How High the Moon? (Part Deux)

I have an experimental data point for the zenith angle of the moon last night.

We have a skylight in our bathroom. I was able to see the glow from right next to the moon, directly to the south, through the frosted glass. But not the moon itself, no matter where I stood. It appeared that I had lucked out and happened upon the moment when the moon was the highest in the sky. Or so I thought.

This morning I used a tape measure to measure the distance from the top of the skylight to where my head was (92 inches), and the horizontal distance that my head moved (40 inches). Assuming those form a right angle, and using the arc-tangent function on my calculator,  I get a zenith angle of about 23.5 degrees.

I don’t believe it!!!! It should be less!

Why is the moon so high in the sky in winter?

And was it in fact directly overhead last night, near the beginning of the eclipse?

It sure looked like it was to me – though I didn’t take any measurements because I was only wearing my pajamas, my coat, and my slippers as I stood in the freezing cold on the snow-free but still-frozen concrete walk in front of our south-facing, Northeast DC  house.

[Yeah, I was being wimpy, only going out twice all night to look at the eclipse, but I was really tired, and I had to get up in the morning to give a full day’s guest lesson on astronomy to four, 70-minute middle school classes for a fellow teacher, so it was kind of  out of the question to stay up all night. (There is no way I could have followed through with the lessons if I had!)]

Maybe I’m just weird, but I have from time to time noticed, and marveled at, the fact that during the winter, the moon at times appears like it’s almost directly overhead. Let me emphasize that: to my unaided, subjective vision, without taking the trouble to measure it, during the winter, the moon sometimes appears to me to be directly overhead (at zenith).

However, everything I know about astronomy of the solar system tells me that this is probably impossible, simply because we do not live in the Tropics (with a capital T: the zone between the Tropic of Cancer and the Tropic of Capricorn). That’s the only part of our planet where the sun is ever directly overhead. (Don’t believe me? Use your internet resource skills and look it up. I’m not going to tell you just how to do that, because since you are reading this blog, you already know how.)

If you live in Washington,  the Sun will never appear directly over your house, no matter where you live in Washington, DC, and no matter how hot it may feel in the middle of summer.

And I figured that if the Sun and the Earth and the Moon were all aligned with each other, as in last night’s lunar eclipse, then the Moon would appear in our sky here in Washington as if it had simply traded places with the Sun for a while, and was at the same elevation. And that elevation just ain’t all that high.

Or so I thought.

Was I suffering from a version of the famous ‘moon effect’? (Which is a poorly-understood but almost-universal optical illusion about the apparent size of the moon,  a visual hallucination of sorts, caused by some internal human visual processing “bug” inside the various centers responsible for actually interpreting the photons and light waves that enter one’s eyes.)

Or is everybody else normal and it’s just me?

Or was the moon, in fact, at the zenith?

Or just very close to it, but within the theoretical and experimental range of error for this sort of thing?

I am going to try to settle this in two ways.

First of all, theoretically.

I used a rather widely-used piece of instructional geometry software called “Geometer’s Sketchpad” (version 5 in this case) and a couple of drawing and painting programs. I also used Google Earth to find out where on Earth are the places that are directly south of Washington and are on the Tropic of Cancer or on the Equator, as well as the spot on our planet that is diametrically opposite in position to Washington, DC.

I was rather surprised to find out where those places were. They weren’t really where I expected, and I of all people should have known better.

For example, I thought I remembered that Havana, Cuba, was just inside the Tropics, but Miami, Florida, was just north of the Cancerous Tropic. Or was that the Topic of Cancer? (Ha, ha, that was two intentional puns. If you don’t get them, or don’t think they are funny, that’s fine with me.) And I also remembered having been to some places in Florida that it was south of DC.  So I kinda figgered that the Tropic of Cancer would intersect our DC line of of longitude (about 77 degrees west) somewhere in the water between Havana and Miami.

Surprise: not very close. Just for fun, try guessing or figuring out the answer yourself. I’ll hide the answer at the end of this column, at (1).

And directly south of DC, on the equator? I always kinda figgered it would be somewhere in Brazil.

No surprise this time, I was wrong again. When I looked carefully, I discovered that 77 W and 0 degrees N or S is located… (2).

How about the point diametrically opposite to Washington, on the exact other side of the globe? Well, on this one I was fairly close. But calculating where this is, is a bit tricky. The latitude is OK. Any point at X degrees north is directly opposite some point that is X degrees south. So wherever it is, it’s at 39 degrees south. But the longitude is harder, because for most locations, Y degrees west is not opposite Y degrees east. What you have to do is change your latitude by exactly 180 degrees. Now here, you can either add or subtract. I would prefer to subtract, here. So 180 minus 77 gives us 103. (Of, if you prefer, 77 minus 180 gives -103.) And the way I interpret that 103, or -103, is to consider that as being 103 degrees east longitude.

Now knowing that DC’s literal antipode is roughly located at 39 degrees south and 103 degrees west, can you guess, or find, where that is? (3)

Here is the diagram that I made.

Bottom Line: if my diagram is correct, the full moon last night, at its greatest elevation or altitude last night, should have been about 15.5 degrees from the vertical (or 74.5 degrees from the horizontal). And that angular distance from the zenith should have been clearly and plainly obvious.

But it wasn’t. To me.

Now that’s just last night. Is it possible for the moon to be inclined a bit to the apparent orbit of the sun – that is – when the moon is not undergoing an eclipse? And can that cause the moon to be even higher in the sky than it was during last night’s eclipse?

Answer: YES. The moon ‘s orbit around the Earth is inclined by just about 5 degrees from the Sun’s apparent orbit. Thus, in different years and months, the details of which I will ignore right now ’cause it’s way too complicated for this here blog today, the moon might be as high as 10.5 from the vertical (79.5 degrees from the horizontal).

Next time: actual measurement

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Spoiler

answers below

or you could interpret my diagram..

(1) 77W and 23.5N turns out to be right next to Nassau, the capital of the Bahamas!

(2) it was about 100 or so miles east of Quito, Ecuador, along the banks of some huge jungle river that probably flows into the Amazon River, but doesn’t even seem to have a name. Nor any towns. Or roads.

(3) It’s located several hundred km, mi, or nm west-south-west of Perth, Australia, in the middle of the Indian Ocean. No land for hundreds of leagues in any direction, as the pirates or sailors or yarntellers of yore might say.