SJAA Ephemeris September 2004 | SJAA Home | Contents | Previous | Next



Dave North


“ ... the Moon's mass is only about 1/81 of the Earth's, and in fact its density as far as I know is only about 60 percent of the Earth's. ”



If there's anything particularly interesting happening on the Moon in September, I don't know about it.

This month's "pseudo event" is the Harvest Moon. It has that name simply by virtue of being the time of year somewhere when people would be harvesting crops, and if they really needed to work late it would throw enough light. There are probably a few other details as well.

Nevertheless, I've been pondering my fuzzy understanding of the size (and therefore volume) and mass of the Moon, and various theories of how it got where it is.

The Moon is about 3,476 Km in diameter, or for local convenience, about 2,160 miles. The Earth, by comparison, is about 7,926 miles at the equator.

Since we're just running rough numbers, let's see how that compares in volume, shall we? First, let's round out a bit for convenience and say the Earth is about 8,000 miles in diameter, and the Moon about 2,000. That gives us a simple 4/1 ratio.

The volume of any two solids of identical shape (but different dimensions) can be compared by taking the cube of any one dimension. So all we have to do is cube 4 (since we're only after a ratio) and we get, of course, 64.

So if the Moon and Earth were made of the same stuff, we'd presume the Moon would have about 1/64 of the Earth's mass. (I think it's interesting to reflect that the Moon, as comparatively big as it is, with over 1/4 our diameter, only has about 1/60 the volume. That's numbers for ya).

But back to mass: in the real world, the Moon's mass is only about 1/81 of the Earth's, and in fact its density as far as I know is only about 60 percent of the Earth's.

It turns out we do share quite a similar mineralogical makeup at the surface, so the consensus is the Moon doesn't have anywhere near the density at the core.

This presumes a lot less iron and nickel, basically. This lack of iron is generally presumed to be the big problem with the idea that the Moon and Earth formed from the same bunch of scraps, dust and whatever and is the primary driver behind the theory that the Moon was formed when an impactor hit the earth and tossed a bunch of stuff into orbit, some of which formed into the Moon.

The basic idea is if the Moon and Earth formed from the same "cloud" or "ring" or whichever/whatever term you prefer, they should have nearly identical constituent elements in similar proportions.

Curiously, in some ways they do. The isotope composition is so similar that they are generally agreed to have been made of the same source matter. But that works for either idea.

But that iron ratio, that's the big problem. And also what I've been mulling.

What I can't figure out is why a coalescing cloud/blotch/whatever should, if it somehow has a major and minor "glob," have the same stuff end up in both globs in the same proportion.

First, let me point out we're pretty sure binary systems do form with some regularity, though not as planets in our solar system. And it is not at all uncommon for those binaries to not be of equivalent size.

So at any rate, it's not ridiculous to think a binary planet could be formed as primarily a coalescing event at least as far as I know.

Given this can happen, what would you expect if one of the clumps started out bigger than the other?

We would hardly expect them to start out identically pure luck would indicate a fairly broad distribution of possibilities.

Given that, do the rich normally get richer and the poor get less? In other words, if one is more massive, would we expect it to attract more mass? And if it were (quite naturally) close to the center of mass of the evolving system, would we not expect some sorting to take place, ending with the more massive "stuff" ending up nearer the center?

And if that were indeed the case, wouldn't it be reasonable to expect something not unlike the Earth/Moon system we see here?

I'm just asking in a "food for thought" kind of way, partly because I haven't seen this issue addressed. I'm not an exhaustive researcher, just curious.

Maybe Kevin or Jeff or someone else will have nothing else to do but read this and can explain (or not).

I'm curious!


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