◎　伝播のあり方
　1)　射出説による伝播(射出後の数秒間)
　2)　エーテル上の伝播
◎　光源の見え方
　1)　数光年以遠の天体は天球(エーテル)上に静止している。射出説の影響は小さ過ぎて見出せない。また各種の光行差。
　2)　月は射出説など。
　3)　太陽系内の天体(月は除く)では惑星光行差などによる。また惑星光行差以外の光行差。永年光行差は相殺されている？
◎　観測者から見た光波と光子(光線)の動き
　光速不変は仮説たり得ない。運動学からしても。物体と同じ。ガリレイ変換による。なお、光波(c=fλ)と光子(光線)とは基本的に別。ことに宇宙空間では。

客車が右方へ加速走行(等加速)しています。車内後部の光源(周波数は一定)から光線が発せられ前部には周波数測定機が。加速中の車内に存在する波の数は加速まえよりも多いでしょう。すなわち、加速と非加速とは見かけの相違ではありません。
註: 　サニヤック効果にも通じる現象でしょう。直線上の。

客車の天井から真下に向けて光線が放たれています。加速中の客車では光線は放物線を描き床に達します。非加速、加速の違いは相対的ではありません。

客車の前壁後壁からやや下向きに放たれた光線が車内中央で交差して干渉縞が。干渉縞と非加速、加速(加速度)の変動とは定性的定量的に対応しているでしょう。

相対論はイカサマ。なにからなにまで。MM実験(空気中で行われた)で干渉縞が動かなかった結果は当然。なぜならば空気中での光速はc/n。

Ｗ．パウリ著「相対性理論」1974には「媒質と一緒に運動している観測者からみれば、光は媒質中をすべての方向に対して、常に一定の速さ c/n で伝播すると考えるべきである」と（第１編§６）。 MM 実験(空気中での)の唯一の説明。

光速は光波の周波数と波長の測定によって求められます。宇宙空間で天球上の反対方向(対蹠点)にある二つの星の光の周波数と波長を測定するとしましょう(測定者は慣性系にあるとする)。二つの星の光速の値はまずは異なるでしょう。しかしその合計は 2c (あるいは 2c をやや下回る定数)でしょう。

このことから二つの星の方向における測定者のエーテルに対する運動のベクトルが算出されるでしょう。また、任意の慣性系のエーテル(天球)に対する等速直線運動のベクトルを知ることができるでしょう。
註: 星の光の波長の測定は慎重に。ガラスを透過した後、鏡により反射された後の光では光速は c となってしまい NG。

一様等方の静止エーテルに対する地球の各種の運動で光行差は生じます。エーテル中から地球の大気上層へ入射する光は地球の運動方向へ曲げられます。光行差は現象としては大気上層で完結しています。一度限りの屈折と同じです。

従って書物にある雨粒と雨傘の図解はNGです。エアリーの水を満たした望遠鏡による実験の結果は当然です。なお、星が見かけ上ずれる方向は地球の運動方向とされていますが実際は逆でしょう。大気上層で光の曲がる方向を紙に描けば確かめられるでしょう。

星の光の平面波(波長は一定)が左上45度から到来しています。宇宙船が右の方向へ航行しています。宇宙船の前端と後端(AとB)に当たる波の数は同じです。よってAB間に存在する波の数は不変です。ローレンツ収縮はあり得ないでしょう。

上記の状況設定で星の光の平面波(波長は一定)は真上から到来しているとします。同時刻の相対性もあり得ないでしょう。

点光源が輝いています(周波数は一定)。二台の宇宙船が同速で光源から反対方向へ遠ざかっています(三者は一条の直線上)。二台の宇宙船は同じ周波数の光を受け取っています。時間の遅れはデタラメ。

定義値となっている光速の値は 1973 年に行われたエベンソンらの測定(波長と周波数の)によっています。誤差はプラマイ 1.1 m/s です。ここで測定器を測定部と光源部とに分離しましょう。そのいずれかを誤差以上の等速度で動かせば(光路方向に)異なる測定値が出るでしょう。

光時計が走行中の客車内で作動しています。書物などのイラストでは光は垂直に往復しますが、この光時計は右に（或いは左に）若干傾いています。従って地上の観測者が見る光路のジグザグは歪んでいます(鋸齒状に)。遅れが二通り？　傾きの異なる二台の光時計が作動していたら？

下記は日本学術会議会員有志による反相対論などのサイトのURLです。2019年の秋にウェブで目にして驚かされました。でもいまに至っても誰もが知らぬ顔のよう。この国には物理学にかかわりある人はいない？
https://reriron.kage-tora.com

平面上(摩擦なし)で物体が二本の紐で左へ、一本の紐で右ヘ引かれています。紐の張力はそれぞれ F。すなわち物体は左への加速運動をしています。慣性力は見かけではありません(物体左端でニュートンの運動の第三法則が成り立っています)。

註: 繰り返しですが、ニュートンの運動の第三法則は作用反作用の法則です。力の作用点すべてにおける法則です。説明の多くは二つの物体についての法則としますが愚かなことです。

宇宙空間で星の光の平面波が真上から到来しています。宇宙船が水平方向へ航行しています。宇宙船の光の波に対する速度(c=fλ)と光子(光線)に対する速度とはどう考えられるべきでしょう。

◎　相対運動をしている系の時間
宇宙船が観測者の目前を水平方向へ航行しています。星の光の平面波(波長は一定)が真上から到来しています。宇宙船の速度にかかわらず時間は絶対、遅れはありません。
◎　異なる重力場の時間
東京スカイツリーの高所に鏡があります。地上から送射された光(周波数は一定)が鏡で反射されて地上へ戻っています。これら三点で測定される周波数は同じ(同じでなければ光路上に存在する波の数が増加または減少します。際限なく)、時間は絶対、遅れはありません。

