Embedded Files
December 3, 2024, started, January 26, 2025, March 8, 2025, released.
Takanori Senoh
Introduction
From the previous results, it was known the Earth motion is not limited in a 2D plane of the Solar-system, but in a 3D space of the Milky-way galaxy. Also, it became clear the Earth motion equations are degenerated and cannot be solved by the observations done with the fixed East-to-West beam system and fixed North-to-South beam system.
In this time observation, additionally switchable East-to-West beam observation system was used.
2. Earth Motion Estimation
From the observations so far, it became clear that the Earth motion consists of the Earth revolution V, Solar-system revolution S, and Milky-way galaxy motion G. Among these motions, the unknown Galaxy motion G and the Solar-system revolution S=220(km/s) to Autumnal equinox direction with the up-ward angle of 60° are fixed constant motion for us. Only Earth revolution V=30(km/s) direction is a variable in 360° depending on the Earth position in the revolution.
In the following discussion, an absolutely rest coordinate (called as Solar-system coordinate, X-axis: from Autumnal equinox to Vernal equinox direction, Y-axis: from down to up direction, same side as the Earth north pole, Z-axis: from Summer solstice to Winter solstice), which is parallel to the Solar-system plane (ecliptic plane), is used for the Earth motion estimation and observation.
2-1. Earth Motion on Solar-System Coordinate
Following figure shows the Earth motion E=[EX, EY, EZ] is expressed by the summation of the Earth revolution V=[VX, VY, VZ], the Solar-system revolution S=[SX, SY, SZ], and the whole Galaxy motion G=[GX, GY, GZ].
The components of Solar-system revolution S=220(km/s) are expressed as follows. They are fixed values.
The Earth revolution speed is constant V=30(km/s), but its direction is a variable, depends on the observation day. This time observation was done on November 27-29, 2024. Because this date is 24days (=2+22days) earlier than the Winter solstice day (December 21, 2024), its motion direction is
360°×24day/356day = 23.7°
rotated to Z-axis (Winter solstice) direction from the Vernal equinox direction (X-axis). In the following figure, because the angle is shown as 66.3° (= 90° - 23.7°) rotated to X-axis (Vernal equinox) direction from the Z-axis (Winter solstice) direction. its motion is expressed as follows. Because the Earth revolution is in the Solar-system plane, its Y-component is always 0 (VY=0). Because the other components (VX, VZ) vary according to the observation date, it is expressed as a variable V = [Vx, 0, Vz].
Because the Galaxy motion is unknown, it remains as a variable.
Then, the Earth motion E is expressed as follows. This equation works always independently from the observation day.
By transforming this vector of Earth motion E[X, Y, Z] on the Solar-system coordinate to Japan coordinate E''[X, Y, Z] on the observation day, the laser beam spot displacement can be predicted.
2-2. Transformation to Earth Coordinate
Next, this vector E[X, Y, Z] on the Solar-system coordinate is transformed to the Earth coordinate E'[X: from Autumnal equinox to Vernal equinox, Y: from South to North Earth axis, Z: equator direction] as follows.
Because the Earth coordinate is 23.4° left turned Solar-system coordinate, the transformation of Earth motion E[X, Y, Z] to Earth coordinate E'[X', Y', Z'] is expressed as follows.
This Earth motion on Earth coordinate shows it includes the motion component EY' along the Earth axis as follows.
EY' = 0.918GY + 0.397(GZ + VZ) + 174.9 (km/s)
2-3. Transformation to Japan Coordinate
Next, this Earth coordinate is transformed to Japan coordinate on November 28, 2024, which is the observation day. The time of Japan coordinate is set to when Japan faces to Vernal equinox day (X-axis), which is the direction where the Solar-system revolution S effect becomes largest. As stated above, because the Earth position is 23.7° before the Winter solstice point, the time when Japan faces to Vernal equinox direction (X-axis) is later than 6:00 AM when Japan faces to Vernal equinox direction at Winter solstice, by
24h × 23.7° / 360° = 1.58h = 1h35m
1 hour and 35 minutes later (6:00 + 1:35 = 7: 35) than 6:00.
