Solar-system is crossing Milky-way Galaxy

November 2, 2024 started, December 8 opened, March 8, 2025, revised.　　　　　　　　　　　　　　　　　　　　　　　　　　　

Takanori Senoh

1. Introduction

According to the ASJ (Astronomical Society Japan) Glossary of Astronomy (https://astro-dic.jp/galactic-plane/), Solar-system is crossing Milky-way Galaxy with the angle of 60°.  The Solar-system motion is not in the Solar-system plane but in the Galaxy plane. The Solar-system is moving at S=220(km/s) along the Milky-way Galaxy rotation, which direction is 60° up from the Autumnal equinox direction in the Ecliptic plane. This structure explains why Milky way looks long from North to South and leaned to left about 30° when facing to South and looking it up at the midnight on summer solstice (around June 20). Also, this structure justifies the observed Earth motion EN along the Earth axis. Because the 2nd milky-way made of the Solar-system galaxy has not been observed, the Solar-system galaxy seems dissolved by the collision to Milky-way Galaxy and the Solar-system alone was left as it was. In one theory, the Solar-system was said bone close to the Milky-way Galaxy center and came to the current position. However, this story doesn't explain why Solar-system plane is not parallel to the Milky-way Galaxy plane. What force rotated the Solar-system plane? It seems difficult to rotate the Solar-system alone without affecting the other starts in the Milky-way galaxy. So, it will be natural to think the Solar-system was bone in the other galaxy and when it collided to the Milky-way galaxy, the Solar-system galaxy was dissolved and reorganized in the Milky-way Galaxy rotation. Fortunately, the Solar-system survived in the original posture. The oval bulge in the center of Milky way galaxy might be the leftover of the Solar system galaxy.

In the following, based on this new knowledge, the Earth motion estimation and the observation are conducted. 

2. Earth Motion Estimation

From the observation so far, the Earth motion cannot been explained only with its orbiting motion V and the Solar-system motion S but requires an unknown motion G which seems the whole Milky-way galaxy motion. In the following discussion, the Earth motion is estimated with the newly known fact, Solar-system is crossing to Milky-way Galaxy. For this discussion, instead of 2D Solar-system plane but a 3D space expanding the Solar-system plane to upward dimension  is used as follows.

2-1. Earth Motion in Solar-System Coordinate

Set absolute rest Solar-system coordinate as follows, 

Solar-system = [X, Y, Z]

X coordinate:  from Autumnal Equinox to Vernal Equinox direction

Y coordinate:  from Solar-system plane to upward direction, Earth north pole side

Z coordinate: from Summer Solstice to Winter Solstice direction

The Solar-system motion direction S is illustrated in the following figure, which is 60° up from -X direction. Its speed is S= 220(km/s).

Hence, the Solar-system motion is expressed as follows.

In the Solar-system coordinates(X,Y,Z), the components of Solar-system motion S are SX=-110(km/s), SY=190.5(km/s), and SZ= 0(km/s). Although the Solar-system is moving with this motion, we can set the Solar system coordinate as the absolute rest coordinate, by taking each axis equal to the current Solar system posture. 

Next, the Earth orbiting motion V is added. Although its speed V=30(km/s) is constant, the direction changes according to the observation time. Because the Earth goes around the Sun 360° in a year = 365days, its direction changes

360°/365days = 0.986°/day.

Because the observation was planned to be done on October 25, 2024, the Earth orbiting motion direction changes from Z (Winter solstice) direction at the Autumnal equinox day (September 22), to X (Vernal equinox) direction by

0.986°/day × (8+25) days = 32.5°

Hence, this motion is expressed as follows.

Add unknown motion G to these motions.

Consequently, the Earth motion is expressed as follows.

By changing this motion in the Solar-system coordinates to Japanese coordinates and changing it to the laser beam spot displacement, the Earth motion is estimated.

2-2. Transformation to Earth Coordinates

The Solar-system coordinates (X, Y, Z) are transformed to Earth coordinates (X', Y', Z') as follows.

Because the Earth coordinates are rotated Solar-system coordinates by 23.4° left turn around the X axis (Vernal equinox direction), the Earth motion E = [X, Y, Z] is expressed as follows as E = [X', Y' Z'] in the Earth coordinates.

