What's a Trillion to CNN?

Clearly CNN has remained untaunted for too long.  Perhaps they have decided to get revenge on me for my previous complaints about their innumeracy and lack of rounding prowess by running this stunningly preposterous item.  Or perhaps they picked up this dog's breakfast of ridiculous numbers verbatim from Reuters.  Either way, they are to blame, and I shall be charging them, along with society, of course.  Copyright be damned, it's a short article and almost every paragraph is afflicted with a greater or lesser howler.  I quote it in its risibly erroneous entirety.

LONDON, England (Reuters) -- A huge daisy-shaped shield that would block out light from parent stars could be used to find Earth-like planets in other solar systems, an American astronomer said on Wednesday.

I don't imagine he's proud to be an "American Astronomer" after reading how they described his project.

He and his team have designed a plastic "starshade" measuring 50 yards (45 meters) in diameter that would orbit in tandem with a trailing telescope and block out light from parent stars to enable scientists to map planetary systems.

Of course that's not exactly what it is.  It's actually a pinhole lens with a 30-foot hole in the center.  But what's a crucial detail or many?  However, according to Google, which provides answers in seconds and doesn't require you to develop "sources,"  50 yards = 45.72 meters, or properly rounding, 46 M.  Not a critical or even significant error — I'm sure the 50 yards is a gross approximation (the "football field effect"), but why not get it right?

Finding other planets is very difficult because their parent stars are about 10 times brighter.

Well, yes, finding other planets is difficult, but not because they're one-tenth as bright.  Spare me a moment for some geometry and astronomy, since I don't actually know the correct number.  Let's do a first order approximation to compare the brightness of the earth to that of the sun. 

The earth has a radius of 4,000 miles, and thus a circular area of about 50 million square miles.  (Of course the earth is spherical, but we're talking about the effective area that intercepts sunlight.)  The earth's distance from the sun is 93 million miles, and the sun radiates its energy in all directions, i.e., spherically.  So the light intercepted by the earth is a percentage equal to the surface area of a sphere with a radius of 93 million miles, which is  1.08*10^¹⁷ square miles divided by 5*10^⁷ square miles.  This would mean that the brightest the earth can be is about two billionths of the brightness of the "parent star."  So their number is off by more than factor of a billion.  The earth's "albedo" or reflectance is less than perfect, too, as presumably are those of planets around other stars.  This, I think, makes the extreme difficulty of the task more apparent than the one-tenth mentioned in the article.

"We think this is a compelling concept, particularly because it can be built today with existing technology," said Professor Webster Cash of the University of Colorado.
"We will be able to study Earth-like planets tens of trillions of miles away and chemically analyze their atmospheres for signs of life," he added in a statement.
The shield, which is known as the New Worlds Observer, is described in the journal Nature. It would be launched into an orbit about 1 trillion miles from Earth and then opened.

Look!  Another trillion!  The space shuttle orbits hundreds of miles above the earth.  Our communications satellites orbit thousands of miles above the earth.  The moon is about a quarter of a million miles up.  The outer planets, which only a tiny number of probes have reached after decades of travel, are single-digit billions of miles away.  But look!  We're going to send this project a trillion miles, a good fraction of the distance to the nearest star, just to look for planets.  I wish!  If we could do that, or even a tiny fraction of that, we would have colonized the planets already and not just be looking for them.  A trillion miles, incidentally, is about two light-months.  At that distance, if we sent a command to the telescope it would receive it in two months and we'd get our reply two months later.  Again I don't actually know the distance of the telescope's orbit, but it is most likely to be somewhere in the high thousands to the very low millions of miles.  That's a factor of about one million off from the silly number in the article, the equivalent of provisioning the Nina, Pinta, and Santa Maria to borrow a cup of sugar from your neighbor.

Three thrusters would be used to keep it steady while the telescope trailing thousands of miles behind follows light from distant planets as it hits the space shield.  "The New Worlds Observer is actively being studied in academia, industry and government," Cash said in a letter to Nature.  He added that if Earth-like planets exist, the starshade could find them within the next decade.

While they have missed the whole point of how the system works — it's a lens, not properly a shield, at least they've managed to produce a paragraph that has a number in it that isn't obviously wrong.  The telescope is unlikely, for instance, to have three trillion thrusters  Even so, I have no faith the "three" is correct after having seen the other bizarre numbers.  I wonder how many thrusters it really has.

So much for CNN. 

Fortunately we have the stately Wall Street Journal (05 July 2006, page A17), whose journalists and editors meet a much higher standard, and produce far better researched items, such as this excerpt about the new Chinese train that travels at high altitude to Tibet.

I checked the original article and they fixed the orbit:
"It would be launched into an orbit about 1 million miles from Earth and then opened."
Which is what I said.  Remarkably, or perhaps unremarkably, they did not fix the "10 times brighter."  Maybe they will eventually correct that, too.

And, when I checked a day later, they "fixed" the brightness:
"Finding other planets is very difficult because their parent stars are so much brighter."
Whether their leaving out any numerical factor is ignorance or humility I won't attempt to guess.