Death by Black Hole: And Other Cosmic Quandaries (24 page)

In any case, the leading edge of our “on-purpose” radio signals (forming a directed radio cone, instead of a bubble) is 30 light-years away and, if intercepted, may mend the aliens’ image of us based on the radio bubble of our television shows. But this will happen only if the aliens can somehow determine which type of signal comes closer to the truth of who we are, and what our cosmic identity deserves to be.

S
cience distinguishes itself from almost all other human endeavors by its capacity to predict future events with precision. Daily newspapers often give you the dates for upcoming phases of the moon or the time of tomorrow’s sunrise. But they do not tend to report “news items of the future” such as next Monday’s closing prices on the New York Stock Exchange or next Tuesday’s plane crash. The general public knows intuitively, if not explicitly, that science makes predictions, but it may surprise people to learn that science can also predict that something is unpredictable. Such is the basis of chaos. And such is the future evolution of the solar system.

A chaotic solar system would, no doubt, have upset the German astronomer Johannes Kepler, who is generally credited with the first predictive laws of physics, published in 1609 and 1619. Using a formula that he derived empirically from planetary positions on the sky, he could predict the average distance between any planet and the Sun by simply knowing the duration of the planet’s year. In Isaac Newton’s 1687
Principia
, his universal law of gravity allows you to mathematically derive all of Kepler’s laws from scratch.

In spite of the immediate success of his new laws of gravity, Isaac Newton remained concerned that the solar system might one day fall into disarray. With characteristic prescience, Newton noted in Book III of his 1730 edition of
Optiks
:

The Planets move one and the same way in Orbs concentric, some inconsiderable Irregularities excepted, which may have arisen from the mutual actions of…Planets upon one another, and which will be apt to increase, till the system wants a Reformation.
(p. 402)

 

As we will detail in Section 7, Newton implied that God might occasionally be needed to step in and fix things. The celebrated French mathematician and dynamicist Pierre-Simon Laplace had an opposite view of the world. In his 1799–1825 five-volume treatise
Traité de mécanique céleste
, he was convinced that the universe was stable and fully predictable. Laplace later wrote in
Philosophical Essays on Probability
(1814):

[With] all the forces by which nature is animated…nothing [is] uncertain, and the future as the past would be present to [one’s] eyes.
(1995, Chap. II, p. 3)

 

The solar system does, indeed, look stable if all you have at your disposal is a pencil and paper. But in the age of supercomputers, where billions of computations per second are routine, solar system models can be followed for hundreds of millions of years. What thanks do we get for our deep understanding of the universe?

Chaos.

Chaos reveals itself through the application of our well-tested physical laws in computer models of the solar system’s future evolution. But it has also reared its head in other disciplines, such as meteorology and predator-prey ecology, and almost anyplace where you find complex interacting systems.

To understand chaos as it applies to the solar system, one must first recognize that the difference in location between two objects, commonly known as their distance, is just one of many differences that can be calculated. Two objects can also differ in energy, orbit size, orbit shape, and orbit inclination. One could therefore broaden the concept of distance to include the separation of objects in these other variables as well. For example, two objects that are (at the moment) near each other in space may have very different orbit shapes. Our modified measure of “distance” would tell us that the two objects are widely separated.

A common test for chaos is to begin with two computer models that are identical in every way except for a small change somewhere. In one of two solar system models you might allow Earth to recoil slightly in its orbit from being hit by a small meteor. We are now armed to ask a simple question: Over time, what happens to the “distance” between these two nearly identical models? The distance may remain stable, fluctuate, or even diverge. When two models diverge exponentially, they do so because the small differences between them magnify over time, badly confounding your ability to predict the future. In some cases, an object can be ejected from the solar system completely.

This is the hallmark of chaos.

For all practical purposes, in the presence of chaos, it is
impossible
to reliably predict the distant future of the system’s evolution. We owe much of our early understanding of the onset of chaos to Alexander Mikhailovich Lyapunov (1857–1918), who was a Russian mathematician and mechanical engineer. His 1892 PhD thesis “The General Problem of the Stability of Motion” remains a classic to this day. (By the way, Lyapunov died a violent death in the chaos of political unrest that immediately followed the Russian Revolution.)

Since the time of Newton, people knew that you can calculate the exact paths of two isolated objects in mutual orbit, such as a binary star system, for all of time. No instabilities there. But as you add more objects to the dance card, orbits become more and more complex, and more and more sensitive to their initial conditions. In the solar system we have the Sun, its eight planets, their 70+ satellites, asteroids, and comets. This may sound complicated enough, but the story is not yet complete. Orbits in the solar system are further influenced by the Sun’s loss of 4 million tons of matter every second from the thermonuclear fusion in its core. The matter converts to energy, which subsequently escapes as light from the Sun’s surface. The Sun also loses mass from the continuously ejected stream of charged particles known as the solar wind. And the solar system is further subject to the perturbing gravity from stars that occasionally pass by in their normal orbit around the galactic center.

