“He, who through vast immensity can pierce,
See worlds on worlds compose one Universe,
Observe how system into system runs,
What other planets circle other suns,
What vary’d being peoples ev’ry star,
May tell why Heav’n has made us as we are.”
Alexander Pope (1732)1
The Nebular Hypothesis
The presently accepted nebular hypothesis for the origin of the Solar System supposes that the Sun and planets were created together during the gravitational collapse of a rotating, interstellar cloud. The spinning gaseous solar nebula kept collapsing until its central regions became so concentrated and hot that the Sun began to shine. The planets formed at the same time within a flattened, rotating proto-planetary disk centered on the contracting proto-Sun (Fig. 8.1).
The earliest known mention of the concept was by the Swedish scientist, theologian, and Christian mystic Emanuel Swedenborg in his Principia in 1734. The German philosopher Immanuel Kant extended Swedenborg’s ideas in 1755, when he reasoned that a rotating gaseous nebula would collapse and flatten due to gravity. Kant described how the stars might have become systematically arranged in the Milky Way through the gravitational collapse of a large rotating nebula, and how the Solar System could have originated by the pulling together of a much smaller rotating nebula.2
Figure 8.1 Formation of the Solar System According to the nebular hypothesis, the Sun and planets were formed at the same time during the collapse of a rotating interstellar cloud of gas and dust that is called the solar nebula. The center collapsed to ignite the nuclear fires of the young Sun, while the surrounding material was whirled into a spinning disk where the planets coalesced. (Courtesy of Helmut K. Wimmer, Hayden Planetarium, American Museum of Natural History.)
Kant was a devout Christian who believed in God, the Divine Creator. The regular, ordered development of the Solar System did not happen by chance, he argued, and it was God who imposed that order, that design, on the material world in His act of Creation. To Kant, it was proof of God’s existence.
So Kant was not casting doubt on Who created the Heavens, but was, instead, humbly considering how God might have gone about it. He also proclaimed that all the fixed stars are suns with similar planetary systems; all formed and produced “out of the smallest particles of the elementary matter that filled empty space — that infinite receptacle of the Divine Presence.”3 He additionally proposed that the stars are not eternal, that they had a beginning, and that they must all perish. But we need not lament their passing, Kant supposed, any more than those of flowers or insects, “all demonstrations of the Divine Omnipotence,” and “while nature thus adorns eternity with changing scenes, God continues engaged in incessant creation in forming the matter for construction of still greater worlds.”4
The French astronomer and mathematician Pierre-Simon Laplace independently proposed the nebular hypothesis for the formation of the Solar System in the same year as Kant did; and additionally proposed that the rotating nebula shed a succession of rings from which the planets formed. The prolific Laplace was elected to the French Académie des Sciences at the age of 24. The Academy had never, observed its secretary, “received from so young a candidate in such a short time so many important papers on varied and difficult topics as the sequence submitted by Laplace.5 His achievements in these and later years included gravitational astrophysics, the Laplace transform, spherical harmonics, potential theory, the proof of the method of least squares, probability theory, and the speed of sound.
Kant and Laplace led quite different lives. Kant never married, and in his entire 79-year life never traveled more than a few kilometers outside of his hometown, in Königsberg, the capital of Prussia at that time, and now Kaliningrad, Russia. In contrast, at the age of 39, Laplace married Marie-Charlotte, just eighteen and a half years old, at the Saint-Sulpice in Paris. Within a few years, they had two children, most of Laplace’s contributions to astronomy had come to a close, and he became involved in French political affairs.
