I noticed something odd the other evening, just before sunset. The moon was slightly more than half full. The sun and moon were clearly visible. The strange thing was that the light part of the moon seemed to be pointing in the wrong direction; a perpendicular bisector of the two “endpoints” of the moon’s terminator would entirely miss the sun. Instead, the perpendicular bisector would pass much higher in the sky than the sun was.
It seems to me that the perpendicular bisector should at least very nearly hit the sun, but this wasn’t anywhere close. Can anyone explain this phenomenon? Thanks,
The mind has a tendency to perceive the sky as the interior surface of a sphere. It could be that this distorts your image of the perpendicular bisector through the moon; next time, try checking it with a straight edge.
Is anyone else amazed with first posts being questions? I’m not criticising this OP, just that I’ve been around a little while and have not gotten around to my first OP. Unfortunately, this was a question that has probably been satisfactorly answered and will probably sink from here on.
I meant to address this in the original post. I didn’t have a straight edge handy at the time, so I haven’t used one yet. However, the sun was very close to the horizon (since it was setting), and the moon was high in the sky. In order for the light to be in the right direction, it would have to have been pointing some number of degrees down from the horizontal. Instead, it was pointing some number of degrees UP from the horizontal…distortion may have made it seem more pronounced than it actually was, but even so it was definitely the wrong direction. So I feel safe in saying it wasn’t a simple optical illusion type effect. I have no idea what it could be!
I think it’s a great circle problem, here. If the Moon was slightly more than half full, then that means that the angle between the sun and the moon was slightly over 90[sup]o[/sup]. The sky is spherical, so shortest paths on the sky are great circles (that is, circles with the same center as the sphere). A shortest-distance path from the Sun to the Moon would curve upwards for half the sky, and then start curving downwards.
Puzzles like this usually show up with the Earth, not the sky. For instance, even though I’m at the same longitude as England here in Montana, if I took a nonstop flight to London, the plane’s path would go considerably further north. You can check this with a piece of string stretched across a globe.
It apparently is a perception problem, as stated in several posts already. This is addressed (as are so many problems) in Jearl D. Walker’s excellent compendium The Flying Circus of Physics. There is, in fact, a diagram showing the bisector etc. on the Moon, pointing towards the Sun. As is usual with Walker, there’s only a brief answer (and you only get that if you get the later edition “with answers”), but there are references showing where this is addressed more fully.
Chronos, I’m not sure I see how great circles would come into it. The sky isn’t really spherical, it’s just this vast three dimensional space that we’re hanging out in. A straight line from the moon to the sun will appear to be a straight line, regardless of your viewing angle; there will be no curve.
Thinking about it a little more, I think I see what the problem could be, but it may be a little difficult to explain; it boils down to three-dimensions vs. two-dimensions, and a little confusion there.
So you’re looking at the moon, trying to pick out the perpendicular bisector…got it. But what may not be so easy to pick out is the third dimension (or “orientation” may be a better word) of the line. For example, picture in your mind a thin crescent moon, sitting right next to the sun. Now picture a line going straight through the center of the moon, pointed straight at you (this line would actually appear to you as a point, since you’re looking right down it). Fix the point of the line at the center of the moon, and rotate the line about this point a tiny amount, in the direction so that in now appears to “bisect” the lit surface of the moon. In fact, there’s an entire plane that you can rotate this line through so that the line always appears to bisect the lit surface of the moon (so basically what I’m saying is that there isn’t a line that bisects the lit surface (to your perspective), but a *plane[/]). Obviously not all of those lines will point to the sun.
So the bottom line is that, not only do you have to pick the perpendicular bisector of the moon, but you also have to consider how it should be rotated/oriented. If you look at the full moon, that line will be going (“almost”) right through you to point to the sun. If the moon is a little shy from full, the line isn’t pointing to the side out from the moon, it’s pointing in your general direction on it’s way to the sun. Conversely, for a nearly new moon, the line is pointing almost directly away from you towards the sun.
I hope that description made sense. Anyway, the final point being that failure to account for this when trying to picture the line may account for the distortion you saw.
This is also easier to visualize if you take it more to extremes, using a closer object than the moon, such as an airplane. Pretend the sun is setting due west of you. You’re standing facing due south, and there is a plane to the southeast of you with its nose pointed directly at the sun. Now turn and face the plane. If you draw a line from its tail to its nose, that line will be pointing up relative to the horizon. In fact, the closer the plane comes to passing directly overhead, the higher that line will point in the sky.
This confuses us when it happens to the moon, because our brains get used to the moon behaving as if it is infinitely far away from us, just like the sun is.
And I hope nobody was watching me sit here at my desk pointing west with a pen held over my head and rotating in my chair…
The line perpendicular to the moon’s terminator is parallel to the line from you to the Sun.
