How could I have been so wrong?

The title of this post would normally lead one to suspect that a sad love story is coming. It's not that bad at the moment, but the mistakes I made were literally astronomical in size.

Up until today, it was my understanding that Vega was the closest star to our solar system at a distance of some twenty-six light years. It was also my understanding that Vega was known as the North Star. I was also deceived by Gerry Rafferty's song "Right Down the Line" into believing that the "Northern Star" is "the brightest light that shines." Apparently, I was wrong on all three counts.

Proxima Centauri--the closest star to our solar system--is, apparently, "only" some 4.22 light years away.

The brightest star--other than the Sun--as seen from our solar system is apparently Sirius.

The North Star is, in the long run, technically not one enduring star. According to Wikipedia, this is "a title of the star best suited for navigation northwards." Currently, that status falls to Polaris, but Thuban was used some 3,000 years ago. In a thousand years or so, Gamma Cephei will apparently claim the title, but it will be another thousand years before the fit is optimal. When I looked up "Northern Star" in wikipedia, I got the name of some rock band. The real name, apparently, is the North Star. Did Gerry know of another source of light that I--and the astronomers--did not?

So, what is the big deal about Vega? According to Wikipedia, it is admittedly "the brightest star in the constellation Lyra." That, however, does not impress me much more than it would likely impress Shania Twain. It is only "the fifth brightest star in the sky."

Vega is apparenlty the star of choice "for the calibration of absolute photometric brightness scales." I have no idea how important that might be. To justify Vega's "cultural significance," Wikipedia notes that it was "first star to be photographed [and later] to have its spectrum photographed." How impressed am I supposed to be?

Now, why did I look up these issues?

An article on CNN's web site (http://www.cnn.com/2007/TECH/space/05/16/odd.exoplanet.reut/index.html) reported the discovery of "an odd planet the size of Neptune" which is apparently the first extra-solar system planet confirmed to have water. Although the water is estimated to have a temperature of some 247 degrees Celcius--almost two and a half the boiling tempreature at Earth sea level--the water is apparently "rock hard." Another CNN article at http://www.cnn.com/2007/TECH/space/05/16/odd.exoplanet.reut/index.html reports that the water at this planet can "survive" because "Smaller stars [like GJA recent article on CNN's web site 436 around which the planet orbits] are cooler and redder." I do not get why this allows the water to persist--even with the lesser heat radiated, 247 degrees Celcius is still extremely hot. It it because the greater mass of this planet results in higher pressure, increasing the temperature needed for boiling?

OK, so what does this have to do with anything, let alone distances from the solar system? The article said that this planet was only some 33 light years away from us. I wondered how likely it would be that some other solar system would be found so close if, as I mistakenly assumed, the closest star to Earth was 26 light years away.

At first, I attempted to calculate the area of a circle with our solar system in the center. I then examined the ratio of area covered to distance. Going from 26 light years to 33, the ratio was only 1.61. That is, one might expect only sixty-one one hundreds of a star to be found there if one assumes that the distribution density of the first star is representative.

It quickly dawned on me that space travel is, realistically speaking, likely to be at least three dimensional. (I say at least because Supersting Theorists might suggest that there are more dimensions involved, but only the three, so far, seem to involve a major distance. For now, I am ignoring the time dimension, holding it constant). Now, "inflation" happens much more quickly:

Still, going from 26 to 33 light years only increases the volume ratio to 2.04. That is when I became suspicious.

Now, when we examine the increase in volume, going from four light years to thirty three, we see the volume ratio increase to 226.87. Even going with the three dimensions, however, 101,540 light years cubed does not seem like all that much. I'm sure, however, that this neighborhood is bigger than it sounds. In a lifespan of some 100 years, one could only expect to be able to travel 1/540 of the distance of one extreme to the other going at the speed of light--if that is even possible. As Crossby, Stills, Nash, and Young remind us, it only takes "trav'ling twice the speed of sound" for it to get "easy to get burned."