Both astronomers realized that the nebular hypothesis would account for the regular arrangement of the orbits of the major planets and their satellites. Any origin theory, Kant noted, must explain the fact that the planets all orbit the Sun within a common plane, which coincides with the equatorial plane of the Sun, and that they all revolve in approximately circular orbits in one direction that is the same as that of the Sun’s rotation. Kant attributed this “conformity in the direction and position of the planetary orbits” to the one “material cause through which they were all set in motion.”6 That cause, he proposed, is the contraction of a diffuse, rotating cloud of gas particles under the influence of gravity. The greatest increase in mass would occur at the center, which would become the Sun, and the surrounding material would consist of independent particles in circular motion within a plane about the central body.7
Laplace Draws Attention to the Nebular Hypothesis
Although Kant’s speculations were prescient, it is not clear how influential they were. At about the same time that his Universal Natural History was printed, the publisher became bankrupt and his holdings were impounded. Only a few copies of Kant’s book reached the public, and his work does not seem to have been noticed by his contemporaries, including William Herschel. In the following century others nevertheless drew attention to Kant’s astronomical speculations, which incidentally contained no mathematical details.
It was Pierre-Simon Laplace who in 1796 first drew public attention to a much more popular, but similar, process for the origin of the Solar System, while apparently unaware of Kant’s related work. Laplace’s account appeared at the very end of his The System of the World (Exposition du Système du Monde), which was published in five editions over almost thirty years, with successive modifications to its famous ending pages on the formation of the Solar System.8
These pages begin with a review of the regular orbital arrangement of the planets and their satellites, which to Laplace could not be accidental. The major planets all revolve around the Sun in nearly the same plane, and the main satellites move about their planet in the same direction and plane that it orbits the Sun. Moreover, the planets and satellites all turn about their axes in the same direction and plane as their orbital motion, which coincide with the Sun’s direction of rotation and equatorial plane.
Although astronomers had previously noted these startling alignments, Laplace was the first to show they could not arise by chance. If the known planets and satellites were haphazardly thrown together into randomly oriented configurations, the probability that they would have the same directions and planes of orbital and rotational motion is exceedingly small and unlikely. Laplace showed that even if millions upon millions of Solar Systems were made in this random way, only one would be expected to look like our own.
Faced with this dilemma, Laplace looked for a solution other than chance alignment. It is provided by the nebular hypothesis in which the planets formed out of the collapsing, rotating extended atmosphere of the young Sun. Laplace supposed that the planets were formed within “zones of vapors,” successively thrown off from the newborn Sun, and that Saturn’s rings illustrate the earliest stages of the formation of the much larger system of planets.
We now turn to Laplace’s friendship with Napoléon Bonaparte and their oft-quoted discussion about God, including Herschel’s on-the-spot account of the exchange.
Laplace, Herschel, Napoléon Bonaparte and God
Immediately after he seized power as First Consul in the coup d’état of 1799, Napoléon Bonaparte named Pierre-Simon Laplace the Minister of the Interior, but after only six weeks in the government, Bonaparte’s brother, Lucien, replaced Laplace. Much later, while exiled to Saint Helena, Napoléon wrote his reminiscence of the short-lived appointment, noting that Laplace “sought everywhere for subtleties, conceived only problems, and in short carried the spirit of the infinitesimal into administration.”9
Realizing that he should retain the allegiance of the eminent scientist, Napoléon appointed Pierre-Simon to the French Senate, named him to the Legion of Honor, and ennobled him as Count of the First French Empire. His wife joined the court of Napoléon’s sister, princess Elisa, where they focused on the world of fashion.
In return, Laplace dedicated the third volume of his Mécanique Céleste to Napoléon and included an adulatory dedication to him in the Théorie Analytique des Probabilités.
Then in 1814, when it became evident Napoléon’s empire was falling and that the monarchy would be restored, Laplace offered his services to the Bourbons. His change in allegiance was affected by his realization that Napoléon had overextended himself, putting the French nation at risk, as well as the fact that Laplace’s son Émile was endangered while participating in the fighting at the Eastern Front.