1) 光源から遠い空間では光の伝播はエーテル系に従います。各種の光行差が示しています。
2) 光源に近い空間では光の伝播は射出説に従います。我々の知る多くの事実 (facts) が示しています。
3) 宇宙空間で等速運動をする鏡がシリウスの光の平面波を反射しています。1)、2) それぞれの前段が示されています。

エレベーターの自由落下は落下運動のひとつでしかありません。自由落下には多くの地つづきの落下運動(空気中での落下、複数の重力源など)。説明も地つづきでなければ。また、エレベーターキャビンにあって相対論が砦とする微小領域には多くの地つづきの微小領域。説明も地つづきでなければ。

エレベーターキャビンが自由落下しています。キャビンは n 個の質点(質量は同じ m)から成っています。落下中のある瞬間を考察しましょう。個々の質点に働く慣性力は同じ ma です。例外はありません。対して個々の質点に働く重力のベクトルは同じではありません。質点の位置によって僅かに異なります。
註: エレベーター全体では慣性力と重力の大きさはイコールです。

光速はつねに不変ではあり得ません。いや、光速不変は以下の二つに限られた(そして殊更特筆すべきことのない)事象でしょう。運動学の見地から見ても光は音波のようなもの。ガリレイ変換に従うでしょう。もとより時間、空間のフレームに影響することはないでしょう。
1) 　測定点と光源とが同じ慣性系で静止してます。両者の隔たりは数光秒以内。光速はｃ。
2) 　測定点(エーテルのフレーム上で絶対静止)にエーテル上を伝播する光が到来しています。光源との隔たりは数光秒以遠。光速はおそらくｃと僅かに異なる定数。

静止している光源に対して観測者が運動(変動する)をしています(真空中で)。光源、観測者それぞれに式 c＝fλ が成り立ちます。観測者の式で c は変数、英語では variable です。二つの式は無謬完璧なのです。

星の光はエーテル中を伝播し到来しています。エーテルは空気と同じ媒質でしょう。よって星の光のドップラー効果の式は音のドップラー効果の式(空気中の)と同じでしょう(光の伝播が射出説に從う部分は無視できます)。

エレベーターが自由落下しています。エレベーター内の空間に規則的に配された質点をイメージしましょう。各質点に働く慣性力のベクトルはすべて同じです。局所慣性系はあり得ないでしょう。

二台のエレベーターが水平に離れてゆきます。一台は加速運動、一台は非加速運動です。いずれが加速かは加速度計で知ることができます。加速運動のエレベーターにあっては局所であれ慣性系は存在しません。

ブラッドレーはりゅう座の γ 星（エルタニン）によって年周光行差を見出しました。書物には楕円の図が載っています。しかしながらこの楕円は永年光行差のために歪んでいるはずです（エルタニンに限らず。歪み様は天球上の位置で異なる）。その歪み様によって対エーテルの太陽系の運動が明らかになるはずです。 エーテルの存在に疑いの余地はありません。

光は以下の三通りの伝播をするのでしょう。
1 　媒質の中では c/n。 MM実験(空気中で行なわれた)はナンセンス。
2 　宇宙空間で鏡が星の光を反射しています。入射光の速度はエーテルに対して一定不変です。
3 　宇宙空間で鏡が星の光を反射しています。反射光の速度は鏡に対して一定不変です。

上記いずれの図においても運動する観測者に対する光速はガリレイ変換に従うでしょう。

慣性力のベクトルは一本の矢印で表わせます。重力のベクトルは通常は一本の矢印では表わせません。無限小の領域でも。加えて両者は異なる物理上の実態。

http://lifeafterdeath.vip/lig.html

加速運動はエーテルに対しての絶対運動です。加速運動と慣性力が主役、二者はことの表裏です。重力はこの問題では関与せず、無関係。

光とわれわれとの相対速度に特別なことはありません。音波、水面波などと同じです(光の伝播はエーテル系に、空気の系に、また射出説に従います)。時間、空間の枠組みは絶対です。

重力のベクトル、慣性力のベクトルはいたる所に。合力もまたあまねく。なぜエレベーターの微小領域に大騒ぎ？なにもない重箱の隅。

射出説に従う光は対光源で等速、エーテルに従う光は対エーテルで等速(光行差のあり方からして)でしょう。それだけのことです。もとより、対観測者の光は基本等速ではあり得ません。

斜面(摩擦なし)を質量mの物体が滑落しています。重力mgの作用に見合う反作用のベクトルは二つのベクトルに分解されます。二つのベクトルの一つ、慣性力は見かけではありません。

射出説による光の伝播は光源から光の放たれた後数秒間に限られ、次いで光はエーテルのフレーム上を伝播するのでしょう。よって我々に見える連星の位置における射出説による影響(視線方向でも左右上下方向でも)はごくごく僅かであって知るべくもありません。

エーテルの存在(一様等方の)はニュートンの運動の第一法則、第二法則の前提条件でしょう。このほかの説明はあり得ないでしょう。

宇宙空間で左上から到来する光の平面波が鏡によって右上へ反射されています(真空中で)。一般に両光の光速は異なり入射角と反射角は異なります。光速不変はデタラメでしょう。

光速は不変か否か。実験次第であろう。ある実験では不変、ある実験では不変ではない。

加速運動と非加速運動との別がより根源でしょう。であれば等価原理なんてガラクタ。

一切すべての運動は対光エーテルの運動として示せます。力学的な手段でこの静止系をあぶり出すことはできません。しかし力学上でも空間は一様等方でしょう。

射出説に従う光の伝播は真空の空間を、エーテルに従う伝播はエーテルの空間を。宇宙空間に浮ぶ鏡がそれらを示します。まざまざと。

In air, light is propagated at c/n. So, the result of M-M experiment (done in air) is only natural.

