The philosophy is simply to apply the Scientific Method to Newton’s Universal Law of Gravitation.
Scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on empirical and measurable evidence subject to specific principles of reasoning. The Oxford English Dictionary says that scientific method is: “a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses.”
Newton’s Universal Law of Gravitation
Newton’s law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
(Separately it was shown that large spherically symmetrical masses attract and are attracted as if all their mass were concentrated at their centers.)
This is a general physical law derived from empirical observations by what Newton called induction.
It is a part of classical mechanics and was formulated in Newton’s work Philosophiæ Naturalis Principia Mathematica (“the Principia”), first published on 5 July 1687.
(When Newton’s book was presented in 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him.)
In modern language, the law states the following:
Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them:
F is the force between the masses,
G is the gravitational constant,
m1 is the first mass,
m2 is the second mass, and
r is the distance between the centers of the masses.
The Falsification of Newton’s Universal Law of Gravitation
The falsification is well documented.
Though in 1932, Jan Hendrik Oort was the first to report measurements that the stars in the Solar neighborhood moved faster than expected when a mass distribution based upon the visible matter was assumed, this measurement was later determined to be essentially erroneous.
A few years later, Horace Babcock reported in his PhD thesis measurements of the rotation curve for Andromeda which suggested that the mass-to-luminosity ratio increases radially. He, however, attributed it to either absorption of light within the galaxy or modified dynamics in the outer portions of the spiral and not to any form of missing matter.
In 1959, Louise Volders demonstrated that spiral galaxy M33 does not spin as expected according to Keplerian dynamics.
Following this, in the late 1960s and early 1970s, Vera Rubin, a young astronomer at the Department of Terrestrial Magnetism at the Carnegie Institution of Washington presented findings based on a new sensitive spectrograph that could measure the velocity curve of edge-on spiral galaxies to a greater degree of accuracy than had ever before been achieved. Together with fellow staff-member Kent Ford, Rubin announced at a 1975 meeting of the American Astronomical Society the discovery that most stars in spiral galaxies orbit at roughly the same speed, which implied that their mass densities were uniform well beyond the location with most of the stars (the galactic bulge), a result independently found in 1978. Rubin presented her results in an influential paper in 1980. These results suggest that either Newtonian gravity does not apply universally or that, conservatively, upwards of 50% of the mass of galaxies was contained in the relatively dark galactic halo. Met with skepticism, Rubin insisted that the observations were correct.
Based on Newtonian mechanics and assuming, as was originally thought, that most of the mass of the galaxy had to be in the galactic bulge near the center, matter (such as stars and gas) in the disk portion of a spiral should orbit the center of the galaxy similar to the way in which planets in the solar system orbit the sun, i.e. where the average orbital speed of an object at a specified distance away from the majority of the mass distribution would decrease inversely with the square root of the radius of the orbit.
Observations of the rotation curve of spirals, however, do not bear this out. Rather, the curves do not decrease in the expected inverse square root relationship but are “flat”, i.e. outside of the central bulge the speed is nearly a constant.
Rotation curve of a typical spiral galaxy: predicted (A) and observed (B).
Sadly, the scientific establishment deviated from the Scientific Method by refusing to accept the [repeated] falsification of a Newton’s [sacrosanct] Law of Universal Gravitation. Instead, the scientific establishment preferred to keep its Newtonian belief system intact by accepting the mathematical invention of Dark Matter.
Dark matter came to the attention of astrophysicists due to discrepancies between the mass of large astronomical objects determined from their gravitational effects, and the mass calculated from the “luminous matter” they contain; such as stars, gas and dust. It was first postulated by Jan Oort in 1932 to account for the orbital velocities of stars in the Milky Way and Fritz Zwicky in 1933 to account for evidence of “missing mass” in the orbital velocities of galaxies in clusters. Subsequently, other observations have indicated the presence of dark matter in the universe, including the rotational speeds of galaxies, gravitational lensing of background objects by galaxy clusters such as the Bullet Cluster, and the temperature distribution of hot gas in galaxies and clusters of galaxies.
Returning to the Scientific Method simply requires letting “reality speak for itself”.
The chief characteristic which distinguishes a scientific method of inquiry from other methods of acquiring knowledge is that scientists seek to let reality speak for itself, supporting a theory when a theory’s predictions are confirmed and challenging a theory when its predictions prove false.
The reality of Spiral Galaxies speaks loud and clear.
Image credit: Wikipedia http://en.wikipedia.org/wiki/Spiral_galaxies
The phenomenon that is called Gravity simply reflects vortex pressure.
The dynamics of a Forced [Rotational or Rigid-body] Vortex provides the rationale [and mathematics] for the “Inverse Square Law” of gravitation.
Pressure in a vortex
The fluid motion in a vortex creates a dynamic pressure (in addition to any hydrostatic pressure) that is lowest in the core region, closest to the axis, and increases as one moves away from from it, in accordance with Bernoulli’s Principle. One can say that it is the gradient of this pressure that forces the fluid to curve around the axis.
In a rigid-body vortex flow of a fluid with constant density, the dynamic pressure is proportional to the square of the distance r from the axis. In a constant gravity field, the free surface of the liquid, if present, is a concave paraboloid.
In an irrotational vortex flow with constant fluid density and cylindrical symmetry, the dynamic pressure varies like P∞ − K/r2, where P∞ is the limiting pressure infinitely far from the axis. This formula provides another constraint for the extent of the core, since the pressure cannot be negative. The free surface (if present) dips sharply near the axis line, with depth inversely proportional to r2.
The Oort constants are empirically derived parameters that characterize the shearing motion and vorticity of the Milky Way galaxy.
The Oort constants (discovered by Jan Oort) A and B are empirically derived parameters that characterize the local rotational properties of our galaxy, the Milky Way, in the following manner:
where V_0 and R_0 are the rotational velocity and distance to the Galactic center, respectively, measured at the position of the Sun. As derived below, they depend only on the motions and positions of stars in the solar neighborhood.
As of 1997, the most accurate values of these constants are A = 14.82 ± 0.84 km s−1 kpc−1 and B = -12.37 ± 0.64 km s−1 kpc−1.
From the Oort constants, it is possible to determine the orbital properties of the Sun, such as the orbital velocity and period, and infer local properties of the Galactic disk, such as the mass density and how the rotational velocity changes as a function of radius from the Galactic center.
The Oort constants can greatly enlighten one as to how the Galaxy rotates.
As one can see A and B are both functions of the Sun’s orbital velocity as well as the first derivative of the Sun’s velocity.
As a result,
A describes the shearing motion in the disk surrounding the Sun, while
B describes the angular momentum gradient in the solar neighborhood, also referred to as vorticity.
Click the following link to view all postings related to Gravity: https://malagabay.wordpress.com/category/gravity/
The philosophical and practical problems associated with Newtonian Gravity are simply stunning:
1) Newtonian Gravity has no mechanism and relies upon a magical action at a distance.
2) Newtonian Gravity somehow travels “instantaneously” throughout the universe.
3) Newtonian Gravity travelling at infinite speed implies the associated mass is a source of infinite energy.
4) Newtonian Gravity produces a force that intelligently adjusts itself so that all objects are uniformly accelerated regardless of their mass.
5) Newtonian Gravity fails to provide a viable explanation for the three-body problem presented by the Sun-Moon-Earth at New Moon.
6) Newtonian Gravity fails to provide a viable explanation for the horseshoe orbit of Asteroid 2010 SO16.
7) Newtonian Gravity is falsified unless 84.5% of the total matter in the universe is composed of a hypothetical form of invisible Fairy Dust called Dark Matter.
For more information see: The Clockwork Universe