Laplace was also offended by Napoléon’s reaction to the death of Laplace’s only daughter Sophie-Suzanne in childbirth. On returning from the rout in Leipzig, Napoléon told Laplace that he had grown thin, to which he replied: “Sire, I have lost my daughter.” Napoléon replied “Oh! That’s not a reason for losing weight. You are a mathematician; put this event in an equation, and you will find that it adds up to zero.”10
In another celebrated exchange, Napoléon looked over Laplace’s Exposition du Système du Monde, and commented to Laplace: “Newton has spoken of God in his book. I have already gone over yours and I have not found this name a single time.” To this, Laplace responded: “Citizen First Consul, I had no need of that hypothesis (Je n’avais pas besoin de cette hypothèse-lá).”11 But Laplace was not claiming that God does not exist. He was instead stating that the gravitational interaction of the planets always remains stable, and that God did not need to intercede to break the laws of Nature and retain their equilibrium, as Newton had once proposed.
In 1802, William Herschel traveled to Paris and had several meetings with Laplace. During that visit, Napoléon Bonaparte had an audience with Herschel, Laplace, and others. The First Consul asked Herschel about his findings on the Construction of the Heavens, and addressed Laplace on the same subject. When asked to explain how that structure came about, Laplace attempted to show it was the result of natural laws. Napoléon argued against that view, and in Herschel’s account of the meeting:
“The difference was occasioned by an exclamation of the First Consul, who asked in a tone of exclamation or admiration (when we were speaking of the extent of the sidereal heavens): ‘And who is the author of all this!’ Mons. De Laplace wished to shew that a chain of natural causes would account for the construction and preservation of the wonderful system. This the First Consul rather opposed. Much may be said on the subject; by joining the arguments of both we shall be led to ‘Nature and nature’s God’.”12
In other words, it is God’s Nature that exhibits the causal, ordered structure described by natural laws that were set into place by the Creator.
There were many more sublime discoveries about planetary worlds in ensuing times, and many of them were related to the nebular hypothesis of Kant and Laplace.
The Quest for New Worlds
If the nebular hypothesis applies to the formation of all the stars, then they should all be surrounded by spinning protoplanetary disks or orbiting planets. The first evidence for these planet-forming disks was obtained in the early 1980s with instruments aboard the InfraRed Astronomical Satellite, and decades later the Spitzer Space Telescope used its powerful infrared vision to detect hundreds of stars that may be surrounded by planet-forming disks. In fact, the youngest nearby stars are usually found embedded in the dense clouds of interstellar gas and dust that spawned them.
Figure 8.2 Dusty disks Starlight is reflected from thick disks of dust that might still be in the process of forming planets. They surround the stars Au Microscopii (left) and HD 107146 (right) that are respectively thought to be 12 million years old and between 50 million and 250 million years old. [Hubble Space Telescope images courtesy of NASA/ESA/STScI/JPL/John Krist – STScI/JPL (left) and David Ardila – JHU (right)]
The Hubble Space Telescope has been used to discover flattened disks of dust swirling around many young stars (Fig. 8.2). They suggest that the nebular hypothesis applies to them, and material in the disks is expected to coalesce into full-blown planets if it hasn’t already done so. The Atacama array of radio telescopes that operates at millimeter wavelengths is now being used to resolve the protoplanetary disks around nearby stars (Fig. 8.3).
Individual planets are almost always too small and too faint to be seen directly by the reflected light from their parent star. Their presence has only recently been inferred from their gravitational effects on the motions of the star they revolve around, or when they chance to pass in front of a star, momentarily blocking the star’s light when viewed from Earth. Such extrasolar planets, which orbit around stars other than the Sun, are called exoplanets.
Figure 8.3 Protoplanetary disk The Atacama Large Millimeter/submillimeter Array (ALMA) has been used to obtain this image of planet formation around a young, Sun-like star HL Tau, which is probably no more than a million years old. Emerging planets may have swept their orbits clear of dust and gas. [Courtesy of ALMA (NRAO/ESO/NAOJ); C. Brogan, B. Saxton (NRAO/AUI/NSF).]
