A Question About the Moon

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JonClarke

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When the Moon is at quarter phase it is 90 degrees away from the Sun.&nbsp; When it is bibbous it is more than this (but less than 180 degrees).&nbsp; Drawing a line by eye more than half way round the sky will introduce a great many errors.&nbsp; if you end up within a couple of degrees of the Sun I think you are doing rather well. <div class="Discussion_UserSignature"> <p><em>Whether we become a multi-planet species with unlimited horizons, or are forever confined to Earth will be decided in the twenty-first century amid the vast plains, rugged canyons and lofty mountains of Mars</em>  Arthur Clarke</p> </div>
 
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onesmallstep

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>When the Moon is at quarter phase it is 90 degrees away from the Sun.&nbsp; When it is bibbous it is more than this (but less than 180 degrees).&nbsp; Drawing a line by eye more than half way round the sky will introduce a great many errors.&nbsp; if you end up within a couple of degrees of the Sun I think you are doing rather well. <br />Posted by jonclarke</DIV><br /><br />True, when the moon is gibbous it is a further distance, but the straight red line misses by way more than a couple of degrees, so it is quite easy to spot.</p><p>At quarter phases or less, you can hold a straight edge, (yard stick or something similar), at arm's length and get enough accuracy to see that this construct still misses the sun.</p><p>&nbsp;</p> <div class="Discussion_UserSignature"> </div>
 
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nimbus

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<p>The only way that can happen is for something to distort the sun's and/or moon's position(s). &nbsp;</p><p>And the above's supposed to mean something between you and the moon/sun, e.g. atmosphere..</p> <div class="Discussion_UserSignature"> </div>
 
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Mee_n_Mac

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Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>True, when the moon is gibbous it is a further distance, but the straight red line misses by way more than a couple of degrees, so it is quite easy to spot.At quarter phases or less, you can hold a straight edge, (yard stick or something similar), at arm's length and get enough accuracy to see that this construct still misses the sun.&nbsp; <br />Posted by <strong>onesmallstep</strong></DIV><br /><br />So you've observed what's been&nbsp;reported here.&nbsp; Perhaps we need to read Dr Scholkopf's paper in <em>Perception</em> (1998 volume 27, pages 1229 - 1232). <div class="Discussion_UserSignature"> <p>-----------------------------------------------------</p><p><font color="#ff0000">Ask not what your Forum Software can do do on you,</font></p><p><font color="#ff0000">Ask it to, please for the love of all that's Holy, <strong>STOP</strong> !</font></p> </div>
 
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onesmallstep

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>So you've observed what's been&nbsp;reported here.&nbsp; Perhaps we need to read Dr Scholkopf's paper in Perception (1998 volume 27, pages 1229 - 1232). <br />Posted by Mee_n_Mac</DIV><br /><br /><font size="7" color="#ff0000">EUREKA!</font></p><p>Hat's off to ya MnM!</p><p>So it is just a perception error?....But, &nbsp;even in&nbsp;this&nbsp;guy's&nbsp;photograph it is&nbsp;clear that they don't line up as you would expect.</p><p><img src="http://sitelife.space.com/ver1.0/content/scripts/tinymce/plugins/emotions/images/smiley-undecided.gif" border="0" alt="Undecided" title="Undecided" /><img src="http://sitelife.space.com/ver1.0/content/scripts/tinymce/plugins/emotions/images/smiley-yell.gif" border="0" alt="Yell" title="Yell" /><img src="http://sitelife.space.com/ver1.0/content/scripts/tinymce/plugins/emotions/images/smiley-cry.gif" border="0" alt="Cry" title="Cry" /></p><p>&nbsp;</p><p>&nbsp;</p> <div class="Discussion_UserSignature"> </div>
 
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Mee_n_Mac

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Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>EUREKA!Hat's off to ya MnM!So it is just a perception error?....But, &nbsp;even in&nbsp;this&nbsp;guy's&nbsp;photograph it is&nbsp;clear that they don't line up as you would expect.&nbsp;&nbsp; <br />Posted by <strong>onesmallstep</strong></DIV><br /><br />Got me there for the moment.&nbsp; I found the Dr's explanation here but haven't had the time to digest it yet. <div class="Discussion_UserSignature"> <p>-----------------------------------------------------</p><p><font color="#ff0000">Ask not what your Forum Software can do do on you,</font></p><p><font color="#ff0000">Ask it to, please for the love of all that's Holy, <strong>STOP</strong> !</font></p> </div>
 
