Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.
|
|
|
|
exerpt on Newton
Posted:
Apr 21, 2012 4:29 PM
|
|
In any event, our problem did not begin with J.J. Thompson. Some 2000
years after the Ancient Greeks, Tycho Brahe's careful observations on
the behavior of celestial bodies and Kepler's subsequent careful
analysis of those observations, revealed that the symmetry was in time
and space. The predictable solar and celestial time-space symmetry was
subsequently co-opted by Isaac Newton, and used as the carrier for our
tactile sense of attraction to the earth, quantified in terms of our
locally isolated (surface planet) "inertial mass", and declared as the
controlling cause of the order we observe in the celestial, least
action consistent universe. This was heralded as Newton's great
synthesis [7] and is so considered even today.
Isaac Newton defined centripetal force in terms of his second law to
act at a distance by setting his first law planet surface object on an
imaginary circular path of motion at a constant orbital speed. Newton
allowed his moving (planet surface like object) to impact the internal
side of the circle circumference at equidistant points to inscribe a
regular polygon. He dropped a radius to the center of the circle from
each vertex (B) of the polygon to describe any number of equal area
triangles. "...but when the body is arrived at (B), suppose that a
centripetal force acts at once with a great impulse". Taking the
length of each triangle base to the limit (approaching zero) the force
vector [ma, mv/t, or dp/dt] at the vertex (B) is by definition
directed along the radius toward the center of the circle as [mv^2/r].
[**] Again, as with Ptolemy we have a perfect circle and perfect
motion where the law of areas falls out as an artifact of the circle
itself.
Newton generalized the equal areas in equal times artifact of the
perfect circle to any curved path directed radially around a point.
"Every body that moves in any curve line... described by a radius
drawn to a point... and describes about that point areas proportional
to the times is urged by a centripetal force... to that point"
Newton extended the property of his planet surface like orbiting
object to all celestial bodies. "Every body that by a radius drawn to
the center of another body.. and describes about that center areas
proportional to the times, is urged by a force.."
Newton then ties the force directly to the force he feels and calls
gravity... "For if a body by means of its gravity revolves in a circle
concentric to the earth, this gravity is the centripetal force of that
body." In short the force acted on any orbiting object as though that
object is identical to Newton's first law planet surface object where
the force [ma] would then be proportional to the areas and times.
We cannot overly generalize sensory quantities that operate solely
within least action parameters, beyond the specific frame within which
they directly apply. Where we quantify a force we feel, in terms of
our inertial mass, as isolated on the planet surface and applicable to
surface planet inertial mass objects within the planet field, we
cannot generalize that notion of force, to serve as the cause of the
least action consistent behavior of the celestial bodies that
apparently generate the field. We can, as inertial objects, use it to
predict our operational and navigational requirements through the
field.
Current web address: http://groups.google.com/group/thejohnreed
|
|
|
|