In a book "Theory of Relativity" by Pauli, W 1958, it's written as follows (quoted from English version ; in 1-6). "Rather should one say that for an observer moving with medium, light is propagated as usual with velocity c/n in all directions".

A passenger car is accelerating to the right. Light is emitted from light sources (frequency is constant) settled on rear and front walls in the car, and interference fringes are formed at the center of the car (as letter X). Varying of interference fringes will reflect varying of acceleration. Sagnac effect will also occur on acceleration in a straight line.

A passenger car is moving in a uniform accelerated motion to the right. In the car, a ray of light emitted downward from the roof will be bent to the left (as a parabola). Defference of acceleration and non-acceleration is not relative (but absolute).

A passenger car is moving in an accelerating motion to the right (in a uniform acceleration). From a light source set in rear of the car, a light ray is emitted to an observer at front. The number of waves existing in the car will be higher than before accelerating. That is, difference between acceleration and non-acceleration will not be relative but be absolute.
PS : This phenomenon is similar to Sagnac effect.

◎ How are light waves propagated ?
1) Emission theory (for a few seconds only)
2) On aether (after the above)
◎ How are light sources visible ?
1) For celestial bodies beyond a few light-years, effect of emission theory is too small to be found (e.g. binary stars). So, every celestial body is visible to be stationary on aether (celestial sphere). Also by various aberrations.
2) Moon is by emission theory.
3) Celestial bodies in solar system (excluding moon) are depending on planetary aberrations. Also, depending on other aberrations (but, is secular aberration offset ?).
◎ Motion of light relative to observers
Same as bodies. Follows Galilean transformation. Constancy of speed of light cannot be hypothesized. By the way, light waves (speed = fλ) and photons (rays) are basically different. Especially in outer space.

Plane waves of starlight (wavelength is constant) are coming from upper left 45 degrees. A spacecraft is sailing to the right. Number of waves hitting the front and rear ends (A and B) of the spacecraft is the same. Therefore, number of waves existing between A and B is invariable. Lorentz contraction will be impossible.

Aberrations occur in various motions of the Earth with respect to aether. Light ray that enters the upper atmosphere of the earth is bent in the direction of the earth's motion. Aberration is a phenomenon that is completed in the upper atmosphere. Same as one-time refraction.Therefore, illustration of raindrops and umbrella is NG. The results of Airy's experiment with a telescope filled with water is only natural.

The position of stars are shifted in the direction of motion of the earth, but in reality it will be the opposite. You can check this by drawing it on a paper.

In outer space, plane waves of starlight are coming from just above. A spacecraft is sailing horizontally in front of an observer. Time dilation will be impossible.

Relativity of simultaneity will be impossible also.

In space of vacuum, propagation of light follows emission theory, and in space aether, propagation follows aether. Mirror floating in outer space shows them evidently (with incident light and reflected light).

Speed of light will be constant (relative to the light source) when light follows the emission theory, and spped of light will be constant (against aether) when light follows aether frame (see aberrations). It just is the thing. Of course, the speed of light relative to an observer cannot be constant.

The defined value of speed of light is based on measurements (with wavelength and frequency) done by Evenson et al. in 1973. Error is 1.1 m / s in pramai. Now measuring instrument is separated into measuring part and light source part. When one of them is moved at a constant speed higher than above error (in the straight line), different value will be shown.

In outer space, a mirror is floating and a light ray of a star is reflected. Generally, angle of incident light and reflected light will be different. Because the speed of both lights is different.

Bradley found annual aberration on gamma star : Eltanin. In books, picture of ellipse is shown. However, this ellipse must be warped because of secular aberration (not only Eltanin). With this warp, the motion of solar system relative to aether (to celestial sphere) must be emerged.

The existence of aether (uniform and isotropic) will be a prerequisite for Newton's first and second laws of motion. There can be no other explanation.

In outer space, lightwaves of a star is coming through aether frame. To a moving observer, Doppler effect will be the same as sound in air. The formula of Doppler effect of starlight will be the same as that of sound.
P.S. Ignore the propagation of starlight that follows the emission theory.

Equivalence principle seems to be inconsistent with momentum, the law of inertia, the law of causality (causal relationship), the law of gravity, accelerated motion and so on.

An elevator cabin is moving on the moon's orbit in an orbital motion (the same as the moon). On every small area of the cabin, gravity of the earth is acting. Equivalence principle will be invalid.

Now, we have aether frame, inertial frame, accelerated frame, inertial force and etc in our hand. How to organize these ? Our sense is tested.

Aether frame will be a frame omnipresent, invariable, homogeneous (flat), isotropic and one and only. Aether frame will be an inertial frame (and it will be absolute rest frame).

Every body shows inertial force as a numerical value (including zero). But what is the standard of the motion ? The standard of the motion will be other bodies or space (unknown are excepted). However, response is without delay and exact perfectly. Standard will be space (if choice between the two is forced).

On the moon's surface, there is a passenger car. To the roof, waves of sun-light (plane waves) are falling horizontally. In the roof, there is a small hole. When the passenger car moves to the left, a point of light on the floor will move to the right.　Moon's horizontal motion will have effect (on the point of light) also. It shows motion of the passenger car relative to aether.