To detect their presence, astronomers had to look for the subtle compressing and stretching of starlight as an unseen planet tugged on a star and pulled it first toward the Earth and then away. This causes a periodic shift of the stellar radiation to shorter and then longer wavelengths (Fig. 8.4). To detect the effect, astronomers have to observe the wavelength of a well-known spectral feature, called a line, and measure the periodic shift of its wavelength.
But an orbiting planet produces an exceedingly small variation in the wavelength of spectral lines emitted from its star. So the effect could not be detected until the starlight was dispersed into fine wavelength intervals and collected by electronic charge-coupled detectors. And since no single line shift is significant enough to be seen, computer software had to be written to add up all the star’s spectral lines, which shift together, combining them over and over again at all possible regularities, or orbital periods, with continued comparison to non-moving laboratory spectral lines.
Figure 8.4 Starlight shift reveals invisible planet An unseen planet exerts a gravitational force on its visible host star, which periodically approaches and recedes from Earth. This motion changes the wavelength of the starlight seen from Earth through the Doppler effect, and reveals the presence of the planet orbiting the star.
It took decades for astronomers to develop these complex and precise instruments. Then, in the 1990s, the time was ripe, and two Swiss astronomers from the Geneva Observatory in Switzerland, Michel Mayor and Didier Queloz, discovered the first planet that orbits an ordinary star, the faintly visible, Sun-like star 51 Pegasi, only 48 light-years away from Earth in the constellation Pegasus, the Winged Horse. As Mayor described it, the occasion “happened like a dream, a spiritual moment.”13
They had detected the back-and-forth Doppler shift of the star’s light with a regular 4.23-day period, measured by a periodic change of the star’s radial velocity of up to 50 meters per second (Fig. 8.5).14 To produce such a quick and relatively pronounced wobble, the newfound planet had to be large, with a mass comparable to that of Jupiter, which is 318 times heftier than Earth, and moving in a tight, close orbit around 51 Pegasi at a distance of only 0.05 AU, where 1 AU is the mean distance between the Earth and the Sun. By way of comparison, Jupiter is about 100 times further away from the Sun than the newfound planet is from the star 51 Pegasi. No one had anticipated that a giant planet would be orbiting so close to its star.
Figure 8.5 Pioneering planet discovery An unseen planet of about half the mass of Jupiter produces a periodic 4.23-day variation in the observed radial velocity of the star 51 Pegasi measured in units of meters per second, or m s–1. The invisible companion is in close orbit around the star, at a distance of just 0.05 of the mean distance between the Earth and the Sun. [Adapted from Michael Mayor and Didier Queloz, “A Jupiter-mass Companion to a Solar-type Star,” Nature 378, 355–359 (1995).]
The intense radiation and powerful winds of a newly-formed star were expected to keep any nearby material from gathering together into a large planet, explaining why Jupiter and the other giant planets were formed far from the Sun in the cold, outer precincts of our Solar System. But it was a good thing for planet hunters, for the large mass of a giant world would produce a more pronounced velocity change than the smaller mass of an Earth-sized planet and the close orbit meant a short orbital period that might be detected in weeks instead of years.
Less than two weeks after the announcement of a giant planet circling 51 Pegasi, two American astronomers, Geoffrey W. Marcy and R. Paul Butler, used their own past observations to confirm the result, and now that they knew that giant planets could revolve unexpectedly near a star, with short orbital periods, they used powerful computers to re-examine their previous observations of other nearby stars and announced the discovery of two more Jupiter-sized companions of Sun-like stars.15
From then on, anyone could look up at the night sky and say that there are definitely unseen planets out there, orbiting perfectly ordinary stars that are now shining brightly in the night sky. Time Magazine celebrated the event, on Februrary 5, 1996, with a cover story entitled: “Is Anybody Out There?” They might have also used: “Are We Alone?” So far, no one knows the answer to either question.