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eburacum45

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<p>I have seen this illusion myself; it is quite odd. The solution is to do with great circles. </p><p>&nbsp;Apparently some people can actually visualise the sky as consisting of great circles;&nbsp; I am not one of them.</p> <div class="Discussion_UserSignature"> <p>---------------------------------------------------------------</p><p>http://orionsarm.com  http://thestarlark.blogspot.com/</p> </div>
 
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skeptic

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<p>This is a significant observation. Aristarchus noticed the same effect in ancient Greece and used it to determine the distance to the Sun.&nbsp; The Greeks knew an amazing amount about astronomy.&nbsp; For instance by measuring the length of the shadow of a vertical stick in Alexandria and also in Aswan on the same day, they calculated the size of the earth.&nbsp; Then by comparing the size of the earth's shadow on the moon during a lunar eclipse they determined the actual size of the moon.&nbsp; By knowing its actual size and its apparent size they could calculate how far away it was.&nbsp; Finally by the method below with the same observation as onesmallstep, Aristarchus was able to calculate the distance to the sun nearly 2300 years ago.</p><p><strong><a name="Aristarchus" title="Aristarchus"></a>Aristarchus of Samos (310-230BC)</strong> Worked in Alexandria. Archimedes was his pupil &ndash; get most of what we know of him from Archimedes &ndash; library of Alexandria burned. What does survive is his <em>On the Sizes and Distances of the Sun and the Moon</em>. When the Moon is at dichotomy (half-phase - 1st or 3rd Quarter), the angle Earth-Moon-Sun is 90&deg;. The angle Moon-Earth-Sun will give the shape of the triangle formed by the three bodies.</p> <p>www.astunit.com/tutorials/aristarchus.gif" alt="aristarchus.gif" width="600" height="400" /></p> <p>Measured angle as 87&deg; &ndash; Thales 300yr earlier measured to half deg! Fragments suggest that Aristarchus could do so as well and that he may have thought that the angle was more than 89&deg; 30', but the uncertainties of the precise dichotomy of the Moon and in measurement led him to play safe (remember Anaxagoras!). He suggested Sun 19x further than Moon, 19x as big as Moon. He obtained size and distance of Moon from time it took to pass through Earth's shadow at eclipse. Sun 7x as big as Earth. Eratosthenes (276-196BC) had measured Earth to within 50 miles of present value using the altitude of the Sun at midday on same day at Syene (Aswan) and Alexandria.</p> <p>http://www.astunit.com/tutorials/greek.htm</p><p>&nbsp;</p>
 
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secondAttempt

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<font size="2"><p>The line connecting the horns is perpendicular to the line that points to the Sun, as it must be.&nbsp;It's an illusion that it does not.&nbsp; This is caused by the fisheye effect.&nbsp; Only lines passing horizontally through&nbsp;the center of your field of view&nbsp;will not be horizontally distorted.&nbsp; If you were at the north pole, and the the moon and sun were both on the horizon, this effect would go away.&nbsp; It's natural to use the horizon as your reference.&nbsp; Check out this picture.&nbsp; It demonstrates the effect you are seeing.&nbsp; The moon appears to point up, while the sun is below it.</p><p>http://koti.kapsi.fi/~leknu/moon-sun.jpg</p><p>&nbsp;</p><p>Here are some pictures I took.&nbsp; I placed the camera on a tripod, and tilted the tripod so I could pan between the sun and moon&nbsp;using only the&nbsp;azimuthal&nbsp;axis.&nbsp; If the tripod were not tilted, I could only do this if the sun and moon were both on the horizon.&nbsp; By tilting the tripod, the horizon is now subject to the fisheye effect and appears curved.&nbsp; This picture shows that the moon is pointed at the sun.</p><p>http://orbitsimulator.com/BA/moonSun1.JPG</p><p>&nbsp;This image is zoomed in on the moon to make it easier to show</p><p>http://orbitsimulator.com/BA/moonSun2.JPG</p></font>
 