A light clock is working in a moving train. Light path of light clock is illustrated vertically (in books). But this light clock leans somewhat to the right. So, to an observer stands on the ground, zigzag of the light path (saw-tooth like) warps. Two kinds of time dilation ? And if two clocks work, and if these lean differs ?

From two point light sources in relative motion, spherical waves of light (light spheres) are sending. What kind of explanation is possible besides emission theory ?

Color of light is said to be due to the difference of wavelength. But it seems to be due to the difference of frequency. Because, when an observer moves relative to light source, color of light will vary. In this situation, wavelength of coming light cannot vary.

The same light rays (laser) are emitted into water and air. Frequency in both medias is the same, but wavelength is different. What is color of color films exposed in both medias ?

A body is pulled with a string to the left on flat plane (without friction). Tension of string is F. That is, the body is accelerated to the left.

At the left end of the body, Newton's third law of motion folds. Action and reaction are equal. Inertial force is not fictitious. But, many explanations start with two bodies. These are invalid.

Existence of aether will be evident in the following phenomena. No explanation needed.

Aberration, Planetary aberration, Light-time correction, Inertial force (Inertial resistance), Difference between accelerated motion and non-accelerated motion, Ways of propagation of light in the accelerated frame.

At the high place of high tower, a mirror is set. Light emitted from the ground (frequency is constant) is reflected by the mirror and returkns to the ground. Frequency measured at these three points are equal (otherwise, number of waves existing in the light pathes increase or decrease endlessly), Time will be absolute (and will be no time dilation).

Whether speed of light is constant or not ? It wiil depend on the experiment. In some experiments, it is constant. In others, it is not.

Below is URL of a site written by volunteer members of the Science Council of Japan (in Japanese). It was published on a day of autumn in 2019. I was surprised.

https://reriron.kage-tora.com

Be!ow is URL of my web-site. Sorry, my English will not be good.

http://lifeafterdeath.vip/eng.html

Aberration on earth is completed in the upper atmosphere. In other words, many of widespread explanations of aberration are wrong. Illustrations of raindrops and umbrellas, etc. But in the moon these will be right.

However, aberration (both on the earth and on the moon) is incompatible with the constancy of speed of light. And the existence of aether is a prerequisite.

Outer space must be filled with uniformly isotroopic aether. Then, how about the effect of the emission theory on the Galileo satellite? Look at the
distance between us and Jupiter, the orbital diameter of satellites, the revolution speed (8.2 to 17.3 km / sec) of satellites, etc. The effect by emission theory for propagations of light (for positions of four satellites) that is limited to a few seconds will never be found. In short, any effect on celestial bodies outside the solar system will never be found also.

In Encyclopaedia of Britannica 1969, there is a passage as follows (in item "Gravitation" ; original text). "If the action of gravitation were not absolutely instantaneous"(omission)"All experiments and observations were, however, consistent with the law, from the short distances employed in laboratory experiments to the long ranges used in interplanetary calculations". It says, action will be instantaneous.

A mass point is accelerating in various ways on a plane (without friction). And, an inertial force corresponding to an accelerated motion is generated.

An elevators cabin is accelerating downward in various ways. And, an inertial force corresponding to an accelerated motion is generated. This includes free fall. Includes any local area of free fall.

The principle of speed measuring instruments using microwave and laser is the same as the principle of the Doppler effect of sound. That is, in the equation, c'= fλ, in inertial frame of a moving vehicle, f of incident wave and reflected wave are the same, and c'and λ are different. In a vacuum, c'of the two waves is different (in both inertial frame of measuring instrument and inertial frame of moving object : according to emission theory).

Intermittent ray of light is coming from outer space. Observer's motion (against light source) has no effect on incoming ray (wavelength, amplitude, waveform, etc.). Observer's motion has no effect at all. In the equation c = f λ, f and c are variable for a moving observer.

Waves of sunlight (plane waves) are coming from directly above to the roof of a passenger car on the surface of moon. There is one small hole in the roof and a spot of light is projected on the floor. The angle of this ray in the passenger car will not be 90 degrees usually. This angle probably will indicate the motion of moon relative to aether.

Perihelion shift of Mercury is about 574 arcsec per century, and main cause is said to be perturbations due to the gravity of other planets (Venus is about 280 arcsec, Jupiter is about 150 arcsec).

There is a question. At the left end and the right end of the orbit of Mercury (a view from above), force that accelerates and decelerates Mercury by perturbation by other planets will be equal (in probability). Especially in the span of the century. Main cause will not be gravity of other planets.

Light will not be bent by gravity. Because...

1) In the center of the Milky Way galaxy (where we live), it's said that a black hole exists. Around it, several stars are revolving. These orbits seems to be natural.
2) How about, before a star is occulted by the moon or Jupiter ?0

On the moon's surface, a passenger car is accelerating to the right. A starlight is passing through a hole A in the front wall, and reaches B in the rear wall of the passenger car. Frequencies of A and B will be the same. Therefore, number of waves existing between A and B will be constant (even at different accelerations). Above is not only for uniform acceleration but also for non-uniform acceleration.

On the moon's surface, a passenger car is accelerating to the right. A light emitted from light source A' in the front wall reaches B in the rear wall. What is frequency of A'B ? How many waves exist between A'B ?

Pertubation due to gravity other planets will be depending only mass and position of these (and speed of gravity will be infinite).

