The 6 most important in the Find out how the speed of light, the gravitational constant, and other big numbers govern the cosmos. by Bill Andrews umbers are special. Every kid and sports fanatic has a favorite, something rarely true for letters or words. As humans, we seem consistently drawn to certain numbers, whether for some mystic mythological significance or their legiti­ mate scientific importance. While scientists don't put much stock in the healing power of 7 anymore, it's the odd physicist who doesn't have at ' least a healthy respect for the inviolate speed of light. From the makeup of the cosmos to the speed of its acceleration, here are a few of the universe's most significant numbers - at least, the ones we know so far. Bill Andrews is an associate editor of Astronomy. He doesn't have a favorite number because he loves them all so much. THE SPEED OF LIGHT Hard as it may be to believe, the light we when he proved that the speed of see all about us doesn't travel around light in a vacuum, or c, is the instantaneously. The time it takes for the maximum speed that matter or illumination of your lamp to reach your energy could ever achieve. eye is infinitesimal, but measurable. The symbol c originally The first to quantitatively measure stood for "constant" (though light's speed was a Danish astronomer some suggest instead the Latin named Ole R0mer, who analyzed how word for swiftness, celeritas). long it took a jovian moon's light to In fact, c is such a reliable reach Earth over the course of our plan­ value that since 1983 the et's orbit in 1675. Although his final fig­ International System of Units ure was too low, his calculations helped has defined the length of a prove the still-controversial idea that meter as the distance light light had a speed. travels in 11299,792,458 sec­ Cosmic distances are so large that ond- the speed is by defi­ even speedy light takes its time getting nition a constant. somewhere, providing a handy way to However, it is possible measure astronomical distances: the for light to slow when it's not propagat­ might end up light-year, or the distance light travels in a ing through a vacuum, and sometimes showing that c isn't as immutable year (about 6 trillion miles [10 trillion space itself can expand faster than c. Cer­ as we think, but for now, Einstein's des­ kilometers]). Albert Einstein cemented tain quirks of quantum mechanics and ignation of the universal speed limit the importance of this universal constant other unexpected scientific discoveries remains the final word. THE ORDER OF MAGNITUDE At first, this might not seem like a wor­ compare to the speed of light or the standard unit of length - the meter - thy choice for our universal pantheon of gravitational constant? Easy: by being and using large multiples or small frac­ numbers. How does the simple 10 useful to scientists. Because of the way tions of it to measure distances, an our number system works, 10 occupies intuitive grasp of the relative sizes of a uniquely powerful position on the objects becomes easier. number line. (True, this is only the case Earth's radius measures about 6,400 in base 10, but it's the most common kilometers (or 6.4 million meters), and way modern humans count.) ultraviolet wavelengths of light peak Multiplying anything by 10 "adds a about 10 nanometers (or 10 billionths of zero" to it, or gives it another order of a meter) apart. Right away, scientists magnitude. A house might be about 30 have a reasonable grasp on these feet (9 meters) tall, but something an extreme numbers, just by virtue of their order of magnitude taller stretches up being related by factors of 10. Even 300 feet (90m). An order of magni­ more importantly, it's easy to convert tude beyond that, and we're up to these measurements to the same unit 3,000 feet (900m). The number lO (namely, meters) without the need for gives us a handy way to scale mea­ messy arithmetic. surements up or down to suit our Although not everyone appreciates or imaginations, whether in the realms uses the metric system, as Americans of the unimaginably huge or the well know, the order of magnitude is a incredibly tiny. valuable tool for a science that dabbles in This is perhaps best exemplified the large and the small. The true power with the metric system of measure­ of lO lies in its ability to link together all ments. By establishing a single of astronomy's various phenomena. www.Astronomy.com 31 THE GRAVITATIONAL CONSTANT Even the most casual student of physics came time for Albert Einstein to revo­ will probably recognize G, the gravita­ lutionize the way physicists under­ tional constant. All