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skeptic

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The line connecting the horns is perpendicular to the line that points to the Sun, as it must be.&nbsp;</p><p><font size="3"><font size="2">Correct</font> </font></p><p>It's an illusion that it does not.&nbsp; This is caused by the fisheye effect.&nbsp; Only lines passing horizontally through&nbsp;the center of your field of view&nbsp;will not be horizontally distorted.&nbsp; If you were at the north pole, and the the moon and sun were both on the horizon, this effect would go away.&nbsp; </p><p>&nbsp;</p><p><font size="2">No it would not go away at the north pole and it is not caused by the fisheye effect.&nbsp; It is caused by the sun being much, much farther than the moon.&nbsp; At first quarter when the moon is due south and the sun is due west, the line that is perpendicular to the line connecting the horns of the moon is parallel to the line beween us and the sun.&nbsp; The only way this can happen is if the sun is essentially at infinity with respect to the moon. </font></p><p><font size="2">&nbsp;</font></p><p><font size="3"><font size="2">If you were to set this up with a sphere infront of you and a light source to your right, you would see the line connecting the horns tilted down towards the light source.&nbsp; As you move the light source farther away directly to your right you would see the line connecting the horns become more and more vertical.</font> </font></p><p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p>
 
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secondAttempt

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>No it would not go away at the north pole</DIV></p><p>I've&nbsp;never been to the north pole, but I have been to Antarctica, and I can tell you first hand that it does go away there.&nbsp; Here's a picture I took.&nbsp; Notice that the&nbsp;gibbous moon is pointing almost parallel to the horizon, even though it is not far above the horizon.&nbsp;&nbsp; The sun, not&nbsp;visible in the picture, is also near the horizon, as it must be in Antarctica.&nbsp; So the moon points along the horizon to the sun.&nbsp; The effect is gone.</p><p>http://orbitsimulator.com/Antarctica/1024/IMG_72191024.jpg&nbsp;</p><p>&nbsp;Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>and it is not caused by the fisheye effect.&nbsp; </DIV></p><p>I gave you photographic evidence in the above post.&nbsp; When the tripod's azimuthal axis is parallel to flat ground, the effect is obvious.&nbsp; When the tripod's asimuthal axis is orientated along the moon/sun line, the effect goes away, and the moon points directly to the sun.&nbsp; As a side effect, a new effect is introduced:&nbsp; the horizon bends, as evidenced in the picture.&nbsp; Imagine two objects sitting on the horizon, pointing to each other,&nbsp;one on the left edge, and one on the right edge.&nbsp; In the middle image they would not appear to point to each other due to the fisheye effect.</p><p>The fisheye effect is most notable in wide-angle photography.&nbsp; The human eye has a very wide-angle view, almost 180 degrees, so the fisheye effect is very prevelant in our vision.&nbsp; Our brains process what we see, and lessen our perception of the fisheye effect.&nbsp; That's why when you take a picture of someone at very close range, they appear to have a large nose, but whey you stand close to them, all looks normal.&nbsp; This sun/moon illusion is just something our brains have not been programmed to correct.</p><p>If you don't trust photographic evidence, there is something very easy&nbsp;you can&nbsp;try.&nbsp; Get a piece of stiff cardboard, or any other flat plane.&nbsp; Go outside at a time when a waxing gibbous moon is in the daytime sky.&nbsp;&nbsp; Hold the cardboard in front of your nose, parallel to the ground, and parallel to the line that connects your eyes, so that half of what you see is above the cardboard, and half is below.&nbsp; In essence, you are creating an artifical horizon.&nbsp; Keeping the cardboard in this orientation with respect to your eyes,&nbsp;tilt your head so that both the sun and the moon are on the artifical horizon.&nbsp; You'll notice that the moon points along your artifical horizon, directly&nbsp;to the sun.&nbsp; This is basically the view you would have from the north or south pole.</p><p>I just tried this again 10 minutes ago, so I can guarantee you it works.&nbsp; Today is a good day to try this, at least where I live (west coast USA).&nbsp; The sky is clear, and a gibbous moon is visible in the morning sky.</p><p>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>It is caused by the sun being much, much farther than the moon.&nbsp; At first quarter when the moon is due south and the sun is due west, the line that is perpendicular to the line connecting the horns of the moon is parallel to the line beween us and the sun.&nbsp; The only way this can happen is if the sun is essentially at infinity with respect to the moon.</DIV>&nbsp;</p><p>It only needs to be at infinity with respect to the viewer, so that both objects sit on what we percieve to be the sphere of the sky.&nbsp; If the sun and moon were equidistant from Earth (of course, hypothetically scale the sun's size, or we'd be in it!), nothing would change.&nbsp; </p><p>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>If you were to set this up with a sphere infront of you and a light source to your right, you would see the line connecting the horns tilted down towards the light source.&nbsp; As you move the light source farther away directly to your right you would see the line connecting the horns become more and more vertical. &nbsp;&nbsp;&nbsp; <br />Posted by skeptic</DIV></p><p>That's because the line that connects the light source to the sphere becomes more and more horizontal as you move it away.&nbsp; The lines connecting the horns must keep up and remain perpendicular to this horizontal-tending line.<br /></p>
 
