I’m naively impressed by facts that seem very improbable. Guess I’m on the lookout for “signs and wonders.” Whatever.
Let’s consider two astronomical facts. First, the visible disk of our Moon, as viewed from the surface of the earth, has precisely the same diameter as the visible disk of the sun. “Precisely” means–pretty dang precise: the difference is so slight that during a total solar eclipse, there is a moment when the sun is blocked-out all the way around by the lunar disk, except for a few small points of light at the periphery, called Bailey’s Beads. These are places where the solar disk is showing through between mountains at the edge of the moon. Considering how slight these elevation-variations are in comparison to the lunar cross-section–that’s a mighty good fit!
But there’s more. The Moon is receding from the earth due to tidal drag (I think). That means the visible disk was once larger; and someday it will be smaller. Assuming constancy on the part of the solar disk, their matching happens only during a portion of earth’s history–the part we’re in right now.
FIRST QUESTION: Given that the diameter of the Moon, its rate of recession, the total age of the earth, and the span of time intelligent life has existed here, are all independent variables–how would one go about estimating the likelihood of things coming together to produce a “human-visible perfect fit,” as they do? Which account is more rationally defensible: A. “Any possible combination of factors will happen sometime, somewhere: no further conclusion is supportable.” B. “The premise of the independence of one or more factors is false.”
And then we have the planet Venus. It turns out that Venus rotates in such a manner that it always has the same face turned toward the earth at the point of closest approach between the planets; to accomplish this feat it has to rotate backwards, the only planet to do so. No one knows why this should be. Doesn’t happen re: Mars and Earth (or Mars and Jupiter). Gravitational interaction (as between Earth and Moon) seems too weak–plus one would think solar tidal effects would interfere. Go figure.
SECOND QUESTION: Basically the same as the first, but as applying to this harmonization of Venus’s rotation.
The situation you discuss with Bailey’s Beads around the whole Sun is rare. Typically they’re only seen during ingress and egress because only rarely does the Moon precisely cover the Sun.
The Moon’s orbit is not circular, so when the Moon is near apogee (its farthest point from the Earth) during a solar eclipse we have an annular eclipse, where the Moon covers all but the outer ring of the Sun. And when the Moon is at perigee (its closest approach to the Earth) it covers a good deal more than the Sun’s disk–the Moon is effectively 40 kilometers “too big” to exactly cover the Sun’s disk.
Assuming that the Moon’s eccentricity (the uncircularness of its orbit) stays constant (bad assumption but it’ll give us a ballpark) and that its rate of recession stays constant at a rate of a couple-few centimeters a year (even worse assumption) it will take on the order of a billion years for the Moon to be so far away that there are only annular eclipses, even with the Moon at perigee. Using the same corny assumptions, you have to go a few billion years into the past to find a time when the Moon’s disk even at apogee covered the entire Sun so that there were no annular eclipses. [Somebody check my math if you don’t mind. These figures are just ballparks, but I’ve been known to fumble a few factors of ten now and then.] Now, roughly speaking the rate at which the Moon moves was faster in the past and will be slower in the future, so the few billion years in the past is an overestimate and billion years in the future is an underestimate. And I really have no clue what the eccentricity of the Moon did or will do, to be perfectly honest. It’s probably all over the place.
But, let’s just say it doesn’t exactly give me chills.
As for Venus, well, yeah, it doesn’t happen for Mars or Jupiter (which would be tough, since Jupiter has no solid surface and rotates at different rates at different latitudes) . . . wouldn’t it be a good deal creepier if Venus wasn’t the only one and there was no plausible physcial explanation? FWIW, my money’s on some sort of undiscovered orbital/rotational resonance . . . but that’s nothing more than a romantic attatchment to the notion that spin/orbit coupling can explain the retrograde rotation of Venus and the high obliquity of Uranus. Could easily be due to the collisional histories (and thus a random coinincidence) in either or both cases.
If the moon is at it’s farthest point when eclipsing, a ring of the sun is still visible around it, so it is not always a total and perfect eclipse. I think this is called an annular eclipse.
Venus. I’m not sure of the question you are asking. Earth and Venus do not have a rotational effect on each other.
As these two figures show: Annular Eclipse of the Sun Total Eclipse of the Sun
The sun and the moon are not exactly the same size as viewed from earth. The moon’s elliptic orbit causes it to appear slightly larger than the sun for part of the month and slightly smaller the rest of the time. “About the same size” is OK as far as coincidences go. I’d only get concerned about heavenly portents if the moon were precisely Phi (1.61803) times the sun’s diameter.
A quick bit of googling on the inferior conjunctions of Venus reveals that the mystery surrounding why the same side always faces us is wrapped in far too much hearsay to be unravelled without some hard data. AFAIK the day length of Venus (243.08 earth days) is not all that close to being an even divisor of the 584 days between close approaches to earth.
The gist of the responses so far is: These coincidences are not as gol-durned precise as you think, so chill. OK, acknowledged.
