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SUMMARY
Here at the beginning of the 21st century,
scientists and educators still teach and still believe that
lighter and heavier bodies — per
Galileo
—
fall at precisely the same rate
(see
falling
rate difference for separate trials), but the truth is far more
fascinating. A trivial and still overlooked consequence of
Newton’s laws is that, because of their asymmetric gravitational
interactions, lighter and heavier bodies do not fall at
precisely the same rate, with only one exception: lighter and heavier
bodies will fall at precisely the same rate —
Newton-theoretically
— when the 3 masses (including e.g. the Earth)
are at the vertices of an equilateral triangle, i.e. when one of the
bodies occupies a
Trojan point (or
Lagrangian point L4 or L5) with respect to the other 2 bodies.
The situation is even simpler for the separate release of the 2 bodies.
Since the heavier body causes e.g. the Earth to accelerate toward it more
quickly, heavier bodies will always fall faster than lighter bodies in
the reference frame of either the Earth or the other body. This is a
potentially
important consequence of Newton’s theory of gravity that was overlooked —
or at least never analyzed and/or commented on — by
Einstein, whose relativity postulates that lighter and heavier test
particles will accelerate at the same rate. By Newton’s theory, they will
only accelerate at the same rate if their acceleration is measured with
respect to the absolute Newtonian space-time framework, and even
then only at the instant of release (t=0) and not after (t>0). This is not the
best fundamental necessity for “relativity”.
Here we will primarily explore the
simultaneous release case since this is the most interesting historically
and astronomically.
Newton should never have overlooked this
mostly non-zero falling rate difference, that it implies the (probable)
existence of Trojan points, and that it is essential to the gravitational
dynamics of these Trojan points and their associated Trojan asteroids
which move in “tadpole”
and “horseshoe” orbits around them. If Sir Isaac — or even his lesser
contemporaries — had only questioned the scientific dogma of their day,
and sacrificed that Sacred Cow as they had Aristotle, he or they could easily have discovered
(well, at least predicted) Trojan points over a century before
Lagrange.
The millennia old “science
wars” that are heating up yet again find a new and crucial twist on an old
wrinkle: science failing, but this time on science’s own terms. As we submit more and more to
science and its control over our daily lives, we must learn to remember that
even “modern” science is not only fundamentally fallible, but that it can
fail in its foundations — even in the simplest things — for hundreds of years without notice.
It is also good to study the overt anger and summary dismissal by leading
scientists when science is seriously questioned, on its own terms; this is
a whole different level of the failure of science on its own terms, but
one that needs to be “fresh-aired” completely, and remembered forever lest
it be repeated.
RECENT HISTORY: The equation(s) showing
the falling rate difference as a function of the mass difference (and
angle of separation) and
linking that to Lagrange’s Trojan points
(Lagrangian points L4 and L5) was first published on the Internet in 1995
(by PAIAS). Since then, it has been expanded with
commentary,
history,
analysis, philosophy and more commentary, and even a look at the future
of Trojan body astronomy, including raising the question of whether
stable ternary star systems are possible.
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