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skeptic

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>I've&nbsp;never been to the north pole, but I have been to Antarctica, and I can tell you first hand that it does go away there.&nbsp; Here's a picture I took.&nbsp; Notice that the&nbsp;gibbous moon is pointing almost parallel to the horizon, even though it is not far above the horizon.&nbsp;&nbsp; The sun, not&nbsp;visible in the picture, is also near the horizon, as it must be in Antarctica.&nbsp; So the moon points along the horizon to the sun.&nbsp; The effect is gone.http://orbitsimulator.com/Antarctica/1024/IMG_72191024.jpg&nbsp;&nbsp;I gave you photographic evidence in the above post.&nbsp; When the tripod's azimuthal axis is parallel to flat ground, the effect is obvious.&nbsp; When the tripod's asimuthal axis is orientated along the moon/sun line, the effect goes away, and the moon points directly to the sun.&nbsp; As a side effect, a new effect is introduced:&nbsp; the horizon bends, as evidenced in the picture.&nbsp; Imagine two objects sitting on the horizon, pointing to each other,&nbsp;one on the left edge, and one on the right edge.&nbsp; In the middle image they would not appear to point to each other due to the fisheye effect.The fisheye effect is most notable in wide-angle photography.&nbsp; The human eye has a very wide-angle view, almost 180 degrees, so the fisheye effect is very prevelant in our vision.&nbsp; Our brains process what we see, and lessen our perception of the fisheye effect.&nbsp; That's why when you take a picture of someone at very close range, they appear to have a large nose, but whey you stand close to them, all looks normal.&nbsp; This sun/moon illusion is just something our brains have not been programmed to correct.If you don't trust photographic evidence, there is something very easy&nbsp;you can&nbsp;try.&nbsp; Get a piece of stiff cardboard, or any other flat plane.&nbsp; Go outside at a time when a waxing gibbous moon is in the daytime sky.&nbsp;&nbsp; Hold the cardboard in front of your nose, parallel to the ground, and parallel to the line that connects your eyes, so that half of what you see is above the cardboard, and half is below.&nbsp; In essence, you are creating an artifical horizon.&nbsp; Keeping the cardboard in this orientation with respect to your eyes,&nbsp;tilt your head so that both the sun and the moon are on the artifical horizon.&nbsp; You'll notice that the moon points along your artifical horizon, directly&nbsp;to the sun.&nbsp; This is basically the view you would have from the north or south pole.I just tried this again 10 minutes ago, so I can guarantee you it works.&nbsp; Today is a good day to try this, at least where I live (west coast USA).&nbsp; The sky is clear, and a gibbous moon is visible in the morning sky.&nbsp;It only needs to be at infinity with respect to the viewer, so that both objects sit on what we percieve to be the sphere of the sky.&nbsp; If the sun and moon were equidistant from Earth (of course, hypothetically scale the sun's size, or we'd be in it!), nothing would change.&nbsp; That's because the line that connects the light source to the sphere becomes more and more horizontal as you move it away.&nbsp; The lines connecting the horns must keep up and remain perpendicular to this horizontal-tending line. <br /> Posted by secondAttempt</DIV></p><p>&nbsp;</p><p><font size="2">My apologies, I misunderstood your post.&nbsp; Yes, at the north pole (and south pole too) since the ecliptic and horizon more or less coincide, what you are saying is true.</font> </p><p><font size="2">However I believe the original post was about why when the a line is drawn between the horns of a half moon (first quarter),&nbsp;a line perpendicular to that line doesn't point to the sun.&nbsp; Your photo </font><font size="2">http://koti.kapsi.fi/~leknu/moon-sun.jpg illustrates this very clearly.&nbsp; That photo was not taken with a fisheye lens but with a panoramic camera.&nbsp; Note that even though the horizon is not at the center of the photo, it isn't curved as it would be with a fisheye lens.&nbsp; Although the photo looks distorted it really isn't.&nbsp; We would see the same image if many photos were taken with a normal camera of all parts of the scene and pasted together.<br /></font></p><p>&nbsp;<font size="2">Now if we do on that photo what the original poster suggested and draw a line connecting the horns of the moon and draw another line perpendicular to that line, it's obvious that line will not point to the sun and it's not due to photgraphic distortion.&nbsp; However, that line does point along the ecliptic and the ecliptic does reach the sun.&nbsp; Only at the poles where the ecliptic coincides with the horizon (as you said), we don't get this effect.</font> </p>
 
