Venerean transit

Even rarer than a Diamond Jubilee is a transit of Venus across the face of the Sun, which (weather permitting) we should get a chance to see near sundown on Tuesday, June 5.  Grab that chance, for you won't likely get another.  Like a solar eclipse by the Moon, a transit occurs only on the infrequent occasions when a celestial object passes between the Earth and the Sun just when the slightly tilted planes of the orbits of the Earth and the other body intersect at a "node."  In the case of Venus, with its 225-day "year," things line up properly according to a 243-year cycle, during which there are a pair of transits about 8 years apart.  Because the last transit occurred in 2004, Earth residents won't see another one until well into the 22nd century.  In ordinary years, Venus will pass the Sun as many as 18 solar diameters above or below, casting no shadow.  (I don't remember hearing a word about the 2004 transit, do you?)

Watching a transit of Venus, like watching a solar eclipse, requires care to avoid eye injury.  Most darkened glasses are considered insufficient.  The safest and easiest viewing results from watching an image projected through a tiny pinprick in paper.  As you can see from the picture, however, the disk of shadow is quite small.  Better viewing probably can be found in a planned NASA webcast.

Though the first documented awareness of a visible transit across the face of the Sun was in the 17th century, ancient cultures have tracked the orbit of Venus for millennia.  Beginning in about 1200 B.C., Babylonian astronomers noticed the regular patterns of the heavenly bodies and produced star catalogues.  By the 7th century B.C., they had produced a careful chart of the risings and settings of Venus over a period of 21 years, perhaps the earliest evidence of an understanding of the periodicity of planetary phenomena.  The Babylonians seem to have concentrated on periods and prediction without developing a spatial, geometric model for the movement of the planets.  It fell to the Hellenistic Greeks to postulate ideal circular motions.  An early 3rd century B.C. astronomer named Aristarchus is said to have been the first to deduce that the Earth spins around its own axis while rotating around the sun.  Although his arguments persuaded a 2nd century B.C.  Chaldean astronomer named Seleucus, most of the ancient world, including Aristotle and Ptolemy, adopted a geocentric model that persisted for over a thousand years.

The geocentric model was supported by careful observations that permitted surprisingly good predictions of the location and timing of astronomical events.  It suffered from two serious drawbacks, however.  First, the planets were required to inscribe all kinds of complicated little circles within circles ("epicycles") in order to conform to astronomical observations of periodic retrograde motion.  These epicycles were not so much errors as unnecessary complications resulting from adopting an extremely inconvenient point of reference.  Copernicus solved the "wheels within wheels" problem in the 16th century A.D. by returning to the heliocentric model that never should have been abandoned in the first place.  Unfortunately, his model could not improve on the Ptolemaic predictions because of the second drawback in both systems:  the over-simplified assumption that planetary motions were the perfect circles that all right-thinking people considered essential for dignified celestial bodies.  As a result, even the more open-minded authorities were slow to jettison the old geocentric model.  Johannes Kepler soon solved that problem by figuring out in the early 17th century that the orbits must be elliptical, with the sun at one focus of the ellipse.  (At about this same time, Galileo Galilei was using the brand-new telescope to discover that Jupiter had its own moons in orbit around itself, and that Venus showed phases just like the Earth's moon, suggesting that it orbited the sun rather than orbiting the Earth.)  It fell to Kepler, with his unprecedented grasp of the mathematical underpinnings of orbital mechanics, to make a successful prediction of a transit of Venus, in 1631, which went a long way toward conferring respectability on the new-fangled model.

Galileo conducted careful experiments with falling bodies and figured out that objects near Earth followed parabolic trajectories, in which the lateral movement varied directly with time but the vertical movement varied with time squared.  It did not occur to him, however, or to anyone else, apparently, to connect this mathematical pattern with the movements of the planets.  It required the incomparable genius of Isaac Newton, late in the 17th century, to connect the two in a single law of gravitation.  He is famously supposed to have considered the falling of an apple from a tree in conjunction with the Moon hanging overhead, and to have imagined stretching the curving path of a thrown object until it could stay aloft all the way around the horizon and describe a full orbit.  All these motions, whether of apples or planets, are varieties of what we now call conic sections:  the shapes that can be derived geometrically from the essential characteristic of an inverse square law, including circles, ellipses, parabolas, and hyperbolas.
  • Circle:  x2 + y2 = r2
  • Ellipse:  x2 / a2 + y2 / b2 = 1
  • Parabola:  x = y2
  • Hyperbola:  x2 / a2 - y2 / b2 = 1
The heliocentric view has not been an unalloyed popular success.  Polls still show that something like a fifth of the population believes the sun revolves around the Earth.  Chances are, the transit of Venus won't change their minds.


Grim said...

The Babylonians seem to have concentrated on periods and prediction without developing a spatial, geometric model for the movement of the planets. It fell to the Hellenistic Greeks to postulate ideal circular motions.

This is correct, but there's an important addendum: the Babylonian system worked better. The Greek system failed to generate accurate results some of the time precisely because it tried to create a model that explained the results, instead of just using the empirical data to predict future phenomena.

In this way the Babylonians were somewhat like the modern physicists we've discussed who 'just calculate!' without worrying about the fact that their methods for dealing with infinities that crop up are theoretically impossible. Like the Greeks, those who are concerned about that are working with models that don't line up with reality in ways we can't quite see yet.

Also like the Greeks, though, they are probably the ones who are someday going to push us to a new level of understanding. The short-term generation of inaccurate theories is what laid the foundation of insight for later scientists. If all we had were the Babylonian tables, we may never have gotten to Galileo.

bthun said...

Thanks for the heads-up Tex...

The 24 hour notice gives all an opportunity to craft a really spiffy pinhole projector.

When I was a wee lad, I used to make them from balsa wood procured from the hobby shop. Cardboard works just as well.

karrde said...

You know, I've heard that explanation of gravity, orbits, and conic sections several times.

But your simple statement, plus a good picture, seems so much better than most textbook versions of it I've seen.

(On the other hand, I recognized the conic-section picture and its meaning immediately. Likely because of those classes...)

RonF said...

Ah, I always learned parabolas as ax**2 + bx +c = y, which I suppose would be comparable to x**2 = y - but not to x = y**2.

Tom said...

Plus, the heliocentric system made a hash out of physics in Galileo's time and offered no replacement theory.

I'll be outside when it happens, but alas I'll have to see photos afterward.