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Comet Origins — The Standard View
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Comet Origins — The Standard View
Just about everyone today has heard that
astronomers now believe that there exist 2 great reservoirs of potential
comets, and of course comets themselves for part of their long orbits
around our Sun: the Kuiper Belt, a disk-shaped “belt”
of comets and-or comet-like substances (depending on their actual orbit;
currently estimated to be in the millions) that orbit our Sun at a
distance of approximately 500 to 1,000 AUs (Astronomical Units, the avg.
distance from the Sun to the Earth), and the Oort
Cloud, a vast “cloud” of comets and-or
comet-like substances (depending on their
actual orbit; currently estimated to number in the trillions)
that orbit our Sun roughly 1 light-year
(a little less than 62000 AUs) away.
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Digressive Question: How long does a comet’s free-fall round trip from-to the Oort Cloud take? No scientific estimate has been
made public. It seems ridiculous that scientists would overlook this, but
is this time length part of the explanation for why Oort Cloud comets don’t
seem to reappear as often (in the sense of multiple times as opposed to
time to orbit the Sun) as Kuiper Belt comets? Scientists are currently
speculating that Oort Cloud comets are made of a more fragile composition
of ice and rock than Kuiper Belt comets. Given the propensity of the Sun
to drive less dense substances like water molecules away from itself
preferentially over denser substances like rock particles, it seems
reasonable that we will eventually find higher proportions of ice in
bodies in the Oort Cloud compared with the Kuiper Belt.
The existence of the Kuiper Belt was verified and named for the
Dutch-American astronomer Gerrit Pieter Kuiper
(1905-1973)
in the 1990s. The Oort Cloud, named for the Dutch astronomer Jan Hendrik
Oort (1900-1992), who proposed it in 1950, is accepted by most astronomers, but is still
(early 21st Century) considered unverified.
But, how do those comet-like substances become actual comets?
This is an unsatisfying theory for some, mainly because stars just don’t
“pass” that often, or that close, not nearly often enough to explain new
comet sightings. The triple star system that includes
Alpha and Proxima Centauri is around 4.2 to 4.3 light-years away from our
Sun, the Oort Cloud roughly 1/4 that. And they aren’t moving very
fast relative to our Sun. E.g. the current guess is that Alpha Centauri
will pass by our Sun at a distance of about 3 light-years in 28,000 years
or so. This doesn’t address the growing sense among astronomers that
comets have trickled into existence (as comets) over much longer periods
of time, instead of gushing into existence only when a star passes.
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SECTIONS
Comet Origin... Oversights
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Comet Origin... Oversights
What has been... oversighted?!
It is actually well-known in the study of gravitational
dynamics that groups of bodies that are orbiting each
other
more or less “chaotically”
— and thus will here be referred to as
“swarms”,
vaguely like swarms of bees
— can at times (and of course depending on the details of the orbits and
interactions)
eject one of their number, giving it “Quasi-Escape
Velocity” from the local swarm. (It need not happen by collisions; just
gravity will do.) Less massive bodies are more likely to
achieve Quasi-Escape Velocity than larger bodies, as should be obvious.
The ones that remain will have a lower collective energy, and angular
momentum comes into it, too.
The use of the term “chaos”
is intended to match what many people might expect from its use in “chaos
theory”. Some interactions of n-bodies can be very regular,
i.e. non-“chaotic”, and some are so “chaotic” that, if one or more of the
bodies were perturbed (position or velocity, etc.) by an amount roughly
equivalent to floating point rounding error in a computer, the
thus perturbed “chaotic” swarm would diverge greatly and relatively rapidly
from what would have been its group trajectory.
Too, the use of the term “swarms”
is intended to accent the chaotic movements and interactions of the bodies
(as opposed to highly regular orbits, easily predictable over very long
periods of time). It should not be taken to mean that the groupings and
interactions are highly defined and-or separated in all cases, or even
usually. It is not just the n-body movements within swarms that
will be chaotic, the interactions of micro-swarms with each other and with
macro-swarms, etc., are all likely to be fuzzy as well as chaotic, except for the shortest
periods of time with the fewest numbers of bodies involved, closest
together, etc.
Relatedly, scientists have begun to note
that many asteroids come in pairs. (See:
http://www.space.com/scienceastronomy/solarsystem/double_asteroids_020411.html)
It shouldn’t be too much longer till they notice the existence of asteroid
“swarms”.
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“Quasi-Escape
Velocity”: The use of this term is intended to accent that a body need not achieve actual escape
velocity to be sufficiently ejected from a swarm to e.g. become a comet,
especially if it can “slingshot” off yet other bodies (as we do deliberately
with our space probes) at a distance from the swarm (and as in fact it does
with the other bodies in the swarm in order to be ejected in the first place).
