Pierre-Simon Marquis de Laplace and the Formation of the Solar System

-----Pierre-Simon Laplace (1749-1827)

Gaining an informed appreciation of the true size and scale of the solar system even today, in light of the tantalizing and astonishing discoveries obtained from interplanetary space probes during the 20^th century, does not always come easy to either astronomers or laypersons. The difficulty of imagining the solar system as it truly extends in space is seen in many textbook illustrations that are never true to scale in all aspects, but instead are usually symbolic graphic representations. The orbits of the inner, terrestrial planets (Mercury, Venus, Earth and Mars) are often drawn so small that they are barely visible in order to fit in the larger orbits of the outer gas giants (Jupiter, Saturn, Uranus and Neptune). Two separate illustrations are often required, one for the inner planets and another for the outer planets. The Sun itself is practically never shown scaled true to life size in most solar system graphics. In reality, of course, its overarching size dwarfs its retinue of planets. It is, in fact, impossible to show true to scale on an ordinary single page the relative sizes of the known planets and their orbital paths around a correctly scaled Sun.

The problem in appreciating the true size of the solar system is one of scale. We are forced to use different units of measurement depending on our chosen perspective and the extent of the view. In comparing the diameters of planets we may use kilometers. In comparing planetary orbits we often use the Earth-to-Sun average distance standard of the astronomical unit (1 AU = 1.496 x 10⁸ kilometers, or 93 million miles). But the true extent of the solar system will ultimately cause us to resort to the light year (1 ly = 9.46 x 10¹² kilometers, or 63,240 AU, or about 6 trillion miles).

"We commonly think of the solar system as ending at the orbit of distant Pluto. However, the Sun’s gravitational sphere of influence actually extends some 2,500 times farther out, halfway to the nearest stars."³ The solar system is more than a central star and its family of planets. It includes leftover building blocks from its origin: asteroids and comets. The majority of asteroids orbit between Mars and Jupiter. Comets, however, originate either from a belt in the vicinity of Pluto or from a vast cloud in near-interstellar space. It is this probably elliptical spheroid cometary reservoir that transforms the dimensions of the solar system from kilometers and astronomical units into one of light years.

Analysis of the elliptical orbits of long period comets (those that take roughly 1 to 30 million years to complete just one orbit of the Sun) indicated to Edmond Halley in 1705 that, "…the Space between the Sun and the fix’d Stars is so immense that there is Room enough for a Comet to revolve, tho’ the Period of its Revolution be vastly long."⁴ Indeed, current thinking on the origin of both short-period (orbiting the Sun in less than 200 years) and long period comets places their origins respectively in the relatively nearby Kuiper Belt and the much further out enveloping Oort Cloud. Pluto lies some 40 AU from the Sun. The Kuiper Belt ranges some 30 to 50 AU out while the Oort Cloud’s outermost edge is perhaps 200,000 AU or 3 light years from the Sun. Clearly any true picture of what we mean by our "solar system" encompasses distances immensely larger than just the orbits of its family of planets!

To visualize the extent of the solar system a comparison between the astronomical unit and the light year proves both useful and startling. All of the Sun’s planets could be contained within a sphere having a radius of about 40 AU. This radius distance is only 0.00063 (40/63,240) of a light year. It is utterly insignificant in comparison to the distance out to the Oort Cloud!

Any workable theory of the origin of the solar system in its entirety, therefore, the only one for which we have amassed such a wealth of data, as well as for any other possible solar "systems" must inevitably account for the whole and the sum of its parts. This includes, but is not be limited to: the birth of the Sun itself (or, perhaps, suns); the subsequent formation of terrestrial and gaseous planets with their own miniature solar systems of moons; plus asteroids, comets and any other such "leftover" building components. It must account for large-scale properties such as planets in nearly circular orbits that are co-planar and revolving prograde (in the same direction around the Sun), isolated in orderly orbital intervals. On the small scale most planets will rotate prograde but there may be exceptions. Terrestrial planets will rotate slowly and have high densities with thin or no atmospheres while gaseous giant planets will rotate rapidly and have low densities with thick atmospheres. Most of the outer solar system objects in our model will be ice-rich.

The ages of the members of our solar system are uniform with all indications pointing to a single formation event some 4.6 billion years ago. Furthermore, even though the overall architecture of our solar system appears to be orderly it doesn’t preclude dynamical evolution over time such as tidal locking between worlds, chemical processing, moon captures, ring formation and a host of other events.

Our understanding of the components and dynamics of the solar system has been evolutionary. Not all of these features have been known or were even apparent through all earlier times. Cosmogony, the study of the origins and development of the entire cosmos, was once confined to just the Sun, Moon, and five planets. For the past two centuries is has been confined to theories of how just the solar system itself was formed. It has expanded beyond a single solar system within the past five years or so with the discovery of extrasolar planets to include all known solar systems.

Serious theories on the origin of the solar system begin with Immanuel Kant (1724-1804) and Pierre Simon Laplace (1749-1827). Meager knowns such as the Sun’s planets nested in almost-circular orbits that lay in a common plane, rotating in the same direction suggested to Kant and Laplace a common origin. Laplace, a mathematical genius and astronomer, was born into a poor family, survived the dangerous intellectual atmosphere during the French Revolution, and was named a Marquis after the Bourbon restoration. He was named "the Newton of France" at the age of 24 for his paper on the stability of the solar system, which applied Newton’s theory of gravitation to planetary orbits.

