Moon phases and how they look

This article in the NY Times (http://www.nytimes.com/interactive/projects/cp/summer-of-science-2015/latest/half-moon-qna) discusses what’s called a first- and third-quarter moon, but looks like a half moon.

OK, yes, no problem. But it throws this in:

I guess that’s because you’re standing, uh, upside down relative to people in the Northern Hemisphere. So, that immediately raised the question in my mind – what does it look to people on the equator? I admit that it would be awesome if it would flip back and forth as you step to one side or the other, but I’m sure that’s not it. Is the light/dark split horizontal? Does it rotate towards the vertical as you move toward the poles?

I have to confess i have never really understood why we see a concave shadow on the moon … I naively assume that the earth, being a spheroid, would always cast a convex shadow.

I also have to confess that I have never spent any great amount of time trying to work it out.

The reason it makes no sense to you is that the dark part of the Moon is NOT caused by a shadow of the Earth. It’s caused by the angle you’re looking at the Moon versus the illumination coming from the Sun.

At any moment exactly one half = one hemisphere of the Moon is totally illuminated by the Sun. And the other half is totally in shadow. Because the Moon has no atmosphere, there is no twilight. On any given spot on the Moon at any given moment it’s either 100% day or 100% night.

So you can simulate the Moon by taking any spherical ball and painting one half one color and the other half another color. Say we use black & white.

Once you’ve done that, you can look at your model from various angles. What you’ll see is that IF you look at it directly towards one colored side or the other you’ll see all white or all black. And if you look at it angled 90 degrees to those choices you’ll two hemi-circles, one of each color separated by a straight line.

At any other angle you hold the model, you’ll see the model is partly one color and partly the other, and the dividing line will appear to be a curve. Because it really is a curve in 3-space. It’s just that in the two special cases in the previous paragraph, the curved line in 3-space becomes a straight line in the plane of your line of sight.

The light-dark split is always 90 degrees to the line that points towards the Sun. If you see a crescent moon and pretend it’s a bow about to shoot an arrow, the arrow is aimed exactly at the Sun. The same logic & geometry applies when the lit part of the Moon is more full. The sunny side always faces exactly at the Sun and the shady side always faces exactly away from the Sun. As explained above, all that’s changing from day to day is the angle we’re watching it from.

The bit about the Mon being “upside down” in the Southern Hemisphere is mostly sloppy thinking and sloppy terminology. And no, it doesn’t flip/flop if you stand right on the equator and hop back and forth between Earth’s hemispheres.

Try this thought experiment: Standing someplace in the Northern hemisphere face towards the North pole. Is East to your right or left? Answer: To your right.

Now teleport to the Southern hemisphere and face the South pole. Is East to your right or left? Answer: to your left. Oh My Gosh: East & West just flip-flopped. :eek:

Not really. All that happened is that left & right point in different directions when you face different directions. On a rotating sphere like the one we live on, the only “natural direction” is towards the nearest pole. All other directions are derivations.

Depends on which way you’re facing.

If you want to view the moon as someone in the southern hemisphere does, simply face north and bend over backwards until you see the moon. Ta da!

Moon in Australia

If you’re standing on the equator during one of the equinoxes, then yes moon will appear to rise straight up from the horizon and travel directly over your head, with the “light/dark split” (called the terminator) horizontal.

But, during April, May, June, July, and August, when you’re standing on the equator, the moon and the sun appear more towards the North than you are, so you’d face North to look at it, and see the moon travel from right to left, the same as if you were viewing it from Australia. However, during October, November, December, January, and February, it appears further South, so you’d turn South to look at it, and see it traveling from left to right, just like people see it from Europe.

I’m not sure about the poles.

Thanks. I must not have been too clear in my questions, because I think this is really the first answer that addresses my questions.

So, when you’re not at the equinox, there must be some other latitude where the terminator appears horizontal, right? And, there must only be a small range (around the equator during the equinox) where it appears horizontal, because it mostly appears vertical everywhere.

If I were in a fast jet plane traveling from north to south and watching the moon, would it appear to be vertical, then (relatively quickly) spin upside down as I pass over the equator (during the equinox) and then appear vertical (but inverted) again?

