randal first noticed the phenomenon while viewing a mountain is significant.
to make sure I understand exactly what was seen I will try to recreate it in words here.

Randal was looking westward toward a mountain with the sun rising in the east behind him at dawn.
the sun first struck the top of the mountain and a distinct shadow line traveled down the mountain and across the level landscape toward Randall
It travelled much slower than the 600 mi/h that Randal calculated as the speed of the terminator.

Hey thanks for listening! And your response is greatly appreciated.

One way to think of it is that this was not the terminator but rather a shadow of another mountain further east from Randall's location.
Another way to think of it is that it was indeed the terminator but that the terminator is not a straight line.
It undulates across the landscape on average at the calculated speed if you consider the earth as a whole but locally it can go much slower or faster.

Let's look at that closer below.

If I understand the scenario correctly the line Randall witnessed was travelling eastward toward the sun, not westward with the sun.
the un-straight-terminator theorem would indicate that sections of the terminator would jump far ahead of the rest of it to kiss a mountain top breaking off into a loop. The small loops would then grow back eastward to rejoin the rest of the approaching terminator as the sun rises further over distant ridges.

does that make sense?
I could draw pictures if that helps but I don't have time this morning.

thanks for taking the time to read this long post

Okay I think you are definitely onto something, but I still don't quite get all of it. However you have definitely keyed onto part of my block in comprehension, because, as you correctly pointed out, the terminator line moves westward ( not eastward as observed ). It also looks like we're headed for some kind of paradox in that technically speaking, the direct rays of the Sun hitting the surface of the Earth is the point of division.

Therefore the direct rays of light from the Sun hitting the mountains in the distance is where that line is, and in theory it should be travelling west from there, yet the line with the direct rays also appears to be coming in my direction from the west because of the shadow effect you described above.

In other words, the terminator line for my elevation hasn't reached me yet at my lower elevation. It's still coming from the east, but the line, which is clearly visible in the West, is at an elevation higher than mine, and is where the terminator line is ( at that location and elevation ). This is a huge step toward me grasping what is happening. Thank you! ( Even Chris didn't quite pick-up on it - lol )

So now my brain is still trying to put into perspective, why if the line is moving at over 1000 KpH these shadows still take so long to move down the sides of the mountains and buildings. In my imagination, moving into sunlight at 1000 KpH should still mean that the shadows should be zooming down the sides of the mountains and across the landscape, instead of inching their way down.

This effect must have to do with geometry and the relative size of the Earth compared to the height of the mountain or building in the context of the Earth's rotation, which due to the Earth's size seems slow, because even though it's rotating at over 1000 KPH it is over 40,000 Km in circumference, and for some as of yet not understood reason that causes this visual phenomenon.

Until this is figured out, I'm sticking with the theory that time slows down for those inside the twilight zone, while those outside it are unaffected .

 

[lewyt]

I made a diagram above
So the red line represents the rays of the sun that for m the edge of the shadow of the eastern mountain (right)
the green line represents the flat landscape between the mountains
if it weren't for the mountains the red line would be sweeping across the green line at 1000 KpH.
the blue line (barely visible [sorry]) is the eastern face of the western mountain
the red line is creeping down across the blue line much slower than 1000 kph
if you think about it that is still much faster than the shadow of a tree moves on the ground in the middle of the day.
it is the same phenomenon, just a different angle
any fixed angle from the sun is sweeping across the earth at 1000kph
the difference in the terminator average speed of 1000kph and the speed on the mountain is because of the difference in angle (green vs blue line)
The speed of the shadow of one mountain on another is really more about the relative position to each other and the sun
it has almost nothing to do with the curvature of the earth in between them
the top of each mountain - in a sense - is a larger diameter of the earth which would have an even faster terminator speed
but you can't perceive that because it is only one little point that sticks up to that diameter

each mountain itself has its own terminator that settles along ridges and almost doesn't move for hours in the morning and the evening.
but the angle of the sun relative to that mountain is continuously changing at the same rate all day long and all night
however you only see the sun strike a surface when it has turned enough toward the sun to not be in its own shadow (or the shadow of something else)

the terminator moves across the landscape at different speeds because of the relative angle to the sun of the local geography
that angle is changed over time by the turning of the earth but the different angles show different illumination because they are different relative to the sun
the abstract concept of the terminator line assumes that the earth is a smooth sphere and only casts a shadow on itself
but when you introduce local irregularities like mountains they can cast shadows on each other, that is a different concept
a cast shadow is similar to - but still different from - the part of an object that is in shadow only because it is facing away from the sun

I hope that helps
I made a video too but then realized I would have to upload it to youtube or somewhere and link it here
let me know if that is till needed

 

[Randall]

