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Even Further InformationFrom: Steven
Subject: Philosophy
Date/Time 2009-06-14 12:02:16
Remote IP: 74.162.17.113
MessageTo elaborate on Derek's post above:
The simplest explanation of the movement of
planets from grade school is that each planet circles
the sun, i.e. sun at the center, and the planets are
in fixed circles around it due to the sun pulling on the
planets.
THIS IS NOT QUITE TRUE.
To be more accurate, each planet also is pulling on the
sun with it's own gravity. Thus each planet doesn't
orbit the sun, but both the sun and planet together
orbit their common center-of-gravity. Since the sun
is so large compared to the planet, the center-of-gravity
is located very close to the sun's center.
Considering the sun and planet together in this fashion,
constitutes the "two-body" problem. In this description,
the planet's trajectory is that of an ellipse (an oval-shape),
with the sun sitting at one of the two foci of the ellipse
(two focal points of the oval that are shortly away from the
center along the elongated centerline).
This is the standard description that most people understand
about the planets motions, following Kepler's laws.
To make things more complicated, not all planetary ellipse paths
lie in one plane (i.e. they don't look like a pancake with the
sun in the center), each have some slight tilt above or below the
plane.
OF COURSE, this description is NOT QUITE TRUE either.
Given a planet, say Earth, we don't just have the Sun pulling
on the Earth and the Earth pulling on the Sun (two-body description),
but ALL the planets and the sun are all pulling on each other, i.e.
they are all experiencing the gravitational potential of the other
bodies to some degree. Thus our "two-body" problem becomes an
"N-body" problem, where N is the number of different objects involved.
See the attached link for N-body problem.
In this case, each planet and the sun . . . and all the moons . . .
all have a gravitational potential they are throwing into the party.
This problem has not been mathematically solved in generality to
determine the actual "correct" motions; there have only been certain
special cases that have been determined.
Of course, our solar system is not isolated either. The sun "orbits"
the core of our Milky Way Galaxy, as well as having interactions with
other nearby stars. The galaxy itself is moving through
the Local group of galaxies and so on.
With so many different interacting variables involved, the system becomes
chaotic--and we get the same situation as what we get when try to
model global climate change. One of the ways to handle such problems
is to run millions of computer simulations with slightly different
initial conditions that are all within current parameters, and then
do an averaging over all these runs to determine different possible
outcomes, each with an assigned probability of occurrence.
This is what the people in the article did.
Apparently, from this type of analysis, we eventually get planetary
collisions about 1% of the time; and apparently it appears that
in these situations, deviations in movement which lead to
these occurrences tend to be amplified where certain
planets happen to have aligned motions--such
as the Jupiter-Mercury example.
As Derek mentioned, certain large planets can have a significant
effect. Jupiter is 1/13 as massive (resp. Saturn is 1/43 as massive)
as what we would be necessary for the planet to be a brown dwarf . . .
i.e. a gaseous substar that is not massive enough for hydrogen fusion
to have ignited it to be a star
S
http://en.wikipedia.org/wiki/N-body_problem
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