To appreciate the task of the solar system dynamicist, consider that the equations of motion allow you to calculate the net force of gravity on an object, at any given instant, from all other known objects in the solar system and beyond. Once you know the force on each object, you nudge them all (on the computer) in the direction they ought to go. But the force on each object in the solar system is now slightly different because everybody has moved. You must therefore recompute all forces and nudge them again. This continues for the duration of the simulation, which in some cases involves trillions of nudges. When you do these calculations, or ones similar to them, the solar system’s behavior is chaotic. Over time intervals of about 5 million years for the inner terrestrial planets (Mercury, Venus, Earth, and Mars) and about 20 million years for the outer gas giants (Jupiter, Saturn, Uranus, and Neptune), arbitrarily small “distances” between initial conditions noticeably diverge. By 100 to 200 million years into the model, we have lost all ability to predict planet trajectories.

Yes, this is bad. Consider the following example: The recoil of Earth from the launch of a single space probe can influence our future in such a way that in about 200 million years, the position of Earth in its orbit around the Sun will be shifted by nearly 60 degrees. For the distant future, surely it’s just benign ignorance if we do not know where Earth will be in its orbit. But tension rises when we realize that asteroids in one family of orbits can chaotically migrate to another family of orbits. If asteroids can migrate, and if Earth can be somewhere in its orbit that we cannot predict, then there is a limit to how far in the future we can reliably calculate the risk of a major asteroid impact and the global extinction that might ensue.

Should the probes we launch be made of lighter materials? Should we abandon the space program? Should we worry about solar mass loss? Should we be concerned about the thousand tons of meteor dust per day that Earth accumulates as it plows through the debris of interplanetary space? Should we all gather on one side of Earth and leap into space together? None of the above. The long-term effects of these small variations are lost in the chaos that unfolds. In a few cases, ignorance in the face of chaos can work to our advantage.

A skeptic might worry that the unpredictability of a complex, dynamic system over long time intervals is due to a computational round-off error, or some peculiar feature of the computer chip or computer program. But if this suspicion were true, then two-object systems might eventually show chaos in the computer models. But they don’t. And if you pluck Uranus from the solar system model and repeat the orbit calculations for the gas giant planets, then there is no chaos. Another test comes from computer simulations of Pluto, which has a high eccentricity and an embarrassing tilt to its orbit. Pluto actually exhibits well-behaved chaos, where small “distances” between initial conditions lead to an unpredictable yet limited set of trajectories. Most importantly, however, different investigators using different computers and different computational methods have derived similar time intervals for the onset of chaos in the long-term evolution of the solar system.

Apart from our selfish desire to avoid extinction, broader reasons exist for studying the long-term behavior of the solar system. With a full evolutionary model, dynamicists can go backward in time to probe the history of the solar system, when the planetary roll call may have been very different from today. For example, some planets that existed at the birth of the solar system (5 billion years ago) could have since been forcibly ejected. Indeed we may have begun with several dozen planets, instead of eight, having lost most of them jack-in-the-box style to interplanetary space.

In the past four centuries, we have gone from not knowing the motions of the planets to knowing that we cannot know the evolution of the solar system into the unlimited future—a bittersweet victory in our unending quest to understand the universe.

O
ne needn’t look far to find scary predictions of a global holocaust by killer asteroids. That’s good, because most of what you might have seen, read, or heard is true.

The chances that your or my tombstone will read “killed by asteroid” are about the same for “killed in an airplane crash.” About two dozen people have been killed by falling asteroids in the past 400 years, but thousands have died in crashes during the relatively brief history of passenger air travel. So how can this comparative statistic be true? Simple. The impact record shows that by the end of 10 million years, when the sum of all airplane crashes has killed a billion people (assuming a death-by-airplane rate of 100 per year), an asteroid is likely to have hit Earth with enough energy to kill a billion people. What confuses the interpretation is that while airplanes kill people a few at a time, our asteroid might not kill anybody for millions of years. But when it hits, it will take out hundreds of millions of people instantaneously and many more hundreds of millions in the wake of global climatic upheaval.

The combined asteroid and comet impact rate in the early solar system was frighteningly high. Theories and models of planet formation show that chemically rich gas condenses to form molecules, then particles of dust, then rocks and ice. Thereafter, it’s a shooting gallery. Collisions serve as a means for chemical and gravitational forces to bind smaller objects into larger ones. Those objects that, by chance, accreted slightly more mass than average will have slightly higher gravity and attract other objects even more. As accretion continues, gravity eventually shapes blobs into spheres and planets are born. The most massive planets had sufficient gravity to retain gaseous envelopes. All planets continue to accrete for the rest of their days, although at a significantly lower rate than when formed.

