The 6 Most Important In

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. Quirky much more complete. Swiss astrophysicist Fritz Zwicky sug gested this could be the result of some unknown substance that had mass but was otherwise invisible and undetect able. It turns out that this odd "dark mat ter" positively litters the cosmos: It makes up 83 percent of all the matter we know of in the universe (and remember, all that matter is still only 27.4 percent of the total energy density of the universe). The other mysterious substance out there is dark energy, first theorized in 1998 by American researchers Adam Remarkably, scientists understand only a tiny percentage of the known Riess, Brian Schmidt, and Saul Perlmutter universe. The bulk of the universe's energy density- 72.6 percent- is dark trying to figure out how much the uni energy, the mysterious force pushing our universe apart. Another 22.8 percent is verse's expansion was slowing down. To still-unknown dark matter, leaving 4.6 percent for regular matter. Asrmnomy,Ke1UeJae9e.

Size of the universe relative to today We seem to live in a "special" time in the universe, when matter and dark energy experience a kind of equilibrium. Because regular matter dilutes as space expands, its den sity in the early universe was much higher than it is now. If dark energy is the cosmological constant, or a form of inherent energy of the universe, then its abundance Age of the universe stays constant. The ratios of these two quantities • Dark energy • Dark matter Ordinary matter change dramatically over the history of the universe. Why are they comparable now? Scientists aren't sure, The distribution of energy density of the universe has likely changed but perhaps we live in one of many universes where dramatically over time. Dark matter had the clear majority when the everything- the laws of physics included- just hap universe was just one-fourth its present size, but as the universe pen to be perfectly tuned for our benefit. -B. A. expands, dark energy increasingly dominates. Asrronomy,Roen Kelly

www.Astronomy.com 33 THE HUBBLE CONSTANT We've all probably heard that the uni he showed that these objects all seem verse is expanding, stretching out ever to be moving away from us, and farther since the Big Bang started it off. from each other, with the farthest But much of our current notions of the galaxies moving fastest of all. Hub cosmos arose thanks largely to one man: ble hit upon the idea that a galaxy's American astronomer Edwin Hubble. velocity is equivalent to its distance So, in addition to that famous space tele times a certain constant, and it's

, scope, he also gets the Hubble constant this constant that became H0 the named after him - the exact rate at Hubble constant. which space itself grows. Its value is commonly The 1920s was a busy decade for expressed as 73 .8 kilometers per astronomy and Hubble. Advances in second per megaparsec. This telescope technology allowed him to means, theoretically, that an make two groundbreaking discoveries. object 1 megaparsec away (about First, he realized that our galaxy, the 3.26 million light-years, or 30.8 Milky Way, is only one of countless star quintillion km) moves away cities studded about the cosmos. Second, from us at about 73.8 kilometers =OTHER IMPORTANT NUMBERS

When Edwin Hubble realized the uni The Hubble Space Telescope has given While the number of planets in our verse was expanding, it was a straightfor scientists an unprecedented view of the solar system is officially settled (if not ward mathematical question to "turn back heavens and allowed them to estimate to everyone's satisfaction), the num the clock" and imagine the cosmos shrink the number of star cities in the uni ber of exoplanets, those bodies orbit all the way back to the single event from verse at a whopping 125 billion. ing stars other than the Sun, is which it sprang, known as the Big Bang. constantly growing.

NUMBER OF GALAXIES

• VlllUE: 13.7 billion years • YEIIR ClllCUliiTED: 2010

34 Astronomy· June 2012 An expanding universe has long been an established fact in astronomy, but it wasn't until scientists learned the Hubble constant that they knew exactly how fast it grows.

, per second. An object 2 megaparsecs decades, using various methods such as an accurate value of H 0 astronomers can away would have twice that speed, or direct measurement of cosmic distances answer more of the universe's funda about 147.6 km/s, and so on. (In real and analyzing the remains of the Big mental questions, from the nature of life, though, other factors are more Bang, known as the cosmic microwave dark energy to the locations of other important in determining the velocity of background radiation. members in our galactic neighborhood, such nearby objects.) Knowing just how fast the universe and even the exact age of the universe. It Astronomers have been refining the grows is an important part of under turns out Edwin's namesake constant is Hubble constant's exact value for standing the way it behaves. Armed with almost as prolific as he was. •!t

Print out each of these trading cards featuring the universe's most significant numbers at www.Astronomy.com/toc.

Astronomers had to work diligently to Proxima Centauri, likely part of the learn about our home galaxy because it's Alpha (a) Centauri system, would be hard to get a good view from right in the an otherwise unremarkable dim red Despite the myriad stars out there, midst of things; still, they've learned not dwarf star were it not for its close prox each with a possible multitude of just the diameter of the Milky Way's imity to Earth. worlds, as far as scientists can tell, disk, but also its average thickness (some Earth is unique in the universe for 1,000 light-years) and can even estimate giving rise to living beings ... for now. its stellar population (about 200 billion).