After astronomers realized that a large planet could be so near to its star, they knew where and how to look. And by monitoring thousands of nearby Sun-like stars for years, they have now found thousands of planets revolving about other nearby stars, many of them massive planets that have been dubbed “hot Jupiters” because of their size and proximity to the intense stellar heat. They are much too hot and too close to their star for life to survive or water to exist.
Finding Habitable Exoplanets
From a human perspective, the most interesting exoplanets will be those as small as the Earth, in circular orbits at just the right distance from the heat of a Sun-like star to permit liquid water to exist on the planet. Scientists call this location a habitable zone. At closer distances, the water would all be boiled away, and at more remote distances it would be frozen solid. A planet in this zone could be inhabited, but that does not mean that life does reside on it.
Such a planet produces too small a gravitational perturbation of their star to be detected by the velocity method with existing technology, so the transit method has to be used to detect them. That is, the planet’s orbit has to be in just the right orientation for it to periodically cross directly in front of, or transit, its host star.
The orbital size can be calculated from the period of the repeated transit and the mass of the star. From the orbital size and the brightness of the star, the planet’s temperature can be calculated. This information would tell us if the planet is warm enough for liquid water to exist on its surface.
The Kepler mission was specifically designed to detect planets comparable to the Earth in size or smaller, and located at or near this habitable zone. By measuring the brightness of 100,000 stars, it has detected the periodic dimming of starlight produced when thousands of planet candidates pass in front of their star, and that is quite an accomplishment. A transit by an Earth-sized planet in the habitable zone will produce a small change of only about 0.0001, or 1/10,000, in the star’s brightness lasting for 2 to 16 hours.
Most of these planet candidates are orbiting nearby stars that are smaller and cooler than our Sun. Since these stars are less luminous than the Sun, the habitable zone is closer to the star than the Earth is from the Sun, and planets within it have orbital periods that are less than our year, which means that they can be recognized in relatively short observation times of a few years. As an example, seven Earth-sized planets have been found orbiting the ultra cool Trappist-1 star, and three of these planets are located in the star’s habitable zone. It is located 39.5 light years from the Sun in the constellation Aquarius.
The Kepler planet candidates require follow-up verification observations with the world’s best telescopes on the ground and in space. Atmospheres have even been detected for some of these exoplanets, but no one knows if any of them are inhabited by living things. That possibility remains as speculative as it has always been.
It has long been thought that there might be living things on planets other than the Earth, either in our Solar System or orbiting stars other than the Sun. The arguments have been extensively documented in two lengthy books — by Steven J. Dick from the ancient Greeks to Kant, and by Michael J. Crowe from Kant to the beginning of the 20th century.16 The scope of our book does not include such all-embracing considerations, so lets just say the idea that there is life out there beyond the Earth just will not go away, and take up the thread of our discussion where we last left astronomers, in the mid-18th century.
According to the nebular hypothesis, the formation of planets should be a natural result of star formation, and planets should encircle most stars. Moreover, some of these planets could be populated with diverse living beings. Immanual Kant and Pierre-Simon Laplace both speculated about life on other planets in our Solar System.17,18 And William Herschel was no less reluctant than Kant or Laplace in populating planetary worlds with imaginary beings. A year before his discovery of Uranus, Herschel speculated that the observed features on the Moon indicate that it is inhabited. Later, he proposed that living creatures also reside on the Sun. The sunspots, he noted, could uncover and reveal a dark and solid Sun where other beings might live, beneath its fiery atmosphere.
Inhabitants of the Sun was a bit too much. As the great English astronomer A. S. Eddington remarked: “It cannot be denied that he [William Herschel] was given to jumping to conclusions in a way which, when it comes off, we describe as profound insight, and when it does not come off, we call wildcat speculation.”19
Eventually astronomers determined the physical conditions on the Moon, Sun and planets in our Solar System, including their temperatures and atmospheres, and concluded that life, as we know it, is not likely to be found on them. They instead focused on then unanswered questions about how the Sun and other stars shine.