In a note to his 1796 Exposition du systeme du monde (Exposition of the System of the World) Laplace proposed the nebular hypothesis: the origin of the solar system was "a large nebula [which] rotated and because of the gravitation of mass to its center, a sun formed itself in the middle, and condensed. The outer parts of the nebula broke into rings, and the rings rolled themselves into globes – the planets."⁶ He went on to insist that it was no accident that the Sun, all known planets, all known satellites, roll in the same direction, counterclockwise. And being a master of probability theory, "he concluded that there are four billion chances against one that this plan is not the result of chance."⁷ Laplace was partly wrong. The rotation of Venus is retrograde as is that of Uranus, later discovered by William Herschel in 1781. Furthermore, more than ten retrograde satellites are now known.

Curiously enough, Laplace also postulated that in order to keep this system together gravitation must have been propagating with a velocity that is fifty million times greater than the speed of light. This means that, to Laplace, the velocity of gravity must be essentially infinite, or instantaneous.

Laplace and Kant had both formed independently a theory of the solar system’s origin. Kant, the Prussian philosopher and metaphysicist, who in 80 years never traveled more than 40 miles from his native Konigsburg, nonetheless had the extraordinary intellectual prowess to envision the origins of a world in his extraordinary 1755 Universal Natural History and Theory of Heaven:

"…if we think of the fact that six planets with ten companions describe orbits with the sun at the mid-point, that all move in the same direction, the very same as the axial rotational of the sun itself, which governs all their orbits though the power of attraction, that their orbits do not deviate far from a common plane, namely, the extrapolated equatorial plane of the sun, that among the furthest celestial bodies belonging to the solar system, in the region where the common cause of movement was, according to our hypothesis, not so strong as in the regions close to the mid-point, deviations from the precision of this condition occur, which are significantly related to the lack of impressed motion, if, I say, we consider all this interconnection, then we will come to believe that one cause, whatever it may be, had a pervasive influence throughout the entire system and that the conformity in the direction and position of the planetary orbits is a consequence of a harmony which they must have had with that material cause through which they were set in motion. [Author’s italics]"⁸

Kant’s earlier treatise was qualititative; Laplace’s later work was more quantitative. Laplace had set himself to the task of writing a book that would "offer a complete solution of the great mechanical problem presented by the solar system, and bring theory to coincide so closely with observations that empirical equations should no longer find a place in astronomical tables."⁹ The popular level Exposition du systeme du monde in which the nebular hypothesis is put forth was followed by the more abstruse Traite de mecanique celeste (Treatise on Celestial Mechanics), his monumental 5-volume work in 1799-1825. Laplace does not seem to be aware that Kant had at least partially anticipated him some 41 years earlier.

There are problems other than exclusive prograde motion with Laplace’s nebular hypothesis. The greater part of the mass in the solar system resides in the Sun itself (more than 99% in fact). But the outer gaseous giant planets carry most of the angular momentum. In short, the Sun ought to have been rotating more rapidly than it does. Laplace theorized that perhaps a large comet had crashed into the Sun with the ejected fragments condensing into planets. Nearly a century later it was suggested that the angular momentum problem could be explained if a passing star (the "encounter" hypothesis) had expelled material onto the Sun with tidal streams forming like spiral arms that cooled and aggregated into "planetesimals" (formative planets). Even in the 20^th century it was posited that a magnetic field around the Sun in the early solar system linked the Sun and the nebula together. This would supposedly slow down the Sun and transfer angular momentum onto the outer regions of the nebula.

The current working model for the solar system’s origin might be termed the protoplanetary hypothesis. Many components of Laplace’s nebular hypothesis are incorporated but the role of dust is emphasized as cores for the condensation of gas. Planets form proportional to mass; largest planetesimals are accreted first and sweep the early solar system clean of large bodies. Lighter compounds are vaporized in the inner solar system with outgassing material provided from comets that fall from the outer solar system after the planets form. The solar system divides into large outer proto-planets and much smaller inner proto-planets. Asteroids, meteors and comets are leftovers. Magnetic braking is the favored explanation for the angular momentum problem. The early Sun’s heavier solar wind with its charged particles was dragged by the magnetic field, which slowed down the Sun’s rotation.

Until five years ago we were working from only one solar system sample. Lately we have several dozen to choose from and they are teaching us that solar systems can form into many other planetary configurations. One anomaly early on is the discovery of Jupiter-size planets and larger that are orbiting their central sun at a distance that would be inside the orbit of Mercury in our own system. This positioning and the potential migration of large planets out to more distant orbits from the central sun are not yet adequately explained. The discovery of this arrangement in many of the extrasolar planets so far brings up new questions specifically about the origin and subsequent evolution of Jupiter’s orbit.

The solar nebular hypothesis should theoretically apply to the formation of nearly all stars, i.e., planets may be a natural by-product of stellar formation. Surrounding the 200 billion stars in our Milky Way galaxy alone, there may be millions or even billions of planets. At some point in a galaxy’s evolution it would seem that solar systems are birthing continuously. If this is so then Laplace’s foundational theory with a number of to-be-expected contemporary modifications stands on relatively solid ground. Laplace was wrong about some of the details but he was right when he said, "What we know is not much. What we don’t know is immense." By some accounts these were his last words. By all accounts that is true for all times, even now.

Jerry Persall
ID#1250396
Swinburne University of Technology
Swinburne Astronomy Online
HET607 – History of Astronomy
Semester 1, 2000
October 15, 2000