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secondAttempt

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<font size="2"><p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>My apologies, I misunderstood your post.<font size="3"></DIV></font></p></font><p>No problem. Don't look at this as an argument, rather a discussion to try to get to the bottom of an interesting phenomenon.</p><font size="2"><p><font face="Times New Roman"><font size="2">Replying to:<BR/><DIV CLASS='Discussion_PostQuote'> Yes, at the north pole (and south pole too) since the ecliptic and horizon more or less coincide, what you are saying is true.&nbsp; </DIV></font></font></p></font><font face="Arial" size="2"><p>The ecliptic really has nothing to do with it. The ecliptic is defined by Earth's&nbsp;<em>motion</em> around the sun. Most solar system objects fall near the ecliptic because they also <em>move</em>&nbsp;in planes similar to the ecliptic plane. But if the Earth suddenly changed direction and jumped into a polar orbit (and we lived to tell about it!), the ecliptic would be completely re-defined, but nothing would change in the picture. The illusion goes away at the north pole because the line that joins the sun and the moon, regardless of where the ecliptic is, is superimposed on<font face="Arial" size="2"> (or very near)</font><font face="Arial" size="2"> the horizon. </font></p></font><font face="Times New Roman"><p>&nbsp;</p></font><font face="Times New Roman" size="2"><p>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>However I believe the original post was about why when the a line is drawn between the horns of a half moon (first quarter), a line perpendicular to that line doesn't point to the sun. Your photo http://koti.kapsi.fi/~leknu/moon-sun.jpg illustrates this very clearly. That photo was not taken with a fisheye lens but with a panoramic camera. Note that even though the horizon is not at the center of the photo, it isn't curved as it would be with a fisheye lens. Although the photo looks distorted it really isn't. We would see the same image if many photos were taken with a normal camera of all parts of the scene and pasted together.</DIV></p></font><font face="Arial" size="2"><p>It's obvious<font face="Arial" size="2"> that picture</font><font face="Arial" size="2"> is a mosaic, where individual pictures were pasted together, as every few inches you can see a vertical seam where sky color is not consistent. I didn't take that picture, so I don't know the details, but you're right, I should have called it panorama, rather than fisheye, the difference being that a panorama is a horizontal slice of a fisheye. I imagine this picture was cropped. Normally when you make such a </font><font face="Arial" size="2">mosaic</font><font face="Arial" size="2">, the last step is to crop it to remove the stair-steps on the top and bottom. The horizon appears to be arched up slightly, while the road, which is probably a straight road is arched heavily down. The true horizontal center of this picture is probably near the top of that red thing in the foreground.</font></p></font><font face="Times New Roman" size="2"><p>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Now if we do on that photo what the original poster suggested and draw a line connecting the horns of the moon and draw another line perpendicular to that line, it's obvious that line will not point to the sun and it's not due to photographic distortion. However, that line does point along the ecliptic and the ecliptic does reach the sun. Only at the poles where the ecliptic coincides with the horizon (as you said), we don't get this effect.<font face="Times New Roman"><font size="3"> </DIV></font></font></p></font><font face="Arial" size="2"><p>But it&nbsp;<em>is</em>&nbsp;due to distortion. That's why simply re-orientating the camera caused the illusion to <font face="Arial" size="2">completely </font><font face="Arial" size="2">disappear in the 2nd image in my 1st post</font><font face="Arial" size="2"> (and the 3rd image which zooms in on the moon so you can see its orientation)</font><font face="Arial" size="2">. There's really no difference between the snowy picture and the picture I took, which is also a panorama made by stitching panned images, except that I orientated the tripod so that it panned along the line connecting the moon and the sun. And when I did that, the distortion, and hence the illusion, </font><font face="Arial" size="2">completely </font><font face="Arial" size="2">went away. The moon pointed along this line to the sun.</font></p></font><font face="Arial" size="2"><p>&nbsp;</p></font>
 
