The Moon from three feet

A really fun problem from Bill Maney this month. I'll start with his explanation:

"I'd like to make a 3D picture of the moon (an old fashioned stereogram type of thing). I figure if I take a picture of the moon at the same phase but on two different lunar cycles, I would get two different librations and if I arrange them correctly, they could be used to make a stereo image."

Sure! Neat idea. He goes on:

"I doubt if this is an original idea, but it's seems like a good project."

I have no idea if the idea is original or not but I hadn't previously thought of it, so if it's old hat at least two of us have to wear it.

This raises some fun issues.

I know Bill knows if you really want to make an accurate stereovision view of the Moon, all you need to do is use the same photo twice. That's how it looks.

From the point of view of our human binocular vision the Moon is effectively at infinity, and we get no "stereoscopic" advantage to using both eyes.

But we do get a three dimensional effect somehow anyway. This can easily be illustrated by looking at the Moon through a good telescope with a binoviewer on it. Of course both those images are identical from a practical standpoint, but the illusion is startling.

But hey, we have this big ol' planetoid hanging up there in the sky, and it has a weird tendency to shake its head at us. How many planet-dwellers can say that?

Seems like we're practically morally obligated to take such a picture, and make the stereogram.

But ... what would you get?

You'd get an image of the Moon that would look like it was about three feet away (no surprise; I gave it away with the title). Or more. But probably not much less.

I managed to establish this by a highly scientific experiment. Since I know the maximum libration totals about 7 degrees either way (east or west, left or right, whatever) I simply moved back from my moon globe until I saw about that effect by closing one eye and opening the other.

This may turn out to be completely bogus, but it's a starting point.

And, of course, it assumes a virtual image about the same size as the globe at that distance. In fact, the more I think about it the more I realize I'm very unclear on how close it would look, but I'm fairly safe in assuming it would look a lot closer than a quarter of a million miles.

I'm fascinated with the idea of noting how many folks who looked at such an image would figure out something was very wrong with it?

Here's another fun point: the image turned toward the right (as you face it) is the one you should put on the left side of the stereograph (and vice versa of course). Your left eye would see more of the left side. This may seem counterintuitive, but so is the universe, so don't let that trouble you too much.

Now about the mechanics he had essentially three questions.

The first is, how to predict when you might be able to get a photo at exactly the same phase with some libration? He was particularly interested in locating a program to manage this.

I would particularly recommend Akkana's "Hitchhiker's Guide To The Moon:" http://shallowsky.com/moon/ It features libration and phase angle prominently, and you can change the date to anything you want to home in on the next similar phase.

However, for this simple problem you don't need software. If, say, you wanted an elevated eight or nine-day-old Moon (excellent choices for such a photograph) and then wanted the next available opportunity to shoot that phase, add 59 days. It's that simple.

But, you say, wait! The Moon has about a 29-1/2 day cycle, so why not ... oh. Because that which is high at night this month will be, alas, high during the day next month. By the time the sun sets, the terminator will be marching toward it (but never quite get there) or already past, depending.

Still, you might be able to get close. It's not clear it would be close enough, though. Besides, we want a lot of libration, don't we? And generally the longer you wait, the more change you'll get. Up to a point.

Wait a year and you'll get next to nothing, for example.

I'm writing this on February 11; let's see what happens if we check position and libration around 8 p.m. tonight ... the terminator is 36.9 West and the libration is 5.75 West (also note: 2.12 South).

First, add 29-1/2 days just to see what happens. Very close. If we add another 90 minutes, we're in the right place. The only problem is, yup, it's 9:30 am, and the sun is up. That won't work!

Okay, let's add 59 days and see what we get. What luck! Due to a calendar quirk, that's April 11! February's weirdness makes for a singularly easy time to calculate 59 days into the future...

So the result is: at 8 p.m., April 11 35.4 degrees west. Hey, wait! That's over a degree off! You'll have to wait until about 11 pm to get the same result! (Actually midnight, after you allow for Daylight Squandering Time). Fortunately, that would still be okay.

But note the western libration is now 7.61 degrees, almost two degrees more. That should be enough to give our Moon illusion. So we're in business, right?

Wait. Bill was also curious about the North/South or Up/Down libration. Where is that now?

It's at 6.64 South. Ouch. It has actually moved more to the south than it did to the West! That would look just a bit weird now, wouldn't it? What are we going to do?

Stereoscopic vision kind of assumes a difference from left-to-right, but no real change from top to bottom. (That is, of course, because our eyes are placed side-by-side and not above-below. Unless you're a Charles Adams fan).

So how to solve the problem? Study the orbit of the Moon, and spot the point where the North/South libration shifts little (if at all) while the East/West libration would shift the most.

Logic tells us this would be when the two apparitions cross the axis determined by the Moon's closest approach to the Earth.

When is that? Why do I say that?

Enough for now.

All the problems in the Universe cannot normally be solved in a single column. If there aren't any better questions over the course of the month, maybe we'll solve this problem in the next column.