At this time, Japan faces to Vernal equinox direction. Because Japan is 35° up-rotated from the X-axis (Vernal equinox direction), the Japan coordinate at 7:35 is 35° up-turned around Z-axis (equator direction). The coordinate transformation from the Earth coordinate E[X', Y', Z'] to the Japan coordinate at 7:35 E{X'', Y'', Z''] is shown in the following figure.
The coordinate transformation from Earth coordinate E[X', Y', Z'] to Japan coordinate at 7:35 E{X'', Y'', Z''] is expressed as follows.
From these estimated motion components E'', the laser beam spot displacement is obtained. However, because the Earth motion cannot be stopped, the origin of the spot displacement is unknown. To overcome this problem, a subtraction between the Earth motion component E'' on Japan coordinate at 7:35 and ones on Japan coordinate at 19:35, when Japan faces to opposite direction of Autumnal equinox direction. is calculated. This subtraction enables the estimation of Earth motion without knowing the beam spot origin. For this purpose, following figure shows the relation between Japan coordinate at 19:35 E'' and Earth coordinate E'.
Because Japan faces to 35° up rotated from Autumnal equinox direction (-X), seeing this rotation as 55° (=90-35) up rotation from Vernal equinox direction (X-axis) around Z-axis (winter solstice direction), the transformation from Earth coordinate to Japan coordinate at 19:35 is expressed as follows, applying the same rotation.
To align Japan coordinate at 19:35 [X'', Y'', Z''] = [South->North, Ground->up, West->East] to Japan coordinate at 7:35 [X'', Y'', Z''] = [ground->up, South->North, East->West], exchange 1st line and 2nd line, and inverse the sign of 3rd line.
2-4. Conversion to Motion Difference
By subtracting the estimated Earth motion E'' at 7:35, when Japan faces to Vernal equinox direction, from the estimated Earth motion E'' at 19:35, when Japan faces to Autumnal equinox direction, it becomes possible to compare the estimated motion difference and the laser beam spot displacement, without knowing the origin of the laser beam spot. The estimated motion difference ΔE'' becomes as follows.
These equations show the Earth motion observed on Japan coordinate. By comparing these equations to observed beam spot displacements, the unknown Galaxy motion G will be obtained. However, because these equations are degenerated, it cannot be solved by themselves. To solve this problem, add the Earth motion component EY' along the Earth axis from the motion vector on Earth coordinate.
EY' = 0.918GY + 0.397(GZ + VZ) + 174.9 (km/s)
With these 4 equations, observed Earth motion results are estimated as follows.
Ground-up: ΔEx'' = -1.638(GX + VX) +180.2 (km/s)
South-North: ΔEY'' = 1.148(GX + VX) -126.2 (km/s)
East-West: ΔEZ'' = 0.794GY - 1.836(GZ + VZ) + 151.2 (km/s)
Earth axis: EY' = 0.918GY + 0.397(GZ + VZ) + 174.9 (km/s)
Here, input the Earth revolution V on November 28, 2024, actual observation day, to above equations.
VX = 27.5(km/s) and VZ = 12.1 (km/s)
Now, we obtain the following equations.
Ground-up: ΔEx''=-1.638(GX+27.5) +180.2= -1.638GX +135.2(km/s)
South-North: ΔEY''=1.148(GX+27.5) -126.2=1.148GX -94.6(km/s)
East-West: ΔEZ''=0.794GY-1.836(GZ+12.1) +151.2 =0.794GY-1.836GZ+129.0(km/s)
Earth axis: EY'=0.918GY+0.397(GZ+12.1) +174.9 = 0.918GY+0.397GZ +179.7(km/s)
3. Experiment
3-1. Observation System
This time, fixed North-to-South beam observation system, fixed East-to-West beam system, and portable East-West beam system, which changes the beam direction between East-West and West-East, were used to observe the beam spot displacement. Before the observation, each element of the observation systems was further fixed tightly by the screws. Also, the brick weights were increased to 68kg per system to stabilize the systems.