Incorrect.
I saw a great video on this about two weeks ago explaining why but I can’t find it right now.

The Sun is at the celestial equator at the equinox, not the moon. In fact a first or last quarter moon is offset 90 degrees in longitude from the Sun; at the equinox the quarter moon is at its extreme north or south point, and at the solstices the quarter-moons are over the equator.

Get this idea about spinning out of your head. The only way to make the moon spin is to rotate your body. If you rotate your body as you cross the equator–which would be pretty difficult in an airplane–then yes, the moon will flip directions.

The convex part of the lighted moon side is always facing the sun. How could it be otherwise? That’s where the light is coming from.

When I travel from NYC to Argentina, I do rotate my body, since my feet are always pointed towards the center of the Earth.

I’m starting to think that the terminator must almost never appear vertical, given an arbitrary point on Earth. It must have an angle equal to the sin of your latitude (at the equinoxes, and some adjusted latitude at other times), right?

It’s day time here, and I think it’s close to a full moon, so I can’t actually check for another week or so.

But your head is facing in the same direction. If your airplane is traveling south, you’re facing south (while you’re in a seat, at least.) You continue to face south after you cross the equator.

Do you mean vertical as in “perpendicular to the horizon”, or vertical as in “aligned with a celestial longitude line”? Put another way, are you using alt-azimuth or celestial coordinates?

[quote=“Freddy_the_Pig, post:13, topic:726961”]

But your head is facing in the same direction. If your airplane is traveling south, you’re facing south (while you’re in a seat, at least.) You continue to face south after you cross the equator.[\QUOTE]

Right, but I go from right-side up to up-side down.

Yeah, I’m starting to feel a bit foolish on this point. I was thinking perpendicular to the horizon, but I’m convincing myself that the terminator is never perpendicular to the horizon (except at a certain latitude). See my thoughts about sine of the latitude (during the equinox, anyway).

Well, you go from “partly right-side-up” to “partly upside down”, unless you’re going pole-to-pole.

So, imagine yourself facing south, looking at the first-quarter moon before you board your airplane. It’s directly in front of you, about halfway up in the southern sky. The lit side is to the right.

You board your super-duper-sonic aircraft, facing south, and it whisks you to the southern mid-latitudes in a few minutes. You watch the moon out an overhead window. As you travel, it gradually climbs higher and higher in the sky–because your body angle is changing with the latitude–and then eventually it passes overhead and moves behind you. As you bend your head back behind you, and look at it, the lit side is still to your right.

When you land, still facing south, it’s still behind you–but you want to look at it, so you rotate your body and face north. Lo, the orientation flips. The lit side is now on the left.

Sure it is. Imagine a first quarter moon, rising at noon and setting at midnight. When it rises, the terminator is parallel to the horizon, facing down. When it sets, the terminator is parallel to the horizon, facing up. At some point in between, during the night, the terminator will rotate through perpendicularity to the horizon. It has to.

I’ve seen such a “Cheshire Cat” moon in northern Florida on a number of occasions.

It’s because the sky appears spherical due to perspective etc - so you have to map the straight lines onto a sphere, then they look like curves.

A hopefully really easy way to grasp that there is more to this than meets the eye:

You’re standing on a railway track; to the west of you the straight tracks appear to be joined at infinity and splay out as they get closer to you, but to the east of you, they get closer together again as they disappear into infinity. How can straight, parallel lines get further apart, then closer together again, and still be straight?

That, of course, has nothing much to do with laying straight lines on a curved surface. If you had an indefinitely large perfectly flat area, and laid down railroad tracks on it, you’d still see it like this.

Johnny Hart, of B. C. fame, addressed the question of whether parallel lines ever meet. B. C., attempting to demonstrate that parallel lines never meet, drew two parallel lines in the ground using a forked stick. He walked for some arbitrary distance, with the two points of the forked stick drawing two parallel lines.

As he proceeded, the two forked ends gradually wore down, so that the lines got closer and closer together. Eventually, as the stick wore down to the point where the two forks met, the lines drawn in the sand also met. Euclid had it all wrong.

The sky isn’t really curved and the sun and moon aren’t in it either. Point is that perspective means you can’t extend straight lines by eye to where they actually go.

Still can’t find that video but here is an earlier discussion of it.