"The rapid motion of the heavenly bodies might conceivably result in some change in either the direction or the amount of their attraction toward each other at each moment ; but such was found not to be the case even with the most rapidly moving bodies of the solar system." Encyclopaedia Britannica 1969, Item "Gravitation"

In outer space, an observer is measuring frequency and wavelength of light (that is speed of light) of two stars staying in opposite directions (antipodal points) on the celestial sphere. The value of two speed of light will be different. But, this different values (of these two speeds of light) can be made equal by observer's motion (at a uniform speed) on the straight line connecting two stars.

Suppose that the observer is the origin and above straight line is X-axis. And, if the same are done for Y-axis and for Z-axis, stationary aether will emerge.

An observer (in an inertial system) is measuring the light of a star in space. The number of stars being measured is reasonable and there is no clumping of stars on the celestial sphere. What is measured is the frequency and wavelength of each star's light, i.e., the speed of light. The results will reveal the existence of a stationary ether.
Note: The existence of a quiescent ether is not in doubt due to the presence of optical line differences.

In outer space, an observer (in an inertial frame) is measuring light of stars. The number of stars being measured is reasonable and there is no clumping of stars on celestial sphere. What is measured is frequency and wavelength of each star’s light, i.e., speed of light. The results will reveal the existence of stationary aether.
Note: Existence of stationary aether is not in doubt due to aberration.　

A planet called Vulcan is revolving the orbit of Mercury. Assume that mass is the same and diameter is half to Mercury. The gravitational force of the Sun and the centrifugal force due to the orbital motion would be Mercury > Vulcan > mass point.

Newcomb's table of perturbation values of the planets below Venus acting on Mercury should be nonsense.

In Wikipedia (in Japanese version : "Apsidal precession　近点移動"), there is a table named "Perihelion shift of planets of solar system". These varies greatly depending on the distance from the sun and the presence or absence of satellites. Newcomb's table and explanation of the theory of relativity would be NG.

Recurring orbits show that this is a two body problem.

Mercury is perihelion shift and binary star is periastron shift. Two shifts are smooth and in one direction. Two each must be considered to be a two body problem.

See again that table (in 近点移動). Values are observed values. And these each will be two body problem.

There is a physical quantity called mass. The force of inertia is F=ma and the force of gravity is F=mg. Assuming that each of above are true, mass is mass. Why inertial mass and gravitational mass ?

Scaled models of Mercury and Vulcan (of my post, April 5) are falling in free fall. Magnitude of acceleration is probably Mercury > Vulcan > mass point. At the beginning of falling, centers of gravity of three models are at the same horizontal level.

A companion star approaches the main star and is passing periastron on the orbit. Actual orbit of companion star is different from orbit of mass point of it. The difference will be due mainly to size of it (mass distribution).

In a close binary, gravity of main star is acting on companion star. Magnitude of gravity is inversely proportional to square of distance. Therefore, if size of companion star is large, gravity that acting is somewhat larger (even if mass is the same).

Note: Here is a horizontal line. From the right, gravity of main star is acting. On the line, we see three masses. Mass of right and left is m/2 and middle is m (interval is the same). Magnitude of gravity acting will be m<m/2+m/2.

A body is falling in free fall. On a plane, an observer is moving in a uniform linear motion. To him, the falling body draws a parabola. Every point of the body is accelerating.

An elevator is falling in free fall. Assume, that there are two sources of gravity and there is a considerable gap berween the two (even when viewed from elevator). How does equivalence principle explain ?

What if Bradley didn't discover aberration ? Now earth is revolving. Suppose, we look at celestial sphere in spring and autumn equinoxes. Light from stars are refracted in upper atmosphere and to ground. In addition, light from stars are slightly bent in the upper atmosphere due to aberration and to ground also. Is this aberration (due to motion of earth in aether ) known now ?

On the celestial sphere, two stars are close by. So, aberration of the two is the same (can be said so). That is, speed and angle of incident lights of two stars (on a point of upper atmospher) are the same.

On the other hand, actual existence of two stars are not the same. Regardless of it, aberration depends solely on motion of earth (excluding celestial bodies of solar system). Only aether can explain.

Motion of earth is various, such as rotation, revolution, uniform linear motion of solar system, and others. And each is known to have aberration. These are reflection of motions relative to uniform isotropic aether. Qualitative and quantitative.

Reviewing the heliocentric theory

Action and reaction (of the third law) are acting at the point of action. This will be the simplest picture of equilibrium of forces. Now, we are begging Newton to comment. He says, reaction of the third law can include inertial forces. He also says, there can be other pictures of equilibrium of forces that include inertial forces.

Not a few books and websites refer to the third law as law of two bodies. Newton's original text is neglected. Third law is a law at the point of action of a force. Now, a piller with mass m is lying on the horizontal plane (without friction). If the piller is continuously pulled to the right, it will be accelerated to the right. At the right end of the piller, magnitude of action-reaction is the same ma. Also, at the other positions (points of action) of the piller, magnitude of action-reaction is the same. This is a single body (even a chain).

On the contraction of the size of galaxies, in Wikipedia, there is not a word. There should be a word about it. Let me post just that.

Is it because gravitational sources (that revolve galaxy) also extend over the disk of galaxy ? Is it because the state of inverse square law of gravity is different from that of solar system ?

In Wikipedia’s “Dispersion (optics)”, there is a video of dispersion. By a prism, white light is spectrally dispersed. The speed of light is different between red and violet light after dispersion (spectroscopy). It is obvious at a glance.

Size of Sun relative to Mercury will be main cause of this problem (however, will be incompatible with Newton's spherical shell theorem).