I made a diagram above
So the red line represents the rays of the sun that for m the edge of the shadow of the eastern mountain (right)
the green line represents the flat landscape between the mountains
if it weren't for the mountains the red line would be sweeping across the green line at 1000 KpH.
the blue line (barely visible [sorry]) is the eastern face of the western mountain
the red line is creeping down across the blue line much slower than 1000 kph
if you think about it that is still much faster than the shadow of a tree moves on the ground in the middle of the day.
it is the same phenomenon, just a different angle
any fixed angle from the sun is sweeping across the earth at 1000kph
the difference in the terminator average speed of 1000kph and the speed on the mountain is because of the difference in angle (green vs blue line)
The speed of the shadow of one mountain on another is really more about the relative position to each other and the sun
it has almost nothing to do with the curvature of the earth in between them
the top of each mountain - in a sense - is a larger diameter of the earth which would have an even faster terminator speed
but you can't perceive that because it is only one little point that sticks up to that diameter

each mountain itself has its own terminator that settles along ridges and almost doesn't move for hours in the morning and the evening.
but the angle of the sun relative to that mountain is continuously changing at the same rate all day long and all night
however you only see the sun strike a surface when it has turned enough toward the sun to not be in its own shadow (or the shadow of something else)

the terminator moves across the landscape at different speeds because of the relative angle to the sun of the local geography
that angle is changed over time by the turning of the earth but the different angles show different illumination because they are different relative to the sun
the abstract concept of the terminator line assumes that the earth is a smooth sphere and only casts a shadow on itself
but when you introduce local irregularities like mountains they can cast shadows on each other, that is a different concept
a cast shadow is similar to - but still different from - the part of an object that is in shadow only because it is facing away from the sun

I hope that helps
I made a video too but then realized I would have to upload it to youtube or somewhere and link it here
let me know if that is till needed

Thanks. I never expected anyone would go into such detail. Please forgive the roughness of my adjustment, but my situation is more like this, as envisioned from a south polar orientation where the Earth appears to rotate clockwise:



I live east of the mountain range at 'C', and eastward from me the land flattens out considerably until it's almost perfectly smooth prairie. So the direct rays of the Sun are at both 'A' and 'B' simultaneously, and I'm still in the shade between them. Interestingly, the areas lit by the direct rays are expanding toward each other, from 'A', down the mountain and across the landscape eastward; and simultaneously from 'B' westward across the plains.

So now to me, given the 1000 KpH rotation of the Earth, it seems that all of 'A' should emerge into sunlight faster. But that line of sunlight moves very slowly down the side of the mountain at 'A', as well as slowly down the side of buildings much closer. I can visualize how this is happening, but only if I speed it up in my imagination. It's odd how imagining things happening really slowly is actually harder for some reason.

Anyway, the math might go something like this: Measure the distance between point 'A' and point 'B', then given how fast the Earth is rotating, determine how long it should take the terminator at 'B' to reach 'A'. In theory, that is when the entire eastern face of the mountain should be illuminated, and that distance will be much farther than from the peak of the mountain to its foot.

So for the line of sunlight at the top of 'A' and the line at 'B' to get to the same spot at the foot of the mountain at the same time, the line at 'A' has to move much slower. In fact, one could probably extrapolate backward and calculate how far away the line at 'B' is using the mountain's altitude relative to the arc of the Earth's surface.

What about that? I think that might be it! ( but it's not as fun as my Twilight Zone Theory )

 

[lewyt]

Thanks. I never expected anyone would go into such detail. Please forgive the roughness of my adjustment, but my situation is more like this:



I live East of the mountain range at 'C', and eastward from me the land flattens out considerably until it's almost perfectly smooth prairie. So the direct rays of the Sun are at both 'A' and 'B' simultaneously, and I'm still in the shade between them. Interestingly, the areas lit by the direct rays are expanding toward each other, from 'A', down the mountain and across the landscape eastward, and from 'B' westward across the plains.

So now to me, it still looks like given such rapid rotation of the Earth, that all of 'A' would emerge into sunlight faster. But that line of sunlight moves very slowly down the side of that mountain, and even slowly down the side of buildings much closer. I can visualize how this is happening, but only if I speed it up in my imagination.

Maybe the math would go something like this: Measure the distance between point 'A' and point 'B', then given how fast the Earth is rotating, determine how long it should take the terminator at 'B' to reach 'A'. In theory, that is when the entire face of that mountain down to it's foot should be illuminated, rather than thinking the line should move down the face of the mountain at 1000 KmH.

What about that? I think that might be it! ( but it's not as fun as my Twilight Zone Theory )

right, that is pretty close to what I'm thinking
I've made another diagram
as the terminator travels from t1 to t2 (1000 km)...
the shadow on the mountain travels from m1 to t1 (maybe only 3 or 4 km)

 

[Randall]

right, that is pretty close to what I'm thinking
I've made another diagram
as the terminator travels from t1 to t2 (1000 km)...
the shadow on the mountain travels from m1 to t1 (maybe only 3 or 4 km)

I'm pretty sure this is the most constructive use of an Internet forum I've ever seen ( besides cat videos of course ). I will have to tell Chris that with a listener's help, we solved the problem. Maybe we'll both get gold stars for our foreheads!

 

[lewyt]

I'm pretty sure this is the most constructive use of an Internet forum I've ever seen ( besides cat videos of course ). I will have to tell Chris that with a listener's help, we solved the problem. Maybe we'll both get gold stars for our foreheads!

Thanks Randall,
I'm glad I could help.