3-2. Observation Results and Conversion to Motion
Following figures show the first 8 pictures taken every 1.5 hours from 12:10 on November 27, 2024 to 10:33 on November 29, 2024. The spot is moving up, down, left, and right according to the time.
Following left graph shows the plot of all spot positions. In this graph, reason that the spot height became high in the 2nd day is because the increased brick weight slightly bent the observation system. Right figure shows the 2day average of the spots taken at the same time in the day. This averaging effectively removed the external noise such as the system deformation and small ground vibrations.
This spot position becomes low when Japan faces to Vernal equinox direction at 7:37, as same as the last time. It becomes high when Japan faces to Autumnal equinox direction at 19:39. This displacement shows the Earth is moving from Autumnal equinox point to Vernal equinox point (X-axis), as same as the last observation.
The height difference from 19:38 to 7:37 is
ΔH＝0.33(mm).
The conversion of this height displacement to Earth motion becomes as follows, considering the Earth motion direction is opposite to the beam spot displacement.
ΔEX'' = -ΔH × light speed / light path length
= -0.33(mm) × 300000(km/s) / 3120(mm)
=-31.7(km/s)
Because this value is equal to the difference of the Earth motion component EX'' on the Japan coordinate, following equation is obtained.
ground-up: ΔEx'' = -1.638GX +135.2 = -31.7(km/s)
From this,
-1.638GX = -135.2 - 31.7 = -166.9 (km/s)
GX = 166.9 / 1.638 = 101.9 (km/s) (1)
In the same way, because the horizontal spot position becomes slightly northward (small X) at 19:39 and slightly southward (large X) at 7:37, the Earth seems moving to South at 19:39 and to North at 7:37. This displacement (19:39 - 7:37) is
ΔX = -0.14(mm)
This displacement is showing the Earth motion component EY'' from North to South direction. Because the component EY'' is from South to North direction, the sign of this displacement must be inverted to -ΔX=0.14(mm). Next, the Earth motion difference ΔEY'' is obtained as follows, by inverting the sign of -ΔX again.
ΔEY'' = ΔX× light speed / light path length
=- 0.14(mm)×300000(km/s)/3120(mm)=-13.5(km/s)
Because this value shows the Earth motion component EY'' on Japan coordinate, next equation is obtained.
South-North: ΔEY'' = 1.148GX -94.6 = -13.5(km/s)
From this,
1.148GX = 94.6 - 13.5 = 81.1
GX = 81.1/1.148 = 70.6 (km/s) (2)
Following figure shows the first 8 pictures of North-to-South beam spot taken at the same time as above on November 27-29. In this figure, the spot position is moving slightly, too.
Following left figure shows the graph of all spots. In this graph too, the spot height moves to high in the 2nd day, caused by the increased brick weight. The right graph shows the 2-day average of the left graph. As seen in it, some small noise still exists in 12:10 sample.
In this graph, a large height displacement exists between 7:37 sample, when Japan faces to Vernal equinox direction, and 19:39 sample, when Japan faces to Autumnal equinox direction. This displacement becomes high at 7:37, when Japan faces to Vernal equinox direction, and low at 19:39, when Japan faces to Autumnal equinox direction. This displacement is just opposite to the East-to-West beam displacement. The reason will become clear later, because the main motions affecting the Earth motion are Solar system revolution and the Galaxy motion, which are almost same speed and far larger than the Earth revolution and their directions are opposite to each other. Hence, the difference of these two large motions will fluctuate around 0.
The height difference from 19:39 to 7:37 is
ΔH = -0.36(mm)
By converting this value to the Earth motion component difference ΔEX'',
ΔEX'' = -ΔH × light speed / light path length
= 0.36(mm) × 300000(km/s) / 3120(mm) = 34.6(km/s)
Consequently, from the North-to-South beam spot observation, following equation is obtained.
