With everything that’s happening, we might count on the sky to give us a sense of stability. But maybe we’re asking too much.
The Moon, which Shakespeare presciently called “inconstant,” moves 1½ inches (3.8 centimeters) farther from Earth each year. Not worth losing sleep over. But on Mars, the billionaire astronauts may be less sanguine. The largest martian satellite, Phobos, orbits more closely to its planet’s surface than any other moon in the solar system, just 3,700 miles (6,000 kilometers) away. It’s also moving closer at some 6 feet (1.8 meters) per century. This produces ever-increasing tidal stresses on Phobos that are creating worrisome stretch marks. Eventually, it will be torn to pieces so that its name — “fear” in ancient Greek — may be frighteningly appropriate.
But far more frightening is Comet 109P/Swift-Tuttle. Much beloved because the fragments it sheds are summer’s Perseid meteors, it was discovered by astronomers Lewis Swift and Horace Tuttle within just three days of each other in July 1862. The giant, fast-moving comet can come as close to Earth’s orbit as 0.0009 astronomical unit, making it the most dangerous celestial object to humankind. (One astronomical unit is the average Earth-Sun distance.) But calculating where it will be in the far future is not easy. Its orbital period is 133.28 years, and if you’re a math savant you probably realize that number is suspiciously close to 11 times Jupiter’s orbital period of 11.86 Earth years. So yes, something interesting happened a thousand years ago: The comet got snagged by Jupiter’s repeated gravitational tugs and adopted an 11:1 resonance, circling the Sun once for 11 jovian orbits.
Will this at least give it enough stability that we can accurately predict its future orbit? No! It’s likely to stay in the same predictable pattern for a few thousand years, sure, but after long enough, all bets are off.
We’d at least like stability closer to home, like in our bodies’ atoms. But it’s a mixed bag even here. You may recall atoms have protons and neutrons in their nuclei. Elements have varieties — called isotopes — characterized by their differing number of neutrons. We breathe oxygen that mostly has eight protons and eight neutrons. But a tiny fraction boasts an extra one or two neutrons. No matter: All oxygen isotopes last forever.
Stability at last? Not so fast. “Forever” isn’t true of their components. A neutron is stable when inside an atom. But when free — like in the continuous streams released by nuclear reactors — the average neutron vanishes in 14 minutes and 40 seconds. Protons do better, with a half-life of around (some say at least) 10 billion trillion trillion years.
What about the rest of the universe’s atoms? Here’s where numbers and patterns enter the picture. Of the hundreds of isotopes in the natural world, all elements with atomic numbers 1 through 82 have at least one stable isotope. And all elements housing more than 82 protons have no stable varieties.
We might assume nature has no preference for odd or even numbers. But that’s not true. The vast majority of the most abundant elements — those atomic numbers 1 through 82 — are stable if they have an even number of protons and of neutrons, and unstable if they have an odd number. Moreover, even-atomic-number elements are not radioactive and last forever.
Sometimes we get surprised. You can go on Amazon and buy a pound block of pure bismuth for a few dollars. It’s a beautiful element, suitable for displaying in your living room. What’s currently fashionable is to melt it down in a saucepan and let it re-solidify, skimming off a surface layer, which spontaneously forms astonishing shapes like jagged skyscrapers. Anyway, until recently, everyone thought bismuth was eternally stable. But measurements in 2003 surprised French researchers, who found it has a half-life of 1.9 x 1019 years. So, while Amazon doesn’t say so, half of your precious bismuth will vanish in 19 million trillion years.
Ah, stability, where art thou?