Check it out sometime, Chronos! I corresponded with a fellow over email over this exact same question. My first response was also, “It’s 'cuz the sky is curved, dufus,” but that’s not the real reason, and I realized that as soon as I saw it with my own eyeballs.
The Sun is so far away that the Sun’s rays are basically parallel by the time they reach the Earth (and the Moon). Because we’re used to thinking of light sources that are much closer, we’re used to thinking of light rays as diverging, not parallel, so it’s very non-intuitive. I call it “the Law of Imponderable Distances” and I had a terrible time with my astronomy homework until I figured it out.
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I meant to address this in the original post…the sun was very close to the horizon (since it was setting), and the moon was high in the sky. In order for the light to be in the right direction, it would have to have been pointing some number of degrees down from the horizontal. Instead, it was pointing some number of degrees UP from the horizontal…**
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As an amateur astronomer of many moons, my instincts say you’re missing the obvious…making this too complicated. It sounds like you’re trying to describe(*) seeing a waxing gibbous just slightly passed 1st quarter - of which the “bulge” of the lit section points up - away from the sun…just like the “horns” of the crescent moon point away from the sun. (I base this on your description of the relative positions of the sun and moon.)
BTW, I’ve read numerous astronomy texts, and I’ve never seen
mention of your method of “taking perpendicular bisector to the terminator”. First, the terminator is a curve since the moon is a sphere (ok, spheroid). Also, I agree with the others that, since the sky appears as a dome above us, a straight line has no practical application here.
(*) footnote: An “older” waxing gibbous would not be too high in the sky with the sun low on the horizon - as you are claiming. Sounds like just passed a 1st quarter moon, The moon’s “phase” is describing a “phase angle” between the apparent position between the sun and moon - as seen b an observer on earth. The phase angle has a direct relation to the moon’s position in the sky as seen at sunset, for example. A “mean” waxing gibbous moon can also be described as having a 135-dgr phase angle. It will appear about 45 degrees above the eastern horizon at sunset. (I am using a “mean” definition for waxing gibbous since the term covers broad range of phase angles.)
Technically, this is an altitude-azimuth (alt-az) analysis which simplifies things - by measuring a position angle (altitude) from a horizon (azimuth).
I hate to be this picky on my third post, but I’m not sure any of your answers work!
Galt: I could be misunderstanding you, but I think if the plane/pen is higher in the sky than the sun, the nose will be pointing downwards relative to the horizon, not upwards.
Cabbage: Good point, but I took all three dimensions into account when I was trying to come up with an explanation for the phenomenon. If you take a look at a crude picture I made of the scenario: http://www.geocities.com/rufftim/
you will see that the entire plane will miss the sun.
CalMeacham: thanks for the reference! I’ll see if I can get it out of the library.
Podkayne: My first reaction was “whoa duh,” but there are two problems: 1) even after the sun was set, so it was “below” me, the moon was still angled upwards. 2) It’s true that the me-sun line is be approximately parallel to the moon-sun line (because the moon and I are close to each other compared to the sun), but that doesn’t explain why the LIGHT part of the moon would not be pointing towards the sun!
Jinx: I said it perpendicularly bisected the “endpoints” of the terminator - that’s from our point of view, where we see the moon as 2D. But I know it’s not good terminology. Also, just because the sky is spherical (encompasses the earth), doesn’t mean that all the straight lines in the universe curve nicely around our planet; mentally drawing a line from the moon to the sun should work just fine as far as I know.
Anyway, take a look at http://www.geocities.com/rufftim/
That’s around a 120 degree view or so, but I’m not sure the curve of the horizon matters much.
Rufftim, my browser doesn’t seem to be accepting your drawing, all I get on the page is a few characters.
Let me try describing it this way, which may apply to your situation, I don’t know. Picture the moon just after it’s first quarter (which sounds like the situation you’re describing, as Jinx mentioned). The line through the moon will indeed be pointing up away from the horizon in this case, it may be interpreted as pointing up away from the sun; the trick is, however, that the line follows all the way down to the horizon.
Picture this: An infinite (straight) line suddenly appears out of nowhere, say 200,000 miles directly above your head. The line is parallel to the plane that is tangent to the earth at the point you’re standing. What does this line look like to you? As it goes off to infinity in one direction, it will appear to be converging down to a point on the horizon of the earth (maybe slightly above, due to the curvature of the earth) in that direction (assuming you have perfect vision and can see it arbitrarily far off). As it goes off to infinity in the opposite direction, it will also appear to converge to a point on the horizon directly opposite the other point. The line will appear to begin on one side of the horizon, rise up and arch until it’s directly over your head, then fall down to the opposite horizon. This is a straight line, it may seem curved because it kind of looks like it’s sitting on the interior of the “sphere” of the sky, but it’s perfectly straight, even though it takes a full 180[sup]o[/sup] of your vision. It’s a little odd to think of a straight line going from one side of you to the other side, through a full 180[sup]o[/sup], but it’s perfectly straight.