Ground-up: ΔEx'' = -1.638GX +135.2 = 34.6 (km/s)
From this,
-1.638GX = -135.2 + 34.6 = -100.6
GX = 100.6/1.683 = 61.4 (km/s) (3)
In the same way, the horizontal displacement ΔX from West to East of North-to-South beam becomes as follows.
ΔX = -0.07(mm)
Next, this value is converted to the Earth motion component EZ'' from East to West. Firstly, to align the ΔX direction to from East to West, its sign is inverted to -ΔX=0.07(mm) and then convert this value to the Earth motion component ΔEZ'' as follows.
ΔEZ'' = -(-ΔX) × light speed / light path length
=-0.07(mm)×300000(km/s)/3120(mm) = -6.7(km/s)
Because this value is the Earth motion component EZ'' of East-West, following equation is obtained.
East-West: ΔEZ'' = 0.794GY - 1.836GZ + 129.0 = -6.7(km/s)
From this,
0.794GY - 1.836GZ = -129.0 -6.7 = -135.7 (km/s) (4)
Next, the Earth motion component EY' along the Earth axis is obtained as follows. Following figure shows the first 8 pictures of portable observation system, placing it from East to West and West to East at the same time, every 1.5 hours on November 27-29, 2024. The spot positions of the same time look different between East-to-West beam and West-to-East beam.
Following figure shows the graph of 16 pairs of beam spot positions (Ew beam and WE beam) from 12:10 on November 27, 2024 to 10:37 on November 28, 2024. Except for 12:10 sample, all sample positions of East-to-West beam are right and low, and the other sample positions of West-to-East beam are left and high. In the graph, "ave" shows the average of all samples from 12:10 on November 27 to 10:33 on November 29, 2024.
The average beam spot height difference ΔH and average horizontal spot position difference ΔX are,
ΔH＝0.1(mm)
ΔX=0.34(mm)
Because the beam spot height will not differ by changing the beam direction between East-to-West and West-to-East, the height displacement will be the measurement error. From the horizontal spot displacement, the Earth motion component along the Earth axis is obtained. When the beam is from East to West, the spot position becomes right (South) and when the beam is from West to East, the spot is left (South). This result shows the Earth is moving from South to North. Because the horizontal displacement ΔX is twice large of true displacement and the South-to-North direction of Japan coordinate always has angle 35° to the Earth axis, the average displacement ΔX of 24 hours becomes 2cos35° of the Earth motion component along the Earth axis EY'. Consequently,
EY' = (ΔX/2) × light speed / light path length / cos35°
= 0.17(mm)×300000(km/s)/1725(mm)/0.819
=36.1(km/s) South-North direction
Because the Earth motion component EY' along the Earth axis is
EY' = 0.918GY + 0.397(GZ + VZ) + 174.9 (km/s)
and the Earth revolution component VZ on November 28, 2024, is
VZ = 12.1(km/s)
Hence,
EY' = 0.918GY + 0.397(GZ + 12.1) + 174.9
= 0.918GY + 0.397GZ + 179.7(km/s)
Consequently, following equation is obtained.
EY'= 0.918GY + 0.397GZ + 179.7 = 36.1(km/s)
From this,
0.918GY + 0.397GZ = -179.7 + 36.1 = -143.6 (5)
3-3. Earth Motion Derivation from Observation
From above equations (1)-(5), the unknown Galaxy motion G=[GX, GY, GZ] and the Earth motion E=[EX, EY, EZ] are obtained.
GX = 101.9 (km/s) (1)
GX = 70.6 (km/s) (2)
GX = 61.4 (km/s) (3)
0.794GY - 1.836GZ = -135.7 (km/s) (4)
0.918GY + 0.397GZ = -143.6 (km/s) (5)
GX is given in 3 ways. Because the reason seems the measurement error of beam spot position, the average is taken as the observed Galaxy motion GX.
