[QUOTE=ewmayer;301391]I measured the diameter of the projected Sun on the paper at 3.5", that of Venus around 3/32", which corresponds to a ratio of ~2.7%. The corresponding areal ratio is ~0.07%, so that must be what the above article referred to imprecisely as "size".

Compare that with what one would expect based on measured diameters and distance from-earth -- note that neither the orbit of Venus or earth is sufficiently noncircular to worry about where each is w.r.to its perihelion/aphelion (Earth's orbit is the more eccentric of the two, fwiw), and computations rounded to around the nearest 1%:
[code]
Venus: radius = 6,000 km, avg. orbital radius = 108,000 km
Sun : radius = 696,000 km, avg. distance from earth = 150,000 km
[/code]So the diametral ratio Venus/Sun = 6/696 ~= 0.062%, but since the Sun is ~150/32 ~= 4.7x[/QUOTE]should be ~150/[B]4[/B]2 ~= 3.6x

[quote]farther from Earth than is Venus, we multiply the two together to get an apparent ratio ~= 4.0%,[/quote]I get 6/696 * 150/42 = 0.03

[quote]slightly more than I measured,[/quote]You were closer than you thought. :-)

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Added:

[quote=ewmayer](although I would think those would make the apparent size of venus larger rather than smaller)[/quote]There's also the irradiation effect, which would make Venus look smaller.

I forgot to link to NASA's page [URL]http://eclipse.gsfc.nasa.gov/OH/transit12.html[/URL] which says:
[quote=Fred Espenak]. . .

... Venus's 58 arc-second diameter disk ...

. . .

Since the apparent diameter of Venus is nearly 1 arc-minute, it is just possible to see without optical magnification (but using solar filter protection) as it crosses the Sun. Nevertheless, the planet appears to be only 1/32 of the Sun's apparent diameter ...[/quote]

[QUOTE=ewmayer;301391]Transit about 3/4 done as I write this - just put away my 4" scope annd misc. accessories a half-hour ago. [/QUOTE]I set up in a local park. Had my 35mm SLR with a 500mm mirror lens (with a front end solar filter). Also toted my eclipse 'glasses' along. Some folks knew about the transit already, others didn't. I actually approached people and offered them 'the view of a life time'.:geek:

NASA has posted a very cool high resolution video of the transit:
[url]http://www.youtube.com/watch?feature=player_embedded&v=4Z9rM8ChTjY[/url]

[QUOTE=cheesehead;301411]should be ~150/[B]4[/B]2 ~= 3.6x

I get 6/696 * 150/42 = 0.03

You were closer than you thought. :-)[/QUOTE]

Like Talking Posable Action Barbie says, "Math is hard." Thanks for the catch.

I had a good view, although clouds rolled in just at the ingress, so I missed the beginning. Still pretty impressive. I would guess that Mercury would appear as a tiny pinprick by comparison. It transits in 2016 and again in 2019.

[URL="http://newscenter.berkeley.edu/2012/06/08/theorem-unifies-superfluids-and-other-weird-materials/"]Theorem unifies superfluids and other weird materials[/URL][QUOTE]The theorem Watanabe and Murayama proved is based on the concept of spontaneous symmetry breaking, a phenomenon that occurs at low temperatures and leads to odd behavior. This produces superconductors, which allow electric currents to flow without resistance; or Bose-Einstein condensates, which have such low energy that every atom is in the same quantum state.

By describing the symmetry breaking in terms of collective behavior in the material – represented by so-called Nambu-Goldstone bosons – Murayama and Watanabe found a simple way to classify materials’ weirdness. Boson is the name given to particles with zero or integer spin, as opposed to fermions, which have half-integer spin.

“Once people tell me what symmetry the system starts with and what symmetry it ends up with, and whether the broken symmetries can be interchanged, I can work out exactly how many bosons there are and if that leads to weird behavior or not,” Murayama said. “We’ve tried it on more than 10 systems, and it works out every single time.”

Anthony Leggett of the University of Illinois at Urbana Champaign, who won the 2003 Nobel Prize in Physics for his pioneering work on superfluids, pointed out that “it has long been appreciated that an important consequence of the phenomenon of spontaneously broken symmetry, whether occurring in particle physics or in the physics of condensed matter, is the existence of the long-wavelength collective excitations known as Nambu-Goldstone bosons.