Still, billions (likely trillions) of comets remain in the extreme outer solar system, up to a thousand times the size of Pluto’s orbit, that are susceptible to gravitational nudges from passing stars and interstellar clouds that set them on their long journey inward toward the Sun. Solar system leftovers also include short-period comets, of which several dozen are known to cross Earth’s orbit, and thousands of asteroids that do the same.

The term “accretion” is duller than “species-killing, ecosystem-destroying impact.” But from the point of view of solar system history, the terms are the same. We cannot simultaneously be happy we live on a planet; happy that our planet is chemically rich; and happy we are not dinosaurs; yet resent the risk of planetwide catastrophe. Some of the energy from asteroid collisions with Earth gets dumped into our atmosphere through friction and an airburst of shock waves. Sonic booms are shock waves too, but they are typically made by airplanes with speeds anywhere between one and three times the speed of sound. The worst damage they might do is jiggle the dishes in your cabinet. But with speeds upwards of 45,000 miles per hour—nearly seventy times the speed of sound—the shock waves from your average collision between an asteroid and Earth can be devastating.

If the asteroid or comet is large enough to survive its own shock waves, the rest of its energy gets deposited on Earth’s surface in an explosive event that melts the ground and blows a crater that can measure twenty times the diameter of the original object. If many impactors were to strike with little time between each event, then Earth’s surface would not have enough time to cool between impacts. We infer from the pristine cratering record on the surface of the Moon (our nearest neighbor in space) that Earth experienced an era of heavy bombardment between 4.6 and 4 billion years ago. The oldest fossil evidence for life on Earth dates from about 3.8 billion years ago. Not much before that, Earth’s surface was unrelentingly sterilized, and so the formation of complex molecules, and thus life, was inhibited. In spite of this bad news, all the basic ingredients were being delivered nonetheless.

How long did life take to emerge? An often-quoted figure is 800 million years (4.6 billion—3.8 billion = 800 million). But to be fair to organic chemistry, you must first subtract all the time Earth’s surface was forbiddingly hot. That leaves a mere 200 million years for life to emerge from a rich chemical soup, which, as do all good soups, includes water.

Yes, the water you drink each day was delivered to Earth in part by comets more than 4 billion years ago. But not all space debris is left over from the beginning of the solar system. Earth has been hit at least a dozen times by rocks ejected from Mars, and we’ve been hit countless more times by rocks ejected from the Moon. Ejection occurs when impactors carry so much energy that smaller rocks near the impact zone get thrust upward with sufficient speed to escape the gravitational grip of the planet. Afterward, the rocks mind their own ballistic business in orbit around the Sun until they slam into something else. The most famous of the Mars rocks is the first meteorite found near the Alan Hills section of Antarctica in 1984. Officially known by its coded, though sensible, abbreviation, ALH-84001, this meteorite contains tantalizing, though circumstantial, evidence that simple life on the Red Planet thrived a billion years ago. Mars bears boundless geological evidence for a history of running water that includes dried riverbeds, river deltas, and flood plains. And most recently the Martian rovers
Spirit
and
Opportunity
found rocks and minerals that could have formed only in the presence of standing water.

Since liquid water is crucial to the survival of life as we know it, the possibility of life on Mars does not stretch scientific credulity. The fun part comes when you speculate whether life arose on Mars first, was blasted off its surface as the solar system’s first bacterial astronauts, and then arrived to jump-start Earth’s own evolution of life. There’s even a word for the process: panspermia. Maybe we are all descendants of Martians.

Matter is far more likely to travel from Mars to Earth than vice versa. Escaping Earth’s gravity requires over two-and-a-half times the energy than that required to leave Mars. Furthermore, Earth’s atmosphere is about a hundred times denser. Air resistance on Earth (relative to Mars) is formidable. In any case, bacteria would have to be hardy indeed to survive the several million years of interplanetary wanderings before landing on Earth. Fortunately, there is no shortage of liquid water and rich chemistry on Earth, so we do not require theories of panspermia to explain the origin of life as we know it, even if we still cannot explain it.

Ironically, we can (and do) blame impacts for major episodes of extinction in the fossil record. But what are the current risks to life and society? Below is a table that relates average collision rates on Earth with the size of impactor and the equivalent energy in millions of tons of TNT. For reference, I include a column that compares the impact energy in units of the atomic bomb that the United States dropped on the city of Hiroshima in 1945. These data are adapted from a graph by NASA’s David Morrison (1992).

The table is based on a detailed analysis of the history of impact craters on Earth, the erosion-free cratering record on the Moon’s surface, and the known numbers of asteroids and comets whose orbits cross that of Earth.