GX = (101.9 + 70.6 + 61.4)/3 = 78.0 (km/s) (6)
From 0.397 × (4) and 1.836 × (5),
0.397(0.794GY - 1.836GZ) = 0.397(-135.7)
1.836(0.918GY + 0.397GZ) =1.836( -143.6)
Hence,
0.315GY - 0.729GZ = -53.9
1.685GY + 0.729GZ = -263.6
By adding both sides,
2GY = -317.5
GY = -158.8 (km/s) (7)
By inserting this result to equation (4),
0.794 × (-158.8) - 1.836GZ = -135.7
=-126.1 -1.836GZ = -135.7
GZ = (-135.7 +126.1) / (-1.836) = 5.2 (km/s) (8)
Consequently, the unknown Galaxy motion G is
G = [78.0, -158.8, 5.2] (km/s)
This absolute speed G is
G = √ (78.02+(-158.8)2+5.22) = 177.0(km/s)
This speed is close to Solar system revolution speed S=220(km/s)
The direction Θ is
Θ = tan-1(-158.8/78.0) = -63.8°
down from X axis (Vernal equinox direction) to -Y axis (down).
This angle is almost opposite to the current Solar system revolution direction. Consequently, on the Earth, the Solar system revolution motion S is almost canceled by the Galaxy motion G and a small difference G+S of them and the Earth revolution V become the absolute Earth motion E. This explains why only small displacements are observed.
The Earth motion E is obtained by inserting the Galaxy motion G = [78.0, -158.8, 5.2] (km/s) and Earth revolution V = [27.5, 0, 12.1] to the next equation.、
From this the absolute Earth motion E and its angle φ are,
E = √(EX2+EY2+EZ2) = √((-4.5)2+31.72+17.32) = 36.4(km/s)
φ = tan-1(EY/EZ) = tan-1(31.7/17.3) = 61.4°
Hence, the Earth is moving to Winter solstice direction (Z-axis), 61.4° up, almost Polaris direction (90-23.4=66.6° up from Z-axis). Its speed 36.4(km/s) is close to the Earth revolution speed V=30(km/s).
Although Solar-system is moving at S=220(km/s) in the Milky-way galaxy, because the Galaxy is moving at G=177(km/s) to the almost opposite direction, the absolute Solar-system motion G+S will become small.
From this, the absolute Solar-system motion Sa and its direction θ are,
Sa = √(SX2+SY2+SZ2) = √(-322+31.72+5.22) = 45.3(km/s) ,
θ = tan-1(SY/SX) = tan-1(-31.7/32) = -44.7°
It is going to about 45° up from -X axis (Autumnal equinox direction) with the speed of 45.3(km/s). Following figure shows the absolute motion of the Earth, Solar-system, and Milky-way Galaxy.
4. What Prediction and Observation Tell
Observed Earth motion E=36.4(km/s) and Milky-way Galaxy motion G=177.0(km/s) are too slow to Big-bang explosion speed which must be more than the light speed c=300,000(km/s). Hence, it seems there is no Big-bang vestige, or even if it happened, it is over, and the universe is not expanding now.
As seen in the observation, Earth motion perpendicular to light path affects the light propagation and changes the beam spot position. In the same way, when the Earth motion is parallel to the light path, the light propagation time will change because the motion of the screen changes the light path length. The reason why Michelson couldn't detect this change is simply his experiment had some problems such as parallel flat wave front, caused by the lens and 10m long light path length, generated no visible fringe pattern but a Newton-ring in the telescope might be mistaken as the expected fringe pattern generated by the propagation time difference caused by the Earth motion. Consequently, the Einstein's Relativity Theory, which was created to justify the Michelson's failed experimental result, where the relative clock delay cancels the light propagation time difference, seems losing its fundamental premise, standpoint.
Page updated
Google Sites
Report abuse