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onesmallstep

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<p><br /><img src="http://sitelife.space.com/ver1.0/Content/images/store/5/6/55094da4-a238-4003-96aa-fd1910a0e402.Medium.jpg" alt="" /><br /><br /><img src="http://sitelife.space.com/ver1.0/Content/images/store/1/4/5155f1e3-51a2-4192-b4bf-a6d3fe6454ac.Medium.jpg" alt="" /></p><p>Really great discussion guys!</p><p>secondAttempt; I disagree that the illusion goes away in the photos you provided.&nbsp; As you can see, the angles of the red lines I drew are not the same.</p><p>The more I think about this, the more I am inclined to believe that the horizon has nothing to do with it. As evidenced by the photographs that eliminate the horizon, the effect still remains. If we were to make this same observation away from the earth, say from a point in space thousands of miles up where nothing on earth could be referenced, would we see the same effect?&nbsp; I tend to say the answer is probably yes.&nbsp; Therefore, I am inclined to agree with skeptic in that the effect is somehow related to the fact that the sun is essentially an infinite distance from both the moon and the observer of the effect.</p><p>Comments??</p> <div class="Discussion_UserSignature"> </div>
 
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secondAttempt

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<p>If I can, I'll have to retake the picture if the weather cooperates.&nbsp; It's off-axis a little, and I suspect that your line doesn't find the sun as a result of distortion from this.&nbsp; To achieve perfection, it's really important that the sun/moon line ride the exact horizontal middle of the image.</p><p>But look at how much closer it comes than in the snowy picture.&nbsp; In that picture, its not even close, demonstrating that off-axis distortion is very significant.</p>
 
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shuttle_guy

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Don't start throwing your physics books at me, I betcha I've had more physics classes than you, having a BS in engineering.&nbsp; I know it is some kind of illusion, that is my question.&nbsp; <br />Posted by onesmallstep</DIV></p><p>MW is correct. </p><p>You must remeber that you can not determine by looking when the Moon is&nbsp;EXACTLY 1/2 full. The difference between .5 full and .49 ful make a hugh difference due to the approx 93 Million miles to the Sun. You your engineering knowledge and think about it.</p> <div class="Discussion_UserSignature"> </div>
 
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onesmallstep

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>MW is correct. You must remeber that you can not determine by looking when the Moon is&nbsp;EXACTLY 1/2 full. The difference between .5 full and .49 ful make a hugh difference due to the approx 93 Million miles to the Sun. You your engineering knowledge and think about it. <br />Posted by shuttle_guy</DIV><br /><br />MW is correct about what?...That you cannot argue with physics?&nbsp; I got that.</p><p>I think you are several posts behind, the effect has been identified and is legitimate, and the difference between .5 and .49 doesn't mean squat.</p><p>You your can also take your sarcastic remarks about my engineering knowledge and go fly a kite.</p><p>&nbsp;</p> <div class="Discussion_UserSignature"> </div>
 
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shuttle_guy

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>MW is correct about what?...That you cannot argue with physics?&nbsp; I got that.I think you are several posts behind, the effect has been identified and is legitimate, and the difference between .5 and .49 doesn't mean squat.You your can also take your sarcastic remarks about my engineering knowledge and go fly a kite.&nbsp; <br />Posted by onesmallstep</DIV></p><p>&nbsp;</p><p>I was not trying to be sarcastic. I was simply trying to get you to think. As in using H.S, Trig.</p> <div class="Discussion_UserSignature"> </div>
 
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onesmallstep

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>&nbsp;I was not trying to be sarcastic. I was simply trying to get you to think. As in using H.S, Trig. <br />Posted by shuttle_guy</DIV><br /><br />If using high school trig answered the question, I would have done so. You need to read some of the more relevent posts of this thread and realize what the actual subject is about.&nbsp; If you do so, and I can get you to think, maybe you would realize your original statement is completely&nbsp;irrelevent to the question posed in the OP.</p><p>&nbsp;</p> <div class="Discussion_UserSignature"> </div>
 
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