There are two drawings in which Mercury and gravity source (considered as a point) are drawn. In one drawing, gravity source is Sun and its mass is m. Distance from Mercury is 100. In the other drawing, there are two alternative gravity sources to the sun, Mass is m / 2 each. Distance from Mercury is 99 and 101(aligned on a straight line extending from Mercury). Magnitude of the gravity acting on Mercury is the latter > the former. It can be ignored on Neptune.

In a drawing, a fixed star F homogeneous true sphere and a planet P orbiting nearby are drawn. F acts gravity on P. Is magnitude of gravity on P dpending solely on mass m of F and distance r between FP ? No, the size of F may also have a slight effect. This will be main reason for the perihelion shift (secondary reasons are omitted). Newton's spherical shell theorem may not be perfect.

Square of 99 is 9801. Square of 101 is 10201. See above my post.

It is said that magnitude of Sun's gravity acting on orbiting Mercury depends only Sun's mass m and distance r between the two. But in reality, in addition, there will be an effect of Sun's size. Gravity will be slightly greater. Therefore, Mercury's orbit that has left aphelion will be slightly inward (and r will also be shorter), and then, perihelion will be shifted.

In my previous post (108), I stated that Mercury's orbit is inward (after leaving aphelion). However, in fact, Mercury's orbit was outward. Effect at perihelion (on orbit) will exceed effect at aphelion. Sorry, I must correct.
P.S. Standard orbit is orbit when gravity source is a point.

Increase in gravity due to size of Sun will depend on distance r between Sun and Mercury. This increase in gravity will be larger at perihelion and smaller at aphelion. Is this the reason for perihelion shift of Mercury ? Sorry for my repetitive posts.　

This is a thought experiment on close binary stars (imagine on a plane no friction). Imagine the same homogeneous true sphere with mass m. Main star is three spheres and companion star is two spheres (these are attached as a single unit). These are on a straight line. Gravity exerted and affected by and to each will depend on size of true spheres (of here and there). Forget the spherical shell theorem. Two-body problem is also complicated.

This is a guess. Because of size of Mercury (in its elliptical orbit), centrifugal force will be increased. And, as Sun is near, effect of size will be larger (other planets are more like point).

Mercury is revolving in orbit. Size of Mercury increases centrifugal force acting on revolving Mercury. This will be reason for perihelion shift of Mercury. The angle is about 5.75 arc-sec in a year.

Size of Mercury will also increase gravity of Sun (which acts on Mercury). But it will not affect direction of long axis of elliptical orbit (after a round: that is, it will be unrelated to perihelion problem).

At each of Mercury's mass points, centrifugal force and Sun's gravity are canceled out. Like an elevator in free-falling. In formula of centrifugal force, "r" (distance between the two) is as it is. But, in formula of gravity, it is inversely proportional to square of distance " r". Therefore, Mercury's size will increase effect of centrifugal force. Sorry, only I can is qualitative saying (and these are guess).

This is an idea. In this problem, planets seem to be treated as a point. Now, planet is divided into two hemispheres. One is closer to Sun and the other is far from Sun (back to back). If the planet is far from Sun, centrifugal force and gravity each acting on two hemispheres will be the same(1/2). But, how about Mercury? We must imagine a spherical surface that centers on Sun, and this spherical surface coincides with center of Mercury ? And then, in whole Mercury, centrifugal force will be larger and gravity will be smaller. It is compared to Mercury as a point.

Sorry, please ignore my two posts immediately preceding this one.

Another inference. Half mentioned already at 1 June. Mentioned was problem posing about a single gravitational source and gravitational sources separated into two. Let's call this effect as the 99-101 effect. The 99-101 effect is equal to the two of binary stars. The 99-101 effect is a candidate for explanation of perihelion shift of Mercury. However, it is incompatible with attempt to explain by Sun's spherical surface. I don't know which one is hopeful.

If gravity source is close, size of gravitational source will increase gravity. Then, Newton's sphericl shell theorem must be reviewed.

Centrifugal force is inertial force and cannot be the first cause of perihelion shift. The 99-101 effect mentioned above (tentative naming: contrary to Newton's spherical shell theorem) will be caused by size of Mercury, size of Sun, and distance between Mercury and Sun. On Mercury, these have effect on gravity and it will be the first cause. And then, direction of elliptical orbit may be shifted. At perihelion, this effect will be greatest.

Magnitude of perihelion shift of planets with satellite is far superior. This is probably because gravity of Sun acting on satellite in half orbit close to Sun is far superior.

Shift is smooth, like a hand of clock. Mainly, it will be two-body problem.

On a mass point, two forces of equal magnitude are acting from the left and right. The two forces are tension, gravity, and inertial force. Wnen, left and right are not distinguished, there are five possible combinations (there is no combination of inertia force and inertia force). Is this still called the equivalence principle?

A horizontally long container is filled with fluid. This container is being accelerated to the right. In the container, pressure of the fluid will be high on the left and low on the right (effect of gravity is separated question). Accelerated motion is not fictitious.

But is this worth writing down ?

Emission theory and aether theory were the most influential in 19th century. The two should be reconsidered.

1) Assuming that emission theory is valid only for a few seconds. In a binary star, it will be impossible to find facts of it (from Earth). 2) MM experiment done in vacuum can be explained by emission theory.
1) MM experiment done in air is completely powerless to deny aether. 2) Various aberrations can be explained only by aether.

The same five bodies (mass m) are lined up sideways on a horizontal plane. Five bodies are tied with strings. Assume that horizontal plane is zero friction, and mass of strings is zero. On right most body, force of 5ma is acting and five bodies start a uniform linear accelerating motion toward the right. Tension acting on four strings are, from right to left, 4ma, 3ma, 2ma, and 1ma. For any observer.