This whole process of
interaction and ejection can be compared with thermodynamic evaporation
(with gravitational interactions replacing elastic collisions). The
remainder of the swarm loses energy to the randomly-chaotically chosen
ejected body, i.e. it “cools”. The ejection of mass from a swarm held
together by gravity is just as statistically inevitable as evaporation in
thermodynamic systems. The mass can be ejected as a body, but it can also
be ejected after being fragmented-melted-vaporized-etc in a
collision-accretion scenario.
If we imagine that we have a swarm of
proto-comets (big hunks of ice and rock that haven’t made it into a
standard comet orbit) in e.g. the Kuiper Belt, every so often one of them will achieve
Quasi-Escape
Velocity from the local group and exit it in some direction at a
relatively high velocity. The direction might be biased by the Sun or a
passing star, and quite obviously by nearby large bodies (“gravitational
anomalies”), but when it is eventually studied
carefully, it will probably be found to be roughly evenly distributed. That direction-velocity and the change of
angular momentum that goes with it-them can fall in a range cause it to fall out of its
more circular, less eccentric, orbit and into a more eccentric orbit that
can take it close to the Sun.
This process need not happen
all at once. As it flies away from the swarm, it can get easily absorbed
by another swarm. Collisions will also happen, but more rarely than misses
of varying degrees. Instead of being absorbed, a body exiting a swarm will
inevitably randomly slingshot off bodies in other groups (not necessarily
chaotically swarming in a dense grouping), randomly increasing (or perhaps
decreasing) the eccentricity of its solar orbit even further.
Swarms will continuingly interact with
each other, perhaps even merging only to diverge again
(like galaxies are known to do). Bodies that get ejected in the “wrong”
direction may (with enough slingshots) achieve escape velocity from our
Sun, and this may take them out on a fantastic voyage to other stars (or
from other stars to Earth!) But more likely they will not have achieved
such escape velocity, and they will wander until they get absorbed by a new
group, or finally get a slingshot kick that takes them toward the Sun. The overall belt or cloud
will only lose total energy when it fully ejects a comet (i.e. that eventually
loses its mass near the Sun), or a “voyager”
in the other direction, toward other stars.
The swarms of bodies present in the Kuiper
Belt and the Oort Cloud are certain to have more than enough kinetic and
potential energy to chaotically eject comets in our direction
every now and then. In fact, with a great enough population of swarms and
the interactions that are likely over time, this process is likely to
yield a vaguely steady supply of comets (and “voyagers”
to and from other stars).
As the swarms lose enough energy to ejected bodies, they will tend to stop ejecting
bodies. But as swarms interact with other swarms, they can gain energy
(and “gain chaos”) and the rate of ejections will probably increase. These
increases in ejection rates could easily balance decreases due to earlier
ejections, a sort of governor effect.
Let’s look more closely at
what happens when bodies are ejected by swarms, or absorbed by them. When
ejecting a body, which thus changes both its momentum and angular
momentum, the swarm will also experience a change in its collective
momentum and angular momentum. This change can take the swarm into a
different orbit, just as the ejected body will experience a change in
orbit, a change that may take it in toward the Sun as a comet, or even out
toward other stars where it may eventually become captured by another
star, perhaps becoming a comet there.
The swarm will also
experience a change in what can be called its “swarm
temperature”, the local average kinetic
energy of the remaining bodies of the swarm as they orbit each other
chaotically (non-chaotic orbits are possible, but much less likely). (It
may be that the quantity of chaos, to the extent that chaos can be
quantified, may or may not change, but the quantity and direction of the
change is not obviously a simple function of the change in the swarm
temperature. This will, for
example, make accretion among the remaining bodies of the swarm more
likely, since they have less energy to stay separated and to shatter and
disperse when colliding (obviously inelastically).
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“Swarm
temperature”: The use of
this term relates not to the standard thermodynamic temperature of the
individual bodies in a swarm, but rather the average kinetic energy of the
bodies that are swarming. It is a macro level version of temperature,
hence the nomenclature. From it we can quickly and fairly accurately
intuit some of the possibilities for interactions among the bodies in and
among swarms, e.g. evaporation-ejection-cooling,
absorption-condensation-warming, etc. The main forces holding the bodies
together are gravitational and possibly electromagnetic instead of
inter-molecular (or quasi-none in the case of gasses). In both cases something like viscosity will tend to keep
the bodies together as the density increases by dispersing escape
velocities, but with swarms the viscous collisions will also be far more
inelastic and the gravitational forces will be much further ranging than
the intermolecular forces. (To my knowledge, this interpolation-blending
of thermodynamics and gravitational mechanics has never been noticed let
alone studied.)
A similar process happens
when a swarm captures-absorbs a body. (Remember that “swarm” is a fuzzy
sort of thing, with no real boundaries.) The swarm will experience a
change in its collective momentum and angular momentum, and in its “swarm
temperature”. It will also
probably have its chaos quantitatively increased. All of this will
fuzzily blend together with accretion-dispersion type events, including
accretions which have temperatures high enough to melt the ice and
increase gravitationally induced “chromatic” separation, yielding rocky
cores with icy surfaces.
