1 Lecture What can the solar system tell us about the
formation & evolution of planetary systems?
Lets consider:
1. The sun.
2. The major planets.
3. Small bodies, including the Kuiper Belt
and laboratory samples.
What is the composition of the sun? Are other stars similar?
H
[O,C] ~10-4[H]
[N]
~10-5[H]
[Si,Fe]~10-6[H]
O
He
C
N
Si
Fe
All
Else
Theansweristimedependent!Impact?
Cosmicbackgroundimaging
(WMAP),=13.7AE(~1%),
no/littlemetals,4%atoms,
23%CDM,75%DarkEnergy.
Largescale
structure.
Pic,anearby
youngstar&disk.
Laplace: The System of the World (1796)
(see http://eee.uci.edu/clients/bjbecker/ExploringtheCosmos/week8c.html)
Although the geometrical elements of the planetary system are physically independent of each other, there are,
nevertheless, certain relationships among them which can clarify their origin. On close consideration, it is astonishing to
find all the planets moving about the sun from west to east and almost in the same plane; all of the satellites move about
their planets in the same sense and nearly in the same plane as the planet; finally, the sun, the planets and their satellites,
whose rotary motion we can observe, turn on themselves in the direction and nearly in the plane of their orbital motion.
Such an extraordinary phenomenon can hardly have haphazard causes; it suggests that a general cause has established all
of the motions. To obtain an estimate of the probability of such a cause, we remark that the planetary system as it is known
today, comprises seven [planets] and fourteen satellites; we have observed the rotation of the sun, of five planets, of the
moon, the ring of Saturn and one of his moons. These form an ensemble of thirty motions directed in the same sense.
An equally remarkable phenomenon of the solar system is that the orbits of the planets are nearly circular, while those of
the comets are highly elongated; the orbits of the system offer no intermediate nuances. Again we are compelled to
recognize the effect of a regular cause; happenstance alone could not possibly give an almost circular form to the orbits of
all the planets. Whatever arranged these orbits also made them nearly circular. Moreover, the same cause must explain the
great elongation of cometary orbits, and the fact that comets move in all directions as though they had been thrown at
random.
Thus to trace back to the cause of the original motions of the planetary system, we have the following five facts: the
motions of the planets in the same direction, and in almost the same plane; the motions of the satellites in the same
direction as that of the planets; the rotary motions of these various bodies, and of the sun, in the same directions as their
trajectories about the sun and in approximately the same planes; the nearly circular orbits of the planets and satellites;
finally, the great elongation of the orbits of the comets, although their orientations have been left to chance .
The critical role of angular
momentum, as illustrated by the
orbits, obliquities of the planets.
George Louis Leclerc, Comte de Buffon: Natural History (1749)
This general law being once discovered, the effects of it would be easily explained, if the action of those bodies which produce them were not too complicated. A
slight view of the solar system will convince us of the difficulties which attend this subject. The principal planets are attracted by the sun, the sun by the planets, the
satellites by their principal planets, and each planet attracts all the others, and is attracted by them. All these actions and re-actions vary according to the quantities of
matter and the distances, and give rise to great inequalities, and even irregularities. How are so many relations to be combined and estimated? Among such a number
of objects, how is it possible to trace any individual? These difficulties, however, have been surmounted; the reasonings of theory have been confirmed by calculation;
every observation has produced a new demonstration; and the systematic order of the universe is now laid open to every man who is able to distinguish truth from error.
May we not conjecture, that a comet falling into the body of the sun might drive off some parts from its surface, and communicate to them a violent impulsive force,
which they still retain? This conjecture appears to be as well founded as that of Mr Leibnitz ], which supposed the earth and planets to have formerly been suns; and
his system ... would have been more comprehensive, and more consonant to probability, if it had embraced the above idea. We agree with him, that this effect was
produced at the time when God is said by Moses to have separated the light from darkness; for, according to Leibnitz, the light was separated from the darkness when
the planets were extinguished. But, on our supposition, there was a real physical separation; because the opaque bodies of the planets were detached from the
luminous matter of which the sun is composed.
Upon examining the course of comets, it is easy to believe that some of them must occasionally fall into the sun. The comet [of] 1680 approached so near, that, at its
perihelion, it was not more distant from the sun than a sixteenth part of its diameter; and, if it returns, which is extremely probable, in the year 2255, it may then fall
into the sun. This must depend upon the accidents it meets with in its course, and the retardations it suffers in passing through the sun's atmosphere.
We may, therefore, presume, with the great Newton, that comets sometimes fall into the sun. But they may fall in different directions. If they fall perpendicularly, or
in a direction not very oblique, they will remain in the body of the sun, serve the purposes of feuel [ sic], and, by their impulse, remove the sun from his place, in
proportion to the quantity of matter they contain.
But, if a comet falls in a very oblique direction, which will most frequently happen, it will only graze the surface, or penetrate to no great depth. In this case, it may
force its way past the sun, detach certain portions of his body, to which it will communicate a common impulsive motion; and these portions pushed off from the sun,
and even the comet itself, may turn planets, which will revolve round this luminary in the same direction, and nearly the same plane.
