Orientation of the Earth, Sun and Solar System in the Milky Way

In summary, the conversation discussed diagrams that illustrate the motion of the solar system around the Milky Way and how the celestial, ecliptic, and galactic coordinate systems are related to each other. The diagrams showed the orientation of the Earth, Sun, and Solar System in the Milky Way and the angles between different planes and poles. Suggestions were made to improve the accuracy of the diagrams, and it was noted that the Earth's orbit is nearly circular and the barycenter is only 449 km from the center of the Sun.
  • #141
Yeah. Density waves. Where they bunch up together, like sound waves.
 
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  • #142
WHT said:
What this implies is that the fast +sideband of the moon's declination cycle is amplified by the stronger lunar force as the moon nears the Earth during its perigee/apogee cycle. The slower -sideband amplification results in the 8.85 year cycle, which is called the apsidal precession cycle. So again this -sideband cycle has a name but the 4.53 year cycle doesn't.

What is intriguing about this 4.53 year cycle is in how it gets conflated with the half-8.85 year cycle, which being 4.4 years is close to 4.53. There are many references to extreme tidal cycles being dominated either by (1) the 18.6 year nodal declination cycle or (2) the 4.4 year half-perigean cycle. So one is a moon declination effect and the other is a moon distance effect. But that specific 4.4 number never made intuitive sense, in that how can extreme tides occur due to both an apogee and a perigee? I think it gets explained as a precession of the apsides, in that an additional apogee occurs when the moon is on the opposite side of the planet from where the strongest direct apogee is. So the moon "sees" through the earth, or if tidal forces are partially tangential and thus tractive to the surface, an apogee would alternate on each horizon. This also means that the 27.5545 day anomalistic period has a virtual harmonic at 1/2 that cycle. One such recent reference is an article on nuisance flooding (NF) 1

The role of long-period tides in modulating NF frequency​

In addition to secular changes in NF frequencies due to tidal changes, we also detect a ~4.5-year cycle in the time series of additional/reduced NF days (fig. S3), which is close to the half perigee cycle that modulates tides at a period of 4.4 years. The perigean (4.4 years) and nodal (18.6 years) modulations of tides affect high water levels (10). We quantify the impacts of these cycles on NF events by removing them from the tidal prediction and recalculating the number of NF days (assuming that these cycles would not exist); this is only done for the dataset with the observed tides, not the one with historic tides, as we assume that changes in the amplitudes of the 4.4- and 18.6-year cycles were negligible. The oscillations in NF days due to the low-frequency tidal modulations are evident, and their influence increases over time (Fig. 4D). The 4.4-year cycle adds up to 20 NF days across all locations (Fig. 4D) when it peaks under present-day sea level, whereas the 18.6-year cycle causes an additional 30 NF days during its peak compared to average conditions (Fig. 4D)
Like the Bay of Fundy example I referenced above, the consensus theory says 4.4 years, but the measurements are closer to 4.5 years. The behavioral difference between the two is that 4.5 years includes both declination and perigee wheres 4.4 years is just perigee.

I guess what I find odd about this is the disparity in precision and detail for this attribution in contrast to the incredible detail needed for total solar eclipse calculations. Consider the grade school science teacher that promised his class in 1978 that they would meet up again in 2024 to watch the eclipse near their school location in upstate New York -- and they did just that. Incredible precision needed for that.

Another piece of evidence is the plotting of data from the JPL Horizons on-Line Ephemeris System. I didn't create this plot (courtesy of Ian Wilson) but I don't doubt that it is correct, since the JPL tool is used for satellite orbit modeling.

Fig_01a[1].jpg



1 Sida Li et al.,Evolving tides aggravate nuisance flooding along the U.S. coastline.Sci. Adv.7,eabe2412(2021).DOI:10.1126/sciadv.abe2412
 
  • #143
I tried recreating this chart I posted using the online NASA JPL Horizons ephemeris program, but couldn't duplicate the 4.53 year modulation cycle that Ian Wilson had managed to find.

fig_01a-1-jpg.jpg


What I always find is the 4.42 year modulation by multiplying the absolute value of the lunar declination cycle by the R lunar distance. This develops the beat 2/27.3216 - 2/27.5545 = 1/(365.242*4.425)

Declination of the moon with respect to the equator is different than with respect to the obliquity of the earth's rotational axis to the earth's orbit around the sun. IOW that's with respect to the ecliptic plane -- and when the moon crosses that leads to total solar eclipse cycles like we had in the USA the other week

The beat frequency when interacting with the perigee/apogee month would be 1/27.3216+2/(365.242*18.6) - 1/27.5545 = 1/(365.242*4.534)

So that the moon's declination wrt to the equator goes in and out of perfect alignment with the ecliptic plane at cycles related to the 18.6 year lunar nodal precession, which is related to the other extreme flooding cycle of 4.53 years (as mentioned upthread, occurring in Bay of Fundy as well as elsewhere). I have to conclude that the extremes at 18.6 and 4.534 years are more likely lunar ecliptic alignments than wrt declination?

I assume some sort of coordinate transformation is needed to get the NASA JPL Horizons output to align with an ecliptic orientation rather than the geocentric equatorial orientation it does now. I think it requires applying a rotation matrix using the obliquity ϵ such as:

x′=x
y′=y⋅cos(ϵ)−z⋅sin(ϵ)
z′=y⋅sin(ϵ)+z⋅cos(ϵ)
 

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