So it is with biblical geocentrism claims.
This is an additional follow-on to Mr. Martin's In Response to Dr Bridgmans “Stupid Geocentrist Tricks“. I've already made some reply in the comments to the original article. Most of Mr. Martin's statements were rants where the same errors were being repeated and expanded upon, but one very fundamental error caught my attention.
Martin: “One of the problems found in the link above is that of the ad hoc nature of the barycenter, which produces conflicts within the Newtonian model and Kepler’s orbital laws.“Any 'conflicts' between the Newtonian and Keplerian model stem from Mr. Martin's own misunderstanding.
The barycenter (AKA center of mass) is a consequence of Newton's laws and is perfectly consistent with them (wikipedia). All objects with mass have a center of mass, and the barycenter can be defined for any combination of masses. A ball has a barycenter, the center of mass of a uniform sphere is at the geometric center of the sphere. A chair has a barycenter. An automobile has a barycenter, as do all the parts within it. A ship at sea has a barycenter. A rock sitting on a hillside has a barycenter.
The barycenter still exists even if the body (or bodies) under consideration is in motion. Imagine the differences in the motions of the moving parts, such as valves, camshafts, pistons, and belts, and their barycenters, in the interior of an automobile engine:
- While the car is at rest
- While the car is moving on the road under its own power
- While the car is idling on a flatbed train car while the train is moving.
The barycenter allows us to analyze a system with many parts by providing a method of analyzing the system a few components at a time.
When combined with a central force law (a force that acts along a line between the two particles under consideration), the barycenter has the additional utility that the motion of a system of particles can be analyzed in two parts - the motion AROUND the center of mass, and the motion OF the center of mass. The center of mass then provides a convienent frame of reference for analyzing the system. Engineers and astronomers use this fact routinely.
Here are derivations, starting from Newtonian classical mechanics, deriving Kepler's laws and the center of mass from Newtonian force and gravitational laws. These derivations illustrate how the motion of the two objects under gravity can be separated into these two separate motions. These are presented for undergraduate physics classes.
- Motion in a Central-Force Field by Alain J. Brizard
- Central Force Motion
- Physics 302: Equations of Mechanics
- Sir Isaac Newton: The Universal Law of Gravitation
Using my N-body code, I've actually run several simulations of how the same Keplerian 2-body system appears in different reference frames, specifically an arbitrary frame, a center-of-mass (barycenter) frame, and a reference frame centered on the more massive object where Kepler's Laws apply (see Doin' Real Science: Simulating Particles). I have a few demonstrations of Mr. Martin's claimed problem configurations (described below) in preparation for future posts.
Mr. Martin elaborates on his nonsense, repeating many of the claims from other posts...
Here’s some simple invalidations of Newton’s and Kepler’s orbital mechanics –All of these statements demonstrate the same conceptual failure, that Mr. Martin regards the barycenter (center of gravity, center of mass) and/or the focus of planetary orbits, as if they must be a FIXED point in space.
1. The orbital mechanics of Newton dictates the earth orbits the sun’s center of mass in an ellipse, yet Newtonian mechanics states the earth also orbits the solar system barycenter. As the solar system barycenter is almost never at the center of mass of the sun, then the earth simply cannot be orbiting the sun in an ellipse. Therefore Newton’s principle of barycentric motion invalidates Kepler’s laws of elliptical motion.
2. Newton’s orbital mechanics dictates the earth orbits the sun’s center of mass in an ellipse. Newton’s orbital mechanics dictates the earth orbits the earth-moon barycenter ever month. Now if the earth is fixed in its elliptical orbit around the sun, then both the earth-moon barycenter and the moon orbit the earth every month, to maintain the earths elliptical orbit shape around the earth every year. Yet if this occurs, Newton’s notion of the barycenter as the center of mass about which the masses orbit as affirmed in the sun-earth motion and then denied in the earth-moon motion. As Newton’s center of mass concludes to a contradiction with more than two bodies in motion, the theory of the center of mass and with it, mass as a cause of gravity, is invalidated.
3. Newton’s orbital mechanics dictates the earth orbits the solar system’s center of mass in an ellipse. Yet, Newton’s orbital mechanics dictates the earth orbits the earth-moon barycenter every month. To properly account for the Earth’s monthly motion around the earth-moon barycenter and the motion of the earth around the solar system barycenter, the earth cannot be orbiting the solar system barycenter in an ellipse as demonstrated above, so the other options available to explain the sun-earth-moon orbits are –
A- The earth-moon barycenter orbits the solar system barycenter in an ellipse. But this option is not in accord with Newton’s notion of a barycenter, where it is a stationary point, relative to the motion of bodies. Furthermore, if the earth-moon barycenter orbits the solar system barycenter, then the earth’s yearly orbit does not conform to Kepler’s orbital laws.
B- The Earth-moon barycentric motion is independent of the earth-solar system barycentric motion. But such movements are never independent in the real, indicating Newton’s notion of the barycenter is not a reflection of the real.
C- The earth does not orbit in the Earth-moon barycentric motion, nor does it move around the solar system barycenter, but is stationary at the barycenter of the universe. This solution gives some respectability to Newton’s notion of the barycenter, but is normally denied by modern science out of blind prejudice.
But that is wrong. I can define a reference frame attached to any object, or point in space, that I choose. All the frames are equivalent. It is a fact that some reference frames are more convenient for calculation than others (which makes the Earth a preferred frame ONLY when we are near the Earth).
The barycenter of the Earth moves around the Earth-Moon barycenter. The barycenter of Earth-Moon system moves around the barycenter of the Solar System (and the Sun). The barycenter of the solar system moves around the barycenter of the Galaxy. There is no conflict in these nested motions, just as there are no conflicts for the moving parts of the engine inside a moving car.
Thanks to Newton's laws, and this can be proven with mathematical rigor, the barycenter provides a point where, in the case of NO EXTERNAL forces, a body can be treated as point moving along the trajectory of the barycenter. It is a useful principle to understand for anyone designing or building mechanical systems as noted in Q4 of Geocentrism: Failing More Basic Physics...
To believe the Geocentrist claim of a problem with barycentric and Keplerian motion is to believe that the past 300 years of the development of mechanics (and all the inventions developed from that knowledge) is incorrect. Perhaps Mr. Martin thinks these developments were some kind of fluke, unrelated to the mathematics that guided the way?
Mr. Martin repeatedly implies that mathematical models have no actual connection to reality, arguing that a condition that exists mathematically does not exist 'in the real'. If the fact that engineers and scientists use these concepts to build real things doesn't make it 'real', then what does make these concepts, and the larger concepts we derive from them, real? Once in this Geocentrist fantasy-land, one's only choice is to believe that all space flight is a hoax. To maintain such a delusion, you have to avoid watching satellites go overhead (Wikipedia, Hobby Space: Satellite Watching).
That the math works might be mysterious to some, but the simple fact is the math does provide accurate predictions of reality (see Mathematics, the Language of Science). The power of that description has made modern technology possible. Mr. Martin and his co-horts have provided no such capability.
The math Works. Geocentrist pseudo-science does not.
Some other interesting resources on the topic:
- Newton's Second Law for an Extended Object
- Wikibooks: Physics with Calculus/Mechanics/Center of Mass
- Here's some visualizations of the motion of objects and their center of mass