#### Zack Bimmel

• 31
##### Short note on perspective : where is the sun at full moon at midnight ?
« on: May 10, 2020, 02:23:06 AM »
Looking at the moon from earth three different phenomena can be observed :

1) The actual path of light from the sun to the moon is of course a straight line but visual observation of the orientation of the phases of the moon seem to contradict this when one draws a straight line between sun and moon when both happen to be visible at the same time.

2) At exactly the same time all observers of the moon see the same side - the near side - of the moon irrespective of their location on earth at least by observing with the naked eye.

3) The apparent rotation of the moon's "face" and the day-night terminator during the course of a night.

All three phenomena are distinct from each other in the sense that the underlying reasons are different. Let me give the explanation for point 1) here by bringing it down to earth - literally.

Let me start off with a statement : If we were able to see light travel from the sun to the moon the light would follow a curved path as seen from an observer on earth. This phenomena is not restricted to the sun-moon problem but very general in nature. Why is that ?

The underlying reason is that we don't have any perception of depth of an object in the sky but describe its location only in terms of two angles : the angle of elevation ( 0 when the object is at the horizon, 90 degrees when straight overhead) and azimuth angle ( 10 deg east of south or something like that ). So let's bring it down to earth.

Imagine you are standing on a big level field - it is pitch dark and all you can see is five very small lights which are NOT moving. Because of the total darkness you don't have any depth perception. You also have no knowledge about how the actual brightness of each light; one might be actually very bright but far away, the next one very dim but close by. So, you do what astronomers do when measuring the positions of objects in space, you measure azimuth and elevation angle. Here are the numbers you measured, assigning 0 deg azimuth to the left most post and 90 deg azimuth for the right most post (you will be able to verify these numbers yourself shortly) :

Post  azimuth [deg]  elevation [deg]
1       0.00              15.00
2      18.43             18.72
3      45.00             20.75
4      71.57             18.72
5      90.00             15.00

Now, before you leave the field you mark the spot you were standing to come back to it during day light.

You go home, take a piece of paper to create a nice x-y drawing, azimuth angle along your x-axis and elevation angle in the y-direction. Connect the five points by a nice arc.

Next morning you come back to the field to the spot you marked the night before and you make the following discoveries : from where you were standing you had looked at five poles with little tiny lights on top. The center post (# 3) being exactly 100 meters away. The posts are located along a line perpendicular to the line from you to the center post. The posts are equally spaced, 25 m apart. They also turned out to be exactly the same height as verified with a laser beam going from the right most to the left most post just grazing all five light bulbs. Of course, if you could have seen the laser light at night it would have followed the nice arc you drew.

With this new information, your calculator and knowledge of trigonometry you can now not only calculate the height of the posts (quite high I might add) and verify the numbers in the above table.

Finally, some food for thought : I presented all the distance in terms of meters. Would you have to make a new azimuth-elevation drawing if they ALL were in feet or all in miles ?
« Last Edit: May 14, 2020, 01:04:57 AM by Zack Bimmel »

#### BRrollin

• 265
##### Re: Short note on perspective : moon-sun
« Reply #1 on: May 10, 2020, 02:39:04 AM »
Looking at the moon from earth three different phenomena can be observed :

1) The actual path of light from the sun to the moon is of course a straight line but visual observation of the orientation of the phases of the moon seem to contradict this when one draws a straight line between sun and moon when both happen to be visible at the same time.

2) At exactly the same time all observers of the moon see the same side - the near side - of the moon irrespective of their location on earth at least by observing with the naked eye.

3) The apparent rotation of the moon's "face" and the day-night terminator during the course of a night.

All three phenomena are distinct from each other in the sense that the underlying reasons are different. Let me give the explanation for point 1) here by bringing it down to earth - literally.

Let me start off with a statement : If we were able to see light travel from the sun to the moon the light would follow a curved path as seen from an observer on earth. This phenomena is not restricted to the sun-moon problem but very general in nature. Why is that ?