“In their paper, Watanabe and Maruyama have now derived a beautiful general relation … (involving) Nambu Goldstone bosons … (that) reproduces the relevant results for all known cases and gives a simple framework for discussing any currently unknown form of ordering which may be discovered in the future.”

“Surprisingly, the implications of spontaneous symmetry breaking on the low energy spectrum had not been worked out, in general, until the paper by Watanabe and Murayama,” wrote Hirosi Ooguri, a professor of physics and mathematics at Caltech. “I expect that there will be a wide range of applications of this result, from condensed matter physics to cosmology. It is a wonderful piece of work in mathematical physics.”[/QUOTE]

[QUOTE=Jeff Gilchrist;301453]NASA has posted a very cool high resolution video of the transit:
[url]http://www.youtube.com/watch?feature=player_embedded&v=4Z9rM8ChTjY[/url][/QUOTE]

A little late, and from the lower resolution end- My teenage sons were able to watch the start and much of the transit from Arizona with a 6-inch reflector, and I was able to see the end of the transit with binoculars in Copenhagen (traveling on business). With proper solar filters, of course. Great views, and worth the preparation. What really amazed me was that as I was watching (early Wednesday morning Copenhagen time), I was receiving pictures from them on my cellphone that they had taken just by holding their cell phones up to the scope eyepiece. I've had to reduce the resolution of the image below, but you can still easily see the umbra and penumbra of the sunspots, faculae, etc.

I'm old enough to have fought with plate film and a bellows camera to get poor pictures of sunspots, and the first computer I used at work was a PDP-8. Today's technology amazes me daily.

Norm

[QUOTE=cheesehead;301411]should be ~150/[B]4[/B]2 ~= 3.6x

I get 6/696 * 150/42 = 0.03

You were closer than you thought. :-)

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Added:

There's also the irradiation effect, which would make Venus look smaller.

I forgot to link to NASA's page [URL]http://eclipse.gsfc.nasa.gov/OH/transit12.html[/URL] which says:[/QUOTE]
How about refraction by the Venus atmosphere?

What fascinates me about Norm's photo is the dimming
of the sunlight towards its perimeter:
A white hot sphere with no "atmosphere" should look uniformly bright.
Refraction again?

David

[QUOTE=davieddy;302057]How about refraction by the Venus atmosphere?[/QUOTE]You can see that here:

[url]http://www.nasa.gov/images/content/657111main_1-SOT_120606_venus_ca_nc_yellow_001_color_full.jpg[/url]

[QUOTE=davieddy;302057]How about refraction by the Venus atmosphere?

What fascinates me about Norm's photo is the dimming
of the sunlight towards its perimeter:
A white hot sphere with no "atmosphere" should look uniformly bright.
Refraction again?

David[/QUOTE]Re-examine your assumptions.

The sphere is nothing but atmosphere --- that is, the sun is gaseous all the way through and the deeper your go the hotter it is (other than a completely negligible amount of mass and radiation high in the corona). Light from limb of the sun has to travel through a thicker layer of gas than that from the center. Consequently, more of that light is scattered out of the line of sight by a longer path through higher-lying layers of cooler gas. Looking towards the centre of the disk means that you can see deeper into the interior where it is hotter and therefore brighter. The two effects give rise to the phenomenon you describe.

The technical term is "limb darkening", which should give you enough to find out more.

If you'd ever looked at the sun with the naked eye (and essentially everyone I know has done so either through mist, fog , cloud or at sunrise/sunset) you should have found limb darkening very easily visible. Perhaps you just weren't paying attention.

[QUOTE=Spherical Cow;302051]A little late, and from the lower resolution end- My teenage sons were able to watch the start and much of the transit from Arizona with a 6-inch reflector, and I was able to see the end of the transit with binoculars in Copenhagen (traveling on business).[/QUOTE]

Very nice - your photo is similar to mine below, but quite a bit sharper.

A little more late ... For both of our recent astronomical events I set up my little 4"-dia-mirror Edmund "red ball" scope on the pool deck behind my place, then left it in the care of the neighbor's kids, who were keen to apply some of their own high-tech to the fun. They produced this pair of little videos from the time-lapse images.

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Here are the solar eclipse videos:

[url=http://www.youtube.com/watch?v=JqVzG7jSbKw]Venus[/url]

[url=http://www.youtube.com/watch?v=zlOdII04SKw]Moon[/url] (only the first part of the clip is interesting, unless you're a foot fetishist).

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And attached is a still of Venus from my neighbor Andrei.