In addition to acceleration, there are jerk, snap, etc. And, inertial force must be varied accordingly. Inertial force cannot be fictitious.

There must be absolute rest frame, and there are acceleration, jerk, snap, etc. In wiki (Japanese), in section "Acceleration", there is a table titled "Comparison of magnitude of acceleration". Many examples of acceleration are shown in 18 division by magnitude.

Starting is to accept inertial forces as inertial forces. In a free-fall elevator, inertial force and gravity acting on the entire cabin is equal. As Newton’s third law of motion shows. Magnitudes of inertial force and gravity acting on each mass point (assume fluid) in elevator are as shown by Newton. That’s all.

Eh, the equivalence principle? Will be worthless at all.

A body is suspended by a string from roof of a passengercar. The same two passengercars started at the same jerk at the same time. Tension of strings is increasing, and strings broke at about the same time (for both persons in the car and on on the ground). Inertial force and gravity will not be equivalent.

Assume that sun's light follows emission theory for a few seconds. Matter of those on few seconds will be indistinguishable from earth. That is, sun is being in aether. So, light-time correction. And,light-time correction will be offset by secular aberration.

Assume that moon's light follows emission theory for a few seconds. So, visible position of moon is exactly where it is. Just like sun. But the mechanism will be different.

In outer space, frequency and wavelength of two star lights (coming from the opposite direction) are measured (at the same time). Sum of the speed of two lights will be constant. It is 2c or close to 2c.

Above shows that in outer space, light is propagated relative to aether. And, speed of light relative to an observer is not constant.

A free-falling elevator is assumed to be a small mass point. And gravity f and inertial force f acting on this mass point. As Newton's third law of motion states, vectors are opposite in direction and magnitudes are equal. Similarly, acceleration g and a are opposite in directions and magnitude are equal. Therefore, gravitational mass and inertial mass are the same. Then, all situations can be described simply by "mass". And above all will be in the range that Newton described.

This is what comes into my mind. Three aberrations; daily, annual, and secular seem to form a closed necklace drawn in one stroke. Pearl are 365 (assuming star is visible even during day time).

The star change its position at all times. Trajectory drawn on celestial sphere in one year will not be a ellipse but be an extended necklace with pearls.

Two spacecrafts are sailing from left to right in outer space. It is as far apart as Mars. Speeds are v and 2v. Two spacecraft flash at the same and long time interval. What is interval between the position of flashes on the celestial sphere as seen from the Earth ?

Inertial frame or non-accelerating frame, is a frame that is non-accelerating with respect to aether. So, in free-falling elevator, there is no inertial frame, even locally. Term "local inertial frame" will be nonsense.

In the elevator,equal acceleration due to falling is acting on every mass point. There are no exceptions. Even locally.

There can be resultant force or partial resultant force of inertial force and gravity. But the two are inviolable to each other. Both qualitatively and quantitatively.

Annual aberration is caused by orbital motion of Earth. Orbital motion has a cycle of 365 days. It cannot be caused by relative motion with stars. It is solely caused by motion of Earth. Both qualitatively and quantitatively. From the side of stars, there will be no influence. By proper motion or by other any motion of stars, there will be no influence. Thus, phenomenon of aberration indicates the existence of aether.

For an observer stationary with respect to aether frame, there will be no aberration, at all.

On a plane (no friction), an elevator cabin is accelerated horizontally by tension of a rope. Tension of rope is controlled so that horizontal acceleration is the same as free fall. Not only at infinite small area (local area), but also on whole area of this elevator cabin is inertial frame ?

An elevator cabin is slowly falling due to gravity of an asteroid below. In addition, a rope is extending below the elevator cabin, and the rope is under artificial tension. Let us assume that acceleration g due to gravity (uniform acceleration) is equal to acceleration a due to tension. The equivalence principle should be forgotten.

Gravitational acceleration is a compound word. But is it worth it? About acceleration, what is special ? Nothing, will be.

In an encyclopedia, as an explanation of light-time correction, there is a diagram of Earth overtaking Mars. The two are on each revolution orbit. What is the position of Mars as seen from Earth ? Explanation is given in the encyclopedia.

What if Mars and Earth were moving in parallel lines at the same speed and in the same direction ? According to the explanation of encyclopedia, light-time correction and secular aberration will be canceled as a total, isn't it ?

Aside from that, aether currents can easily be found in various ways.

On the moon's surface, a passenger car is moving to the right. From the point at the center of ceiling, light rays are emitted at 45 degrees downward to the left and right. So, on the floor, there are two points of light. Position of two points are symmetrical for an observer in the car and stands on the moon's surface. This drawing should be understood by the emission theory.

In an encyclopedia, there is a drawing as an explanation of light-time correction. In it, Earth is overtaking Mars (on each orbit). Where is the position of Mars as seen from Earth ? Explanation is given in the encyclopedia.

What if Mars and Earth were moving in parallel lines at the same speed and in the same direction ? According to the encyclopedia, light-time correction and secular aberration seem to be canceled as a total.

Light-time correction will be a phenomenon caused by aether.

Einstein seems to have considered inertial frame to be rest frame. Now, there are two rest frames. The two are in different uniform linear motions. Let's imagine that mass point m in each rest frame starts uniform linear accelerated motion a and b (toward point p on the celestial sphere). Each is accompanied by inertial force ma and mb.

Are two rest frames physical real ? Two, three, and countless rest frames ? No, rest frame is one and only. It is absolute rest frame. Uniform isotropic. It is physical real. Both a and b of above mass points should be understood to be motions relative to absolute rest frame. So is the inertial force. Accelerated motion and absolute rest frame are directly connected.