The underlying reason is that we don't have any perception of depth of an object in the sky but describe its location only in terms of two angles : the angle of elevation ( 0 when the object is at the horizon, 90 degrees when straight overhead) and azimuth angle ( 10 deg east of south or something like that ). So let's bring it down to earth.

Imagine you are standing on a big level field - it is pitch dark and all you can see is five very small lights which are NOT moving. Because of the total darkness you don't have any depth perception. You also have no knowledge about how the actual brightness of each light; one might be actually very bright but far away, the next one very dim but close by. So, you do what astronomers do when measuring the positions of objects in space, you measure azimuth and elevation angle. Here are the numbers you measured, assigning 0 deg azimuth to the left most post and 90 deg azimuth for the right most post (you will be able to verify these numbers yourself shortly) :

Post  azimuth [deg]  elevation [deg]
1       0.00              15.00
2      18.43             18.72
3      45.00             20.75
4      71.57             18.72
5      90.00             15.00

Now, before you leave the field you mark the spot you were standing to come back to it during day light.

You go home, take a piece of paper to create a nice x-y drawing, azimuth angle along your x-axis and elevation angle in the y-direction. Connect the five points by a nice arc.

Next morning you come back to the field to the spot you marked the night before and you make the following discoveries : from where you were standing you had looked at five poles with little tiny lights on top. The center post (# 3) being exactly 100 meters away. The posts are located along a line perpendicular to the line from you to the center post. The posts are equally spaced, 25 m apart. They also turned out to be exactly the same height as verified with a laser beam going from the right most to the left most post just grazing all five light bulbs. Of course, if you could have seen the laser light at night it would have followed the nice arc you drew.

With this new information, your calculator and knowledge of trigonometry you can now not only calculate the height of the posts (quite high I might add) and verify the numbers in the above table.

Finally, some food for thought : I presented all the distance in terms of meters. Would you have to make a new azimuth-elevation drawing if they ALL were in feet or all in miles ?

I’m going to guess “no,” that you would not need to make new drawings. If you’re computing angles using trig, then it is the ratios of distances that matter.

Am I right?
“This just shows that you don't even understand the basic principle of UA...A projectile that goes up and then down again to an observer on Earth is not accelerating, it is the observer on Earth who accelerates.”

- Parsifal

“I hang out with sane people.”

- totallackey

#### Zack Bimmel

• 31
##### Re: Short note on perspective : moon-sun
« Reply #2 on: May 11, 2020, 01:15:46 AM »
Yes you are.
Here is another question. Let's say you put a basket ball on the left-most post and a spot light on the right-hand post illuminating the basket ball at night. What would the lit/unlit pattern on the basketball look like and which way would it be oriented from the point of view of the person standing at the original observation point. Two options : a) w.r.t. a straight line from one post to the other ? b) w.r.t. the curved path ?

#### BRrollin

• 265
##### Re: Short note on perspective : moon-sun
« Reply #3 on: May 11, 2020, 01:25:39 AM »
Yes you are.
Here is another question. Let's say you put a basket ball on the left-most post and a spot light on the right-hand post illuminating the basket ball at night. What would the lit/unlit pattern on the basketball look like and which way would it be oriented from the point of view of the person standing at the original observation point. Two options : a) w.r.t. a straight line from one post to the other ? b) w.r.t. the curved path ?

Uh, I’m not sure if I’ve got the layout of the observer correct. If it goes like this from a birds eye view:

Ball

Person

Spotlight

Then I’m going to guess that you see a gibbous ball, with the darkened part forming a crescent on the left part of it, from your view. So option b.
“This just shows that you don't even understand the basic principle of UA...A projectile that goes up and then down again to an observer on Earth is not accelerating, it is the observer on Earth who accelerates.”

- Parsifal

“I hang out with sane people.”