It is still the case that the average visible disk of the Moon is mighty close to that of the Sun, and that Venus’s rotation is harmonized enough with Earth’s recurrent close approach to have frustrated radar astronomers in the 60’s-70’s. “Between one close approach to Earth and the next, Venus rotates exactly five times, so at its closest approach it always presents the same side to the Earth. This fact was extremely galling for the pioneers of radar astronomy…” (Nigel Henbest, THE PLANETS, 1992).
Correcting my stated factoids as necessary-- anyone want to take a crack at my questions?
I was trying to take a crack at your probablities by way of estimating the timescale over which total and non-annular eclipses are possible–compare that the the lifetime of the human race, and you can get the feeling that, given the Earth-Moon system, it’s not highly imporobable that we would happen live at the right time see “prefect” eclipses.
I’m not a statistician, but it seems that if you want a numerical probability for the Moon being approximately the right size (or the whole Venus thing) you’d have to know much more about planetary formation than we do. So far we have only set of terrestrial planets to study . . . I think it’d be pretty hard to estimate how likely it is for planets like ours to have moons, let along a large moon. To know the probability for there to be a relationship between a planet’s rotational period and the orbital period of the next planet out, you have to know the distribution of rotational rates of terrestrial planets, something it’s probably not safe to generalize from just four examples!
Perhaps someone who’s more skilled at lies, damn lies, and statistics could shed some more light.
Scott, I have to concede with you there that there is some mighty strange coincidences going on. But then, if you look at systems as a whole, there are often strange coincidences. There is a famous numerological coincidence involving the distances of planets to the sun involving a famous mathematical sequence. Utter numerology. That doesn’t mean that it isn’t interesting, it’s just a coincidence. What are the chances of such a coincidence? Well, for any GIVEN coincidence, the chance is extremely high. Ridiculously high. The fact of the matter is, we live in a universe that is ridiculously complex and there are BOUND to be some coincidences. How many? Well, actually it’s probably pretty arbitrary. I could state a number of other coincidences that have seemed to be mind boggling, but I won’t bother. The point is, it doesn’t make much sense to evaluate the PROBABLITIES of such events occurring because really what we’re talking about is a whole slew of POSSIBLE coincidences that never really occur and a small handful that do.
Sematantics! you say? Just gimme the dirt? Well, I don’t think that that is possible because I don’t know how I’d use Bayseian analysis to conduct this study. I say, stop worrying about this and enjoy them for what they are… especially the solar eclipse coincidence, because it’s really one of the most amazing things to witness!
Of course we all know that Venus is in fact a cometary body produced from within Jupiter in the past few thousand years, and has come in close contact to earth on several occasions.[/velikovsky]
The coincidence you refer to is known as the Titus-Bode relationship (“Bode’s Flaw”) which was popularised in 1772 by Johannes Bode and correlated quite well with the known data as well as Uranus (discovered in 1781) led Bode to predict the existance of a planet between Mars and Jupiter, where the largest of the asteroids Ceres (discovered in 1801) was later found to be. However, it later failed rather dramatically when it was applied to Neptune and Pluto after their discovery.
Fun things to ammuse ones mind with, but unlikely to be more than co-incidence…
What!!? You mean my eyes can detect light in the ONLY region of the spectrum that is NOT absorbed at all by the Earth’s atmosphere??! :eek:
I get the point, GrimPixie: it’s the same logical flaw as that involved in being amazed that Reality happens to exist at all. (Like, what’s the alternative?) But my question involves factors not obviously correlated to the present existence of sentient beings; therefore I think the parallel does not apply.
As to “coincidences just happen, etc.”. --That was one of the alternatives I mentioned in my OP. But when I flip a switch and the light comes on, I don’t say “it’s a big universe and a large scale coincidence of switch-flipping and bulb-activation is bound to happen somewhere.” I look for a causal account. This implies that it is the degree of the improbability of the “match” that matters. And I’m looking for some rule-of-thumb way to estimate that degree. For example, humans have been here for, what, about one two-thousandths of the span of earth’s existence; how much has the size of Luna’s visible disk changed during that span, versus the whole time since earth attained more or less its final shape and mass? Can’t some sort of very rough probability judgment be based on that info?
BTW, I do think solar eclipses are beautiful, and deserve to be contemplated just for that.
“how much has the size of Luna’s visible disk changed during that span, versus the whole time since earth attained more or less its final shape and mass?”
So use 375,000 km as an average distance to the Moon, and use use 1.75 cm/year as an average recession rate.
Toss in a bit of geometry:
The moon would be twice its angular size at half the distance, and half its size at twice the distance.
375,000/2 = 187500 km = 18750000000 cm
18750000000 cm/1.75 cm/year = 10,714,285,714 years.
So the moon would have appeared twice its present size if the solar system had been around 11 billion years ago. Omitting the math, the moon will appear half its present size in about 44 billion years.
So there’s a pretty long stretch of time during which the moon will appear about the same size it is today. That doesn’t much room for mystery does it ?
could shed some more light.