Barycentric Orbits are presented by Wikipedia as the scientifically correct mechanism that controls celestial orbits:
The center of mass plays an important role in astronomy and astrophysics, where it is commonly referred to as the barycenter. The barycenter is the point between two objects where they balance each other; it is the center of mass where two or more celestial bodies orbit each other. When a moon orbits a planet, or a planet orbits a star, both bodies are actually orbiting around a point that lies away from the center of the primary (larger) body.
For example, the Moon does not orbit the exact center of the Earth, but a point on a line between the center of the Earth and the Moon, approximately 1,710 km (1062 miles) below the surface of the Earth, where their respective masses balance. This is the point about which the Earth and Moon orbit as they travel around the Sun.
The Moon makes a complete orbit around the Earth with respect to the fixed stars about once every 27.3 days (its sidereal period). However, since the Earth is moving in its orbit about the Sun at the same time, it takes slightly longer for the Moon to show the same phase to Earth, which is about 29.5 days (its synodic period).
Unlike most satellites of other planets, the Moon orbits nearer the ecliptic plane than to the planet’s equatorial plane. The Moon’s orbit is subtly perturbed by the Sun and Earth in many small, complex and interacting ways. For example, the plane of the Moon’s orbital motion gradually rotates, which affects other aspects of lunar motion. These follow-on effects are mathematically described by Cassini’s laws.
The Wikipedia wording is very interesting to say the least:
the Moon does not orbit the exact center of the Earth, but a point on a line between the center of the Earth and the Moon, approximately 1,710 km (1062 miles) below the surface of the Earth, where their respective masses balance. This is the point about which the Earth and Moon orbit as they travel around the Sun.
Firstly, the point [barycentre] that is approximately 1,710 kilometres below the surface of the Earth is not really a point at all. It continually moves up and down [over a range of 610 kilometres] because at Maximum Perigee the barycentre is 2,039 kilometres below surface while at Maximum Apogee the barycentre is 1,429 kilometres below the surface.
The point [barycentre] is also continually moving longitudinally within the Earth as the Earth performs its daily axial rotation and the Moon performs its regular 360 degree observed orbit around the Earth. The point [barycentre] is additionally continually moving latitudinally due to the 5.14 degree inclination of the Lunar orbit and the Earth 23.44 axial tilt.
Therefore, the point [barycentre] is continually moving through all three dimensions and cannot seriously be considered a pivot point about which both the Earth and the Moon orbit.
Curiously, Wikipedia [in an article about Barycentric Coordinates] indicates that the Earth really only “wobbles” [in an unspecified manner] and does not actually orbit the barycentre!
When the barycenter is located within the more massive body, that body will appear to “wobble” rather than following a discernible orbit.
The non-specific Earth “wobble” seems to be the point where Wikipedia becomes evasive. The “wobble” can be interpreted [as in their animation] as the Earth rotating around an internal pivot point [the barycentre]. However, this interpretation seems unrealistic because it would cause a centrifugal tidal bulge on the side of the Earth most distant from the barycentre. I am not aware of any barycentric tidal bulge.
The barycentric perception also implies that the Earth’s dense core is significantly out of alignment with the Earth’s barycentric pivot point. The pivot point is located 1,429 kilometres below the surface in the Earth’s ductile mantle and it seems very doubtful that the other 11,313 kilometres [worth of mass including the dense core] could pivot around the barycentre without significant deformation [or disintegration] of the spheroid Earth.
Image credit: Wikipedia http://en.wikipedia.org/wiki/Earth_core
Secondly, the concept of an Earth-Moon barycentre is fundamentally flawed because the underlying barycentre formula derives from the familiar terrestrial machine called a lever which consists of a beam [rigid rod] that pivots around a fixed hinge [fulcrum] that is resting upon firm ground [or a solid surface].
Image credit: Wikipedia http://en.wikipedia.org/wiki/File:Palanca-ejemplo.jpg
Applying these principles to the Earth and the Moon highlights several problems:
1) There is no rigid bar or beam in space upon which the planets can rest.
2) There is no hinge or fulcrum resting on solid ground.
3) Gravitation between the Earth and Moon is a horizontal vector [not vertical].
Image credit: Wikipedia http://en.wikipedia.org/wiki/File:Moon_Earth_Comparison.png
Overall, the Earth-Month barycentric orbital concept is fundamentally flawed especially as the Earth does not orbit the barycentre [it just “wobbles” in some way] and the pivot point is not fixed [in wanders about in all three special dimensions].
The [claimed] barycentric “wobble” of the Earth can not be separated from other factors that generate “wobble”. For example, an uneven mass distribution would also cause the Earth to “wobble” during its daily axial rotation. Additionally, it is impossible to perform a control experiment [“with the Moon” and “without the Moon”] that demonstrates the barycentric Earth “wobble”.
Similarly, the [claimed] barycentric “wobble” of the Sun around the solar system barycentre cannot be separated from other factors that generate “wobble”.
Additionally, the [claimed] barycentric “wobble” of the Sun [around the solar system barycentre] does not apparently have any impact on the distance between the Earth and the Sun because any Earth “wobble” is apparently attributed to perturbations by Jupiter and Venus.
The barycentric theory is non-scientific because it does not provide any specific [observable] verifiable predictions.