The energetics of some famous impacts can be located on the table. For example, a 1908 explosion near the Tunguska River, Siberia, felled thousands of square kilometers of trees and incinerated the 300 square kilometers that encircled ground zero. The impactor is believed to have been a 60-meter stony meteorite (about the size of a 20-story building) that exploded in midair, thus leaving no crater. The chart predicts collisions of this magnitude to happen, on average, every couple of centuries. The 200-kilometer diameter Chicxulub Crater in the Yucatan, Mexico, is believed to be the calling card of a 10-kilometer asteroid. With an impact energy 5 billion times greater than the atomic bombs exploded in World War II, such a collision is predicted to occur about once in about 100 million years. The crater dates from 65 million years ago, and there hasn’t been one of its magnitude since. Coincidentally, at about the same time, Tyrannosaurus rex and friends became extinct, enabling mammals to evolve into something more ambitious than tree shrews.

Those paleontologists and geologists who remain in denial of the role of cosmic impacts in the extinction record of Earth’s species must figure out what else to do with the deposit of energy being delivered to Earth from space. The range of energies varies astronomically. In a review of the impact hazard to Earth written for the fat book
Hazards Due to Comets and Asteroids
(Gehrels 1994), David Morrison of NASA Ames Research Center, Clark R. Chapman of the Planetary Science Institute, and Paul Slovic of the University of Oregon briefly describe the consequence of unwelcome deposits of energy to Earth’s ecosystem. I adapt what follows from their discussion.

Most impactors with less than about 10 megatons of energy will explode in the atmosphere and leave no trace of a crater. The few that survive in one piece are likely to be iron-based.

A 10-to 100-megaton blast from an iron asteroid will make a crater, while its stony equivalent will disintegrate and produce primarily air bursts. A land impact will destroy the area equivalent to that of Washington, DC.

Land impacts between 1,000 and 10,000 megatons continue to produce craters; oceanic impacts produce significant tidal waves. A land impact can destroy an area the size of Delaware.

A 100,000-to 1,000,000-megaton blast will result in global destruction of ozone; oceanic impacts will generate tidal waves felt on an entire hemisphere of Earth while land impacts raise enough dust into the stratosphere to change Earth’s climate and freeze crops. A land impact will destroy an area the size of France.

A 10,000,000-to 100,000,000-megaton blast results in prolonged climactic effects and global conflagration. A land impact will destroy an area equivalent to the continental United States.

A land or ocean impact of 100,000,000 to 1,000,000,000 megatons will lead to mass extinction on a scale of the Chicxulub impact 65 million years ago, when nearly 70 percent of Earth’s species were suddenly wiped out.

Fortunately, among the population of Earth-crossing asteroids, we have a chance at cataloging everything larger than about a kilometer—the size that begins to wreak global catastrophe. An early-warning and defense system to protect the human species from these impactors is a realistic goal, as was recommended in NASA’s
Spaceguard Survey Report
, and, believe it or not, continues to be on the radar screen of Congress. Unfortunately, objects smaller than about a kilometer do not reflect enough light to be reliably and thoroughly detected and tracked. These can hit us without notice, or they can hit with notice that is much too short for us to do anything about. The bright side of this news is that while they have enough energy to create local catastrophe by incinerating entire nations, they will not put the human species at risk of extinction.

Of course Earth is not the only rocky planet at risk of impacts. Mercury has a cratered face that, to a casual observer, looks just like the Moon. Recent radio topography of cloud-enshrouded Venus shows plenty of craters too. And Mars, with its historically active geology, reveals large craters that were recently formed.

At over three hundred times the mass of Earth, and at over ten times its diameter, Jupiter’s ability to attract impactors is unmatched among the planets in the solar system. In 1994, during the week of anniversary celebrations for the 25th anniversary of the
Apollo 11
Moon landing, comet Shoemaker-Levy 9, having been broken apart into two dozen chunks during a previous close-encounter with Jupiter, slammed, one piece after another, into the Jovian atmosphere. The gaseous scars were seen easily from Earth with backyard telescopes. Because Jupiter rotates quickly (once every 10 hours), each part of the comet fell in a different location as the atmosphere rotated by.

And, in case you were wondering, each piece hit with the equivalent energy of the Chicxulub impact. So, whatever else is true about Jupiter, it surely has no dinosaurs left!

Earth’s fossil record teems with extinct species—life-forms that had thrived far longer than the current Earth-tenure of
Homo sapiens
. Dinosaurs are in this list. What defense do we have against such formidable impact energies? The battle cry of those with no nuclear war to fight is “nuke them from the sky.” True, the most efficient package of destructive energy ever conceived by humans is nuclear power. A direct hit on an incoming asteroid might explode it into enough small pieces to reduce the impact danger to a harmless, though spectacular, meteor shower. Note that in empty space, where there is no air, there can be no shock waves, so a nuclear warhead must actually make contact with the asteroid to do damage.