When the moon is just after the first quarter, picture the sun and moon on this line (with the line bisecting the moon). The moon may be a little to the left of “straight up”, the sun will be far to the right (near the horizon). The line comes up and out of the moon, passes through the “straight up” point, then comes down to meet the sun at the horizon.
Imagine that the lit part of the moon is shaped like a cup. The opening of the cup should be angled upward, whether the perpendicular bisector is pointed toward the Sun (the Sun is close) or whether it’s parallel to the observer-Sun line (the Sun is far away). Somehow I don’t think that’s what you’re describing though.
If you mean that the bottom of the cup is pointing upward, then maybe we’re running into Chronos’ great circle problem. Unfortunately, I can’t see the picture you linked to.
All I know is that since that email exchange, I’ve paid more attention to the orientation of the lit part of the Moon, and the parallel-rays explanation has always worked perfectly.
Careful, it’s the line perpendicular to the terminator (the perpendicular bisector you were talking about) that’s parallel to the observer-sun line–not the moon-sun line (which, you’re right, is parallel anyway). Just to make sure we’re using the same terminology: the terminator is the line between light and dark on the Moon–the lip of the cup, as it were. The line perpendicular to the terminator represents the Sun’s rays.
Honestly, *Rufftim, I know exactly what you’re talking about, and I’ve been through it before with someone else–it just seems that past experience isn’t helping me communicate the solution any better!
I think it’s much simpler, along the lines of Podkayne’s first response.
You are getting the illusion that the Sun is low on the horizon, and that the sun’s light rays are therefore aimed upward. This is NOT the case. The sun is not a 2 in or 12 in or 500 ft or 2 mile wide ball in close orbit. It is friggin’ huge and friggin’ far away.
This is what you(*) think you see. The sun is low on the horizon (==), and the moon is high above. Note the terminator line (|) is not perpendicular to a projected line between the sun and the moon positions. But that is wrong.
This is more proper. The sun’s lines are parallel. Note the sun itself is not shown - it’s too far away to be in the picture at this scale. Stretch the image down the block for three miles, then paste the sun. See how the perspective from your position is distorted. You see the sun low on the horizon because it is so far away from you. But the moon looks exactly the same direction to see the sun, which seems high to you.
The effect is well-known and mentioned in Minnaert’s classic The Nature of Light and Colour in the Open Air (much reprinted - I’m using the Dover edition of the 1954 translation where the passage below is p151-2).
“A searchlight casts a slender beam of light horizontally over a wide open space. Although I know that the beam runs in a perfectly straight line, I cannot get rid of the illusion that it is curved, highest of all in the middle and sloping down to the ground on both sides…
Immediately related to this is the observation that the line connecting the horns of the moon, between its first quarter and full moon, for instance, does not appear to be at all perpendicular to the direction from sun to moon; we apparently think of this direction as being a curved line. Fix this direction by stretching a piece of string taut in front of your eye; however unlikely it may appear at first, you will now perceive that the condition of perpendicularity is satisfied.”
Thinking of the sun and moon as isolated bodies in space, this has to be true, independent of our vantage point. Our brain does however seem to impose odd ideas on how we perceive the sky and this is one of them. Minnaert discusses numerous others.
Nope, not the case. I’ve come up with an even easier way to demonstrate it. Face north. Point your right arm and index finger in the northeast direction, pointing up at about a 45 degree angle. Imagine that your fingertip is the sun. Grab a pen (or just your finger works ok too) in your left hand and hold your left hand up in a similar position, but to the northwest. Point your pen/finger at your right fingertip. Now turn your head and look at your left hand. The pen/finger should appear to be pointing up relative to the horizon. Here’s a really crude drawing
To make it even more obvious, put your hand up higher, so it’s almost above your head. Now when you turn your head and look up at your hand, the pen is almost perpendicular to the horizon, pointing nearly straight up.
Watching the gibbous moonrise tonight, I wanted to add (to my previous posted thoughts) that I think I see what’s puzzling you. Our perspective of the moon, as the earth revolves, changes the apparent angle of the terminator. For example, consider the 1st quarter moon. When the 1st quarter moon culminates on the meridian (i.e.: reaches max height in the night sky), the terminator would appear as vertical. However, the perpendicular bisector would be horizontal (assuming the terminator is a line, not a curve).
Thus, would you expect the sun to fall along that horizontal line somehow? This wouldn’t make sense, would it?
In short, don’t let how you observe the terminator, and its apparent angle, fool you. Try to picture the BIG picture: how the earth-moon system is being illuminated by the sun, and how, from earth, we’re getting like a bit more than a profile view - when in gibbous.
Another way to visualize it with the moon and sun: imagine the moon and the sun are both on the horizon, with the sun behind you and the half-moon in front of you. You’d expect to see the curved part of the half-moon pointing straight up, right? If it’s a little to the side, you’d expect it to point almost straight up, not down…
