In researching the works of Galileo, it was discovered that Galileo1 had precluded the establishment of the theory of universal gravitation and that his work went unheeded. He did so with a mathematical analysis and an experimental demonstration that clearly reaffirmed the irreducible qualitative difference between curvilinear and linear motion, thereby precluding the validity of considering linearity as being the fundamental building block of curvilinearity – a necessary premise of the theory of universal gravitation. We had previously discovered that universal gravitation was a theory that never became a fact under the tutelage of Rudolf Steiner2,3,4, etc. and were thereby read) to detect what others had missed. A minimum case is presented; an elaboration will follow.
In order to demonstrate that solar system dynamics are machine dynamics, Newton5 and Borelli6 theorized that the curvilinear (conic section) motions of the solar system were reducible to centric linear motions. This was supposedly justified by their assumption that when a curve becomes infinitely small it becomes a line. This idea was readily acceptable because theoretical scientists of their times had begun to believe that natural motion was straight line motion in contradiction to the ideas held by King Solomon and all great thinkers up to and including Galileo who considered that natural, creative motion is curvilinear. Newton went so far as to define the circle as being a polygon with an infinite number of infinitely small sides.
Having theorized geometry and kinematics so that an arc equals a line Newton extended his theorizing into the realm of dynamics and deduced that since an orbiting object is at all times moving in a straight line, linear inertia is operative in curvilinear motion. As a consequence the orbiting object is tending to fly off on a tangent to the orbit, thus Newton attributed centrifugal motion to the tendency of orbiting objects to fly off on a tangent. He attributed it to a cause that was within the orbiting system. He went on theorizing and deduced that since the moon, for example, does not depart from its orbit, despite its tendency to do so, it must be restrained from doing so by a centripetal opposing balancing force that results in the moon's orbit. This is the force he called universal gravitation. He theorized further that the moon held in its orbit continues to tend to move out on its tangents and thereby provides the momentum to propel itself along in its orbit. Thus Newton theorized the perpetually propelled solar system dynamics as being machine dynamics. Newton confirmed his theories by observing that the stone in a whirling sling, when released to flight, moves out of its orbit on a tangent to the orbit. Thus the theory has stood for 300 years.
However, we have determined through various experiments both machine and manually operated that an orbiting object does not “fly off on a tangent;” it is pulled out radially. The most convenient observation of the phenomenon is the pitched baseball. The pitcher's arm and the orbiting ball in his hand constitutes the dynamic equivalent of the stone and sling. The pitcher executes a semi circular orbit with outstretched arm and hand and releases the ball when it intercepts his line of sight to the target. The ball is seen to be pulled out radially to its target. If the ball were acted upon by linear inertia it would move away from its orbit on a tangent at right angles to the line of sight from pitcher to batter and baseball would have been impossible.
A mechanically driven system used to demonstrate that orbiting objects move out radially was a modified record turn table that was provided with a continuously variable speed ac-dc motor from a sewing machine. A 1/8 inch hole to serve as an indent to hold a 5/8 inch glass marble at a radius of rotation of 4 inches was drilled in the table and a pouch was fashioned to catch the marble as it moves radially outward. The turn table speed is gradually increased and stabilized at the increasing speeds until the critical speed is reached and the marble is pulled out radially. An improvised, but quite adequate experiment can be conducted by placing a 25 cent coin in the middle of the heel of the dominant hand, fully extend the arm and rotate it palm upward in the horizontal plane at constant speed. It will be very obvious that the coin is pulled out radially. Many variations of these experiments are possible and were performed.
It is our experience that one who is enslaved to the concept that orbiting objects fly out tangentially will not be able to extricate himself without conducting at least one of the above or equivalent experiments. We have confirmed the experiment used in college courses in which an orbiting object is released to flight via an electromagnetic coupling and is seen to fly off on a tangent or near tangent. The reason that this is so is that the orbit is deformed into linearity by the lengthening of the radius as the tether momentarily elongates during the disengagement process allowing linear inertia to be expressed.
It is obvious that Galileo was very impatient with the concept of universal gravitation. His response to it was totally at odds with the entire community of theoretical scientists. He said that those who would make the arc into a line, especially mathematicians do not err, they lie because they know the truth that the arc is a line when the radius is of infinite length.1 Thus Galileo, the father of modern science and a professor of mathematics was ignored by the scientific community when he reminded them of the simple fact that curvature of an arc is proportional to the radius and not to the length of the arc. That he did so to no avail, indicates that in accepting theories, we must not abandon reason.
In addition to his demolition of the concept of – the arc is a line – by mathematical analysis, Galileo conducted an experiment that demonstrated that curvilinear dynamics were not translatable to linear dynamics. He allowed two bodies to fall (roll) through the same distance simultaneously; one through an arc of a circle and the other through the much shorter chord of the arc. He found that the object that traveled the arc was the first to reach the common terminal of arc and chord. Thus an object falling in an arc is pulled down with a greater force than one falling in a line. This force which Galileo detected but did not identify is the force of levity. We repeated Galileo's experiment and reproduced his result.
Let us explain Galileo's experiment in which curvilinear and linear dynamics were compared. Levity is a force with a source outside the earth. Since it approaches the earth from every direction, it must have a source in the cosmic, spherical periphery at least as far as the sphere outlined by the orbit of the moon. Like gravity it permeates all matter. It pulls radially outward on every rotating object from the earth as planet to the molecules and submolecular particles in living cells and inanimate matter. It is passive to linearly moving objects. Thus in Galileo's experiment it is passive to the object falling in the chord but pulls radially outward on the object traveling in the arc. Thus the object moving in the arc is being pulled vertically downward by the vertical component of the radially directed force of levity. This force adds to the force of gravity and accounts for the increased acceleration of the object traveling in the curvilinear path.
When it was found that linear inertia is inoperative in curvilinear motion and that centrifugal motion was radially directed, it was obvious that we had discovered a new force – a centrifugal force acting from outside the orbiting system. This force was described by Rudolf Steiner but as is his style of teaching, he left its actual discovery to others. He stated that humankind is obliged to live amidst error and lies and truth and that we gain our individual freedom by working to understand and extricate the truth from the errors and lies. This he called the special moral battle of the 20th century and beyond. “Ye shall know the Truth and the Truth shall set Ye Free.” Of course, such a battle must be fought with the battle cry of “Love Your Enemies.” We close with an aphorism from Rudolf Steiner to whom this work is dedicated: “One must be able to confront the idea in living experience or else fall into bondage to it.”
Steiner Research Center
Reprinted, with permission from the author, from
Frontier Perspectives, Volume 7, Number 1,
Also by Ralph Marinelli:
The Heart is not a Pump: A Refutation of the Pressure Propulsion Premise of Heart Function,
Torsional Ventricular Motion and Rotary Blood Flow, What is the Clinical Significance?
Galileo Versus Newton.