[Later note: see
When Stars Collide by Michael Shara in the
November 2002
issue of
Scientific American, p. 29. It talks about stars
being ejected from clusters of stars and the resultant cooling of the
remaining swarm by “evaporation”. Scientists know that this
process of ejection happens in
gravitational systems, but... oversights this when it comes to comet
origins... and the origins of new Earth crossing asteroids.]
Scientists should also start
looking for extremely large “failed” proto-comets (planet sized balls of
ice and rock) in the Kuiper Belt (and perhaps eventually the Oort Cloud).
They can be consider failed comets since they accreted (by cannibalism) until
they became too big to be ejected from a swarm with Quasi-Escape Velocity,
but their size means that they will act as more effective slingshots for
other proto-comets. Far from the Sun, out past the orbit of Pluto, the Sun
is far less likely to drive vaporized water atmospheres away from
colliding-accreting proto-comets, and the extremely low temperatures will
mean that it is much more likely to be recaptured-refrozen, which combination is
probably a very large part of the explanation of the high ice-to-rock
ratios of comets.
Larger proto-comets are somewhat less likely to form
closer to the Sun, for Roche Limit type reasons (as well as for solar wind
reasons, since those winds carry water molecules away from the Sun more
readily than they carry rock particles away). But, wherever they form,
the large bodies are more likely to remain there than the smaller ones in their
swarms because the smaller ones having a better chance to slingshot and achieve Quasi-Escape
Velocity. (Also, the surface area to mass ratio will be smaller for large
bodies, meaning that the ice sublimation to mass ratio will be smaller.)
It should be obvious that circular orbits allow for
planetary accretion better than eccentric orbits if for no other reason
than Roche Limit-type factors, which will tend to counter the mutual
gravitational attractions of the bodies, even well beyond the standard
Roche Limit of the Sun. Eccentric orbits will cause 2 bodies that are
trying to stay together to experience a much wider range of Roche type
forces that tend to cause them to separate, even if their gravitational
attraction is stronger. If we add centrifugal forces due to the angular
velocities of their orbiting each other, well...
The Kuiper belt will probably eventually be found to
“fuzzy”
its way out to the Oort Cloud, instead of having more distinct thresholds like
the known asteroid belts (due to orbital resonances with Jupiter, etc.),
unless there are some awfully big planet-sized failed proto-comets or
other bodies out there marking out belt-like territories
(or other “regions” if they have highly eccentric orbits but ones that
keep them out beyond detection). And even huge planets in the Kuiper Belt would
orbit the Sun so slowly that they may not have
had time to clear belts by orbital resonance, and far less in the Oort
Cloud.
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ASTEROID DANGERS
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ASTEROID DANGERS
By now it should be obvious that the same mechanism
that turns proto-comets into comets can easily turn asteroids that seem
totally innocuous into dangerous Earth-busters. Luckily, chaotic swarms of
asteroids will also tend to eject their smaller bodies, not their larger
ones. But, even smaller asteroids can be distinctly dangerous if they
collide with the Earth. Just in the last week a
“small” asteroid roughly the size of a football field managed to pass
within 120,000 kilometers of Earth (about 1/3 of the distance to the Moon)
at a relative speed of about 10 km/sec. If it had hit us, well... it would
probably
have spoiled someone’s day.
(See:
http://www.cnn.com/2002/TECH/space/06/20/asteroid.miss/index.html)
Such asteroids can be ejected from a swarm and
cross Earth’s orbit with no warning.
Scientists can only track
asteroids they can see. Football field-sized asteroids are still almost
impossible to detect with current technology. Asteroids large enough to be
detected are also so large that it currently will not be easy to determine
if they are a part of a swarm (since their large mass will damp their
local swarm dynamic), or if they have a good chance of acting as
slingshots for asteroids ejected from swarms.
This means that we will need to closely watch more than
just asteroids that cross Earth’s orbit, we will
need to start searching for chaotic swarms of asteroids, even if they seem
to be moving slowly, and try to predict ejection and follow up with better
predictions for any that are ejected. Almost all the asteroids in swarms
will be too small for our current technology to detect, but we can at
least start to detect, analyze and model (probably only statistically, at
first) asteroid swarming and the all but inevitable ejections of smaller
asteroids. The more chaotic the swarm, the more difficult it will be to
predict ejection on a non-statistical basis, since errors in computation
will tend to swamp the results. (In fact, discrepancies previously
attributed to calculation errors will need to be re-evaluated to see if
they are indicators of swarm dynamics.) But once ejected, it should be easier to
predict its orbit, unless it interacts chaotically with other swarms. It
should be relatively easy to track the larger asteroids that are more
likely to act as slingshots for smaller ones.
Asteroid watching just got a
little more interesting.
You may be interested in
looking at the
Near-Earth Object Program at NASA
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