the various displays stand gravity, G was a common term of gravity's effects, from planetary orbits in his equations. around a star to stellar orbits around a As important as G is to astronomers black hole to galactic interactions over - they literally can't understand the millions of years, would be impossible universe without it - it's an unusually to determine without G. A fundamen­ hard value to pin down. Its minuscule tal constant of the universe, it defines magnitude alone (written out long­ how the masses of two objects and the hand, G=0.00000000006673) shows distance between them are related to how weak the gravitational force is - the gravitational attraction they feel far weaker than the other three funda­ toward each other. mental forces. Isaac Newton first theorized G in Thus, it's been a difficult value to his law of universal gravitation (for­ measure, and a study in the January 2 mally stated as F=G(Mm/r )), but 2007 issue of Science suggested a new 2 2 the genius physicist never knew the value ofG=6.693 x 10-" N m /kg • Cur­ actual value of G. It was British rently, the Committee on Data for Sci­ scientist Henry Cavendish who ence and Technology and the National first measured it in 1798, 71 years Institute of Standards and Technology after Newton's death. When it recommend staying with the older value. PI For as long as people have understood universe, whether it's one the size of mathematics, they've known pi. The your hand or the size of the galaxy. ancient Greeks may have given us its The fact that it's an irrational and common symbol, 1t (from their word for transcendental number, so its exact "perimeter"), but the Egyptians, Babylo­ value is impossible to express hand­ nians, Indians, and others knew of it. ily (beyond the common approxima­ One of the simplest and best-known tion 3.14159), only adds to its allure. universal constants, 1t represents the ratio In addition to its importance in of a circle's circumference to its diameter. geometry, n pops up in a number This is true for any flat circle in the of important places. Werner Heisenberg's uncertainty principle - a pillar of quantum mechanics and thus our knowledge of the subatomic realm - features n. Albert Einstein's general theory of relativity equations also include the number, as do Johannes Kepler's laws of planetary motion and countless other scientific for­ mulae. Our very understanding of the c cosmos seems dependent upon n. way to prove God's existence, or a plot cr=n And the universe isn't the only one device in science fiction, the ancient con­ Calculating n is as simple as dividing any fond of n. Whether it's as part of a nerdy stant enjoys a special place in the public's circle's circumference (c) by its diameter (d), no matter its size. This simplicity belies school's sports cheer, an excuse to make imagination. Any number that can com­ the transcendental number's true and share pies every March 14, a device bine everyday situations, the imagination, COmplexity. Astronomy: Ke llieJaeger for testing the limits of memorization, a and the universe must truly be special. 32 Astronomy·June 2012 DISTRIBUTION OF ENERGY DENSITY It's a disorienting fact that 95.4 percent their great surprise, not only was of the universe's energy density (the stuff all the mass of the cosmos not it's made of) is still a mystery to scien­ managing to pull back against tists. That remaining 4.6 percent, bary­ the expansion, but something onic matter, encompasses everything on was actually speeding it up! Sci­ Earth, all the other planets, every star, entists dubbed this "something" every molecule of interstellar gas, and dark energy, and apart from its everything else scientists used to think tremendous prevalence in the made up the entirety of the universe. universe - it's 72.6 percent of While we are now aware of the unknown everything - scientists know 95.4 percent, about all we understand is almost nothing about it. that it's out there; just what it is and how It might seem alarming to it works are still up for debate. think that we're ignorant about The first part of that mysterious stuff the vast majority of stuff out is dark matter, and it makes up 22.8 per­ there, but dark matter and cent of the energy density of the uni­ dark energy also present a verse. When astronomers first started great opportunity: These are observing distant galaxies in the early just problems awaiting solu­ 20th century, they noticed something tions, and once science finds funny: Galactic movement didn't make them, our understanding of sense unless there was a lot of extra the cosmos will be that unaccounted-for mass out there.