- totallackey

#### Zack Bimmel

• 31
##### Re: Short note on perspective : moon-sun
« Reply #4 on: May 14, 2020, 01:03:03 AM »
Hi BRrollin,
Well, you are right again. The mathematical proof that the perspective view of the light from the right post (the curved line) and the line connecting the two "horns" on the ball are exactly perpendicular to each other is actually quite tedious;  algebra, trigonometry and a little bit of calculus are needed.
Anyhow, an important question is now concerning the position of the observer when he/she wants to see the  ball on the left-most post in the "full moon" mode. The answer tells you where the sun is located when you watch the full moon at mid-night high up in the sky. That's really bad for those folks who think the sun is circulating above the flat earth.
By the way did you check out the height of the posts ?

#### BRrollin

• 265
##### Re: Short note on perspective : moon-sun
« Reply #5 on: May 14, 2020, 04:28:26 AM »
Hi BRrollin,
Well, you are right again. The mathematical proof that the perspective view of the light from the right post (the curved line) and the line connecting the two "horns" on the ball are exactly perpendicular to each other is actually quite tedious;  algebra, trigonometry and a little bit of calculus are needed.
Anyhow, an important question is now concerning the position of the observer when he/she wants to see the  ball on the left-most post in the "full moon" mode. The answer tells you where the sun is located when you watch the full moon at mid-night high up in the sky. That's really bad for those folks who think the sun is circulating above the flat earth.
By the way did you check out the height of the posts ?

Well, I’ll probably stay away from that proof then, and leave it to more talented folks such as yourself. Calculus...yikes!

I’ll go for the hat-trick and say that in order to see the full moon ball, the spotlight would have to be....like, behind me? How would that work?

Oh, FYI, it’s only bad for FEers if the moon reflects light only. I’ve heard them propose that the moon is a source of light. Now the details get a little fuzzy regarding how the moon does this. But that WOULD solve the geometry problem.

Naa, I never checked out the height of the posts. Does it matter?
“This just shows that you don't even understand the basic principle of UA...A projectile that goes up and then down again to an observer on Earth is not accelerating, it is the observer on Earth who accelerates.”

- Parsifal

“I hang out with sane people.”

- totallackey

#### Zack Bimmel

• 31
##### Re: Short note on perspective : where is the sun at full moon at midnight ?
« Reply #6 on: May 17, 2020, 01:24:49 AM »
BRrollin,
you are good. Congrats to the hat trick. And yes, the height of the posts really does not matter except one has to check whether they are all of the same height as I claimed. If you can do it, do it. Never trust anybody's math or statements just because they seem to know what they are doing. Doesn't hurt either to brush up on your own math skills or even learn new stuff - including calculus. That's by the way where the fun really starts; before that its sometimes a real drudgery.

Anyway, concerning your comment about light from the moon being generated by something/somebody on the moon ? Haven't seen that yet. Do you know how that should work ?

#### BRrollin

• 265
##### Re: Short note on perspective : where is the sun at full moon at midnight ?
« Reply #7 on: May 17, 2020, 01:43:11 AM »
BRrollin,
you are good. Congrats to the hat trick. And yes, the height of the posts really does not matter except one has to check whether they are all of the same height as I claimed. If you can do it, do it. Never trust anybody's math or statements just because they seem to know what they are doing. Doesn't hurt either to brush up on your own math skills or even learn new stuff - including calculus. That's by the way where the fun really starts; before that its sometimes a real drudgery.

Anyway, concerning your comment about light from the moon being generated by something/somebody on the moon ? Haven't seen that yet. Do you know how that should work ?

Thanks man , I’ll try and practice my math skills!

I have no idea how it’s supposed to work. They propose that it’s a possibility but I haven’t seen anything more.
“This just shows that you don't even understand the basic principle of UA...A projectile that goes up and then down again to an observer on Earth is not accelerating, it is the observer on Earth who accelerates.”

- Parsifal

“I hang out with sane people.”

- totallackey