From the 2nd row, the Earth axis component (Y') exists in the Earth coordinates.

EY'=0.918GY+0.379GZ+184.9(km/s)

2-3. Transformation to Japanese Coordinates

Next, transform the Earth coordinates to Japanese coordinates, where Japan is facing to the Vernal equinox direction on October 25, 2024. For the simplicity, start from the Earth posture on the Autumnal equinox day. On the day (September 22, 2024), Japan faces to the Vernal equinox direction (to Sun) at  noon, 12:00.

Because the observation day is 8+25=33 days later, the Earth goes around the Sun by

33day×360°/365day=32.5°

to  Winter solstice.

Because of this rotation, the time when Japan faces to Vernal equinox direction becomes earlier than noon 12:00 by

32.5°×24h/360°=2.17h=2h10m.

Consequently, the time becomes 12:00-2:10=9:50.

At this time, because Japan is facing to almost Vernal equinox direction (to X') but 35° up to North pole direction, the Japan coordinates (X''Y''Z'') at 9:50 is the rotated coordinates of the Earth coordinates (X'Y'Z') by 32.5° around the Z' axis (Winter solstice direction), which is the Japanese West direction.

This transformation to Japan coordinates at 9:50 from the Earth coordinates becomes as follows.

From the components of this Earth motion, the beam spot displacement can be estimated. Because the Earth is always moving, the origin of the beam spot position is unknow. To overcome this problem, two beam spot positions, 12 hours different to each other (9:50 and 21:50) are used to estimate the motions. The comparison of difference of estimated motions to observed beam spot position difference will provides the Earth motion without knowing the beam spot origin, 

To do this, the transformation of the Earth coordinates (X'Y'Z') to Japan coordinates (X''Y''Z'') at 21:40 is done as follows.

Because Japan is facing 35° up from the Autumnal equinox (-X) direction, assuming its coordinates (X''Y''Z'') are rotated by 90-35=55° left turn around the Z' axis from the Earth coordinates (X'Y'Z'). This transformation is expressed as follows.

In this coordinates, because the 21:50 components of X'': South-North, Y'': Ground-up, Z'': West-East are different from 9:50 components of X'': Ground-up, Y'': South-North, Z'': East-West, exchange the X'' component and Y'' component to each other and inverse the sign of Z'' component of the 21:50 coordinates as follows.

Subtraction of the components of 9:50 coordinates from 21:50 components becomes as follow.

This estimated difference provides the beam spot position difference. However, because these equations are degenerated, another estimation equation is required to solve them. However, increasing the observation points (times) is useless, because it just rotate the estimation matrix. For an example, the difference between  the estimated motion differences at 15:50 and 3:50 becomes as follows.

Each row of this equation (15:50-3:50) is just a permutation of the other row with some magnification in it or the first equations (21:50-9:50). This fact becomes clear in the following experiment.

3. Experiment

3-1. Observation System

Current North-to-South beam observation system can measure the beam spot displacement in East/West and up/down. However, it cannot measure the North/South displacement. To solve this requirement, another observation system was built and placed in East-to-West direction as follows. The both light path length were aligned to 3.12(m) and the laser ON/OFF switches were fixed by screws and attachment metals, which increased the system stability.

The beam spot displacements of these two observation systems have following feature. As shown in the following figure, the beam direction of North-to-South beam system varies only on a corn surface of vertex angle 2×35°=70°. Consequently, the beam spot displacement is small and the accuracy of the measurement becomes low. On the contrary, the beam direction of East-to-West beam system varies in a 360° plane and its accuracy becomes high. This feature may be one reason why the North-to-South beam spot displacements were large (measured speed = 80-90km/s) but the East-to-West beam spot displacements were small (measured speed = 10-40km/s).

3-2. Observation Result

Following figure shows the first 8 pictures of observed beam spots from 3:52 on October 25, 2024 to 3:40 on October 28 on the East-to-West beam system. The spot position is moving up and down.

Following left figure shows the graphs of all spots positions. The spot height varies up and down in a 24 hours period.  The reason of descending spot positions every day seems the temporal deformation of the observation system. The right graph shows the 3-day average of the same observation time. Actually, one day = 24 hours is the time from a southing to next southing. Because the Earth is orbiting around the Sun, the southing direction increases 

360°/365day=0.986°

every day. Consequently, the time when the Earth faces to the same direction becomes 

0.986°×24h/360° = 0.0658hour = 3.9min

earlier every day. According to this fact, the observation time is hastened 1 minutes every 6 hours. 