A calculation, perhaps, might be made of the quantity of matter, velocity, and direction, a comet ought to have, order in to force from the sun masses equal to those
which compose the six planets and their satellites. But it is sufficient here to observe, that the whole planets, with their satellites, make not a 650th part of the sun's
mass; for, although the density of Saturn and Jupiter be less than that of the sun, and though the earth be four times, and the moon near five times more dense than the
sun; yet they are only atoms when compared to his immense volume.
The correspondence between the density of the whole planets, and that of the sun, deserves also to be noticed.... We may, therefore, conclude, that, in
general, the matter of the planets is very nearly of the same kind with the solar matter, and, of course, that the former may have been separated from the
latter.
To this theory, it may be objected, that, if the planets had been driven off from the sun by a comet, in place of describing circles round him, they must,
according to the law of projectiles, have returned to the same place from whence they had been forced; and, therefore, that the projectile force of the
planets cannot be attributed to the impulse of a comet.
I reply, that the planets issued not from the sun in the form of globes, but in the form of torrents, the motion of whose anterior particles behoved [ sic] to
be accelerated by those behind, and the attraction of the anterior particles would also accelerate the motion of the posterior; and that this acceleration,
produced by one or both of these causes, might be such as would necessarily change the original motion arising from the impulse of the comet, and that,
from this cause, might result a motion similar to what takes place in the planets, especially when it is considered, that the shock of the comets removes
the sun out of its former station.
Rebuttal from Laplace.
The circularity of the planetary orbits is not only very difficult to explain with this
hypothesis, the facts seem to contradict it. If a body moving in an orbit about the sun comes
close to the surface of this star, it will return unfailingly at each revolution; from this it
follows that if the planets had originally been detached from the sun they would touch it
again at each return and their orbits would be far from circular. It is true that a mass of
matter driven from the sun cannot be exactly compared to a globe which touches its surface,
for the impulse which the particles of this mass receive from one another and the reciprocal
attractions which they exert among themselves, could, in changing the direction of their
movements, remove their perihelions from the sun; but their orbits would be always very
elongated, or at least they would not be nearly circular except by the most extraordinary
chance. Finally, there is no evident reason in the hypothesis of Buffon why the eighty
comets observed thus far should have such elongated orbits. This hypothesis is far from
fitting the facts. Let us see whether it is possible to deduce their true cause.
Orbital dynamics & the impulse
approximation, to which we shall return.
And his hypothesis
Whatever the sun's nature, it must have encompassed all of the planets; and considering the enormous distances separating these bodies, it
must have been a fluid of an immense extent. In order to have given the planets almost circular motions in the same direction, this fluid must
have surrounded the sun like an atmosphere. The consideration of the planetary motions thus leads us to think that, by virtue of an excessive
heat, the solar atmosphere originally extended beyond the orbits of all the planets and that it progressively shrank to its present limits. This
might have occurred through causes similar to those which made the famous star of 1572 suddenly shine so brightly for several months in the
constellation of Cassiopeia.
The great eccentricity of cometary orbits leads to the same result; it suggests the disappearance of a large number of comets with lesseccentric orbits, as though they had been destroyed by passing through an atmosphere. If this were the case, the only comets existing today
would be those which were outside the atmosphere during its enormous extension; and, as we can only observe comets which come quite
close to the sun, the observable comets would not be those with very eccentric orbits. And, at the same time, we can see that the orientation
of their orbits would be scattered at random, because the solar atmosphere could not have influenced them.
But how did the extended atmosphere of the sun produce the rotations of the planets? As these bodies would have fallen into the sun if they
had penetrated the atmosphere, we may conjecture that they were formed at the successive limits of the atmosphere, in zones of material
abandoned as it contracted toward the surface of the sun. We may further conjecture that the satellites were formed in a similar fashion from
the atmospheres of the planets.
Whatever may be the fate of this theory, which I present with the diffidence appropriate to what is not the result of observation or
calculation, it is certain that the arrangement of the solar system is such as to assure its greatest stabilitysupposing no trouble from
external forces. To that end, the motions of the planets and the satellites are almost circular and are directed in the same sense and nearly in
a common plane. This system will merely oscillate by a small amount about its average state. It seems that nature disposed everything in
the sky to assure the stability of the planetary system, by a design similar to what it follows so wonderfully on earth for the preservation of
humans and for the perpetuity of species.
(see also Kant 1755. if you can make sense of it.)
What else do the planets tell us?
Bodes Law
Relatively smooth
variation in the
amount of material
available to build
planets with distance
(so-called Minimum
Mass Solar Nebula).
Volatiles are critical
even in the assembly
of the largest units
apart from the Sun.
Gas Giant Size/Mass Relationships
What about small bodies?
Lab samples
Comets/KBOs
Ages, thermal history.
Primordial composition
(the least processed
material in the solar
system), dynamics
associated with the early
S.S. & local
environment.
What can the solar system tell us about the
formation & evolution of planetary systems?
Mass transport, lighthouse
Angular momentum transport, hierachical growth.
Dynamics, environment
Pre-history, timescales