The average spot position becomes high at 21:48 and becomes low at 9:50. From this the Earth seems moving from Autumnal equinox direction to Vernal equinox direction. The height difference was 

ΔH21:50-9:50 = 0.65(mm).

The height difference between 15:50 and 3:50 was

ΔH15:50-3:50 = 0.3(mm).

The horizontal position (North-South) becomes slightly northward at 21:50 and becomes slightly southward at 9:50. The difference was 

ΔXNS, 21:50-9:50= -0.15(mm).

This result shows the Earth seems moving to North or South but it is difficult to judge the direction because the origin of spot position is unknown. Also, the horizontal spot position displacement between 15:50 and 3:50 was 

ΔXNS,15:50-3:50 = -0.15(mm).

Following figurer shows the first 8 pictures of beam spots of North-to-South beam, taken at the same time on October 25 to 28.

In these pictures, the spot is moving to left, right, up, and down.

Following left figure shows the graph of all samples for 4 days. The right figure is the average graph of the same time points for 4 days. From this graph, the spot position is slightly eastward 21:50 and also at 9:50. The difference was

ΔXWE, 21:50-9:50 = -0.01(mm).

The East and West difference between 15:50 and 3:50 samples were 

ΔXWE, 15:50-3:50 = -0.1(mm).

The height difference between 21:50 and 9:50 was

ΔH21:50-9:50 = -0.05(mm).

The same difference between 15:50 and 3:50 was

ΔH15:50-3:50 = -0.15(mm).

These differences are far smaller than the sample of East-to-West beam. The reason is not clear but might be the narrow beam direction range. In the following discussion, ΔH=0.65(mm), 0.3(mm) and ΔXNS=-0.15(mm), -0.15(mm) of the larger data of East-to-West beam system are used because they seem more reliable. For the East-West displacement, ΔXWE = -0.01(mm), -0.1(mm) of North-to-South beam are used.

Because the measured   direction of ΔXNS and ΔXWE are opposite to the estimated value of Y axis: South-to-North and Z axis: East-to-West, their signs are inversed.

ΔXSN, 21:50-9:50 = +0.15(mm)

ΔXSN, 15:50-3:50 = +0.15(mm)

ΔXEW, 21:50-9:50 = +0.01(mm)

ΔXEW, 15:50-3:50 = +0.1(mm)

3-3. Displacement Conversion to Motion

Because the Earth motion is opposite to the beam spot displacement, the Earth motion is expressed as follows.

ΔE = -Δ × light speed / light path length

This differences must be equal to the estimated differences as follows.

From these equations, although GX is given in 3 equations,

GX = -(-62.5 -153.8)/1.638 = 132.1(km/s)

GX = (-14.4 +107.8)/1.148 = 81.4(km/s)

GX = (-9.6+187.8)/2 = 89.1(km/s)

GY and GZ are given in the same equation with different magnifiers.

0.794GY - 1.836GZ = -1.0 -104.8= -105.8, GY -2.312GZ =-133.2

0.65GY - 1.504GZ = -28.8 - 85.8= -114.6, GY -2.314GZ =-176.3

-0.456GY + 1.054GZ = -14.4 +60.2= 45.8, -GY +2.311GZ =100.4

Because these 3 equations are almost same, except for the right side, the solution of GY, GZ from these equations are unreliable. Hence, the Galaxy motion components GY, GZ cannot be given from increasing the number of Japanese coordinates. 

Only GX component is given in 3 ways from the above equations. The reliable GX value will be their average.

GX = 132.1 +81.4+ 89.1)/3 = 100.9(km/s)

This component is almost inverse of the Solar-system motion component SX.

SX = -110 (km/s)

4. What Results Tell

The measurement of laser beam spot displacements according to the Earth rotation only is not enough to obtain the full Earth motion. To solve this problem, another equation on a different coordinate other than the Japan coordinate is required. For this purpose, the portable observation system will work because it provides the Earth motion component on the Earth axis.

Go back to Observe Earth Motion