All uniform linear motion is through. All accelerated motion follow rules and is therefore perceived by us. Absolute rest frame governs these. By the way, absolutely rest frame could be easily measured (as aether drift) by light.　　　　　　　　　　

ネットではアンチ玉川さん圧倒的。動員されて？

Newton's Bucket" is a thought experiment that assumes the existence of absolute rest frame because of the rotational motion accompanied by inertial forces. Let's take the thought experiment one step further. Inertial force must occur by "all motions except uniform linear motion" of a body with respect to absolute rest frame. Without exception. And inertial force is real existence in physics.
Note: Uniform linear motion and other motions can be superposed. And, superposition is very universal.

Aether frame can be highlighted by optical means (by measuring aether drift). And perhaps aether frame will be one and only, homogeneous, isotropic. Also, it will be an inertial frame and will be reality in physics. This will be that absolute rest frame.

It would be easy to reveal the aether frame by optical means. By measuring aether drift. On the other hand, non-accelerated motion, accelerated motion (uniform linear motion and all other motions) of bodies are distinguished. And accelerating bodies show inertial forces. This is probably due to absolute rest frame. Aether frame and absolute rest frame each is probably one and only, homogeneous, isotropic. And perhaps the two are the same frame. One thing two functions. Surprising.

Imagine that an incoming star light is intermittent (on and off: by human work). An observer is observing this ray of light. It will be certain that observer’s motion (in the light ray direction) does not affect anything of coming ray (intermittency, wavelength, amplitude, waveform, etc). So, in the equation c = f λ, it is f and c that vary for the moving observer.

Light of binary stars that emitted from light source follow emission theory for a few seconds. After that, it follows aether frame. Observer A is in valid area of the emission theory and is stationary relative to the binary star frame. Observer B is outside the valid area of the emission theory and is stationary relative to the aether frame. Speed (c'), frequency (f), and wavelength (λ) of light of approaching star for two observers will be as follows. In addition, binary star frame is stationery relative to aether.

For A. c' is high, f is high, λ is const.
For B. c' is const, f is high, λ is low.

Light of constant wavelength is passing through a tube (from left to right). Imagine that this tube is in motion to the left or the right. Frequency at the front end A and rear end B of the tube are the same always. Therefore, number of waves (it is invariant) existing in the tube is constant. So, wavelength does not vary. On the other hand, depending on the motion of the tube, the frequency at A and B varies. It is c and f that vary in the formula c = f λ.

Starlight is coming from outer space. When an observer moves in the direction of the light path, frequency of starlight varies. For speed of light, there is a formula c ＝ f λ. As for varying of frequency, what varies (in the formula above) ? λ seems to be widely accepted ?

There seem to be a lot of physicists who don't care.

Speed of light coming from approaching and receding stars of binary star is the same. This is one of proofs of the existence of aether.
Note) It will not be possible to distinguish part of propagation by the emission theory.

Speed of light coming from approaching and receding stars of binary star is the same. This is one of evidence of the existence of aether.
Note: However, as an evidence, aberration (caused by motion of Earth relative to aether) will be more definite.

◎ Stating on the formula: c = f λ is from the view point of the mirror (stationery or in uniform linear motion).
◎ Light will follow the emission theory for a few seconds after leaving light source, and then follow aether.　　　　

It seems that for incident light from outer space, the wavelength is supposed to vary with the frequency variation due to the motion of an observer. It is λ that varies in the formula c = f λ.

There is a word "wavenumber". It is the number of waves in a unit length (1 cm or 1 m) and is called Kayser. Like 25,000 K (visible red). This wavenumber and wavelength are reciprocals of each other. Therefore, since the wavenumber is an invariant, the wavelength will also be an invariant. That is, the wavelength cannot be varied with the motion of an observer. It is the speed of light that varies.

Inertial force is not fictitious force. See, Newton's third law of motion (law of action and reaction). Also see, formula F = ma in the second law of motion. This is a big problem.

P.S. There are two types of motion: uniform linear motion and all other motions. In the latter, inertial forces appear during the motion, and corresponding to the motion.

In free-falling elevator cabin, and at the specific local area, gravity and inertial force are equal in magnitude. This seems to be the reason for the equivalence principle. However, at many local area, gravity and inertial force are not equal in magnitude. Is it possible that the principle is based on this specific local area ?

When a mass point is accelerated, inertial force appears. Its vector can be at our will. On the other hand, gravity acting on a mass point is unrelated to the accelerated motion of this mass point. And, the vector is not at our will. In the first place, inertial force and gravity are two different things, like water and oil (even if the vector of the two acting on a mass point happen to cancel each other out).

◎ Inertial force is reaction of Newton's law of action-reaction (the third law of motion). It is not a fictitious force.
◎ In the entire elevator cabin in free-falling, gravity and inertial force are action and reaction. And the two are equal. So, it is not surprising that in this cabin, there is a local area where the magnitude of gravity and inertial force are equal. In this local area, magnitude of inertial force is not zero. That is, this local area is not an inertial frame.
◎ There are two points that are not in relative motion. It is impossible to say for one to be an inertial frame and for the other an accelerated frame. There can be no such thing as a local inertial frame.

As for speed of light, constancy of speed of light, and the formula c = f λ seem to be all. But is it so simple ?

A ray of light is propagating through aether. An observer is moving in a uniform linear motion lerative to this ray at various angle. The speed of the observer relative to aether is also varies. And, the observer's motion can be accelerated motion, jerk (on a straight line), or can be curvilinear motion. Besides, there will be areas where the propagation of light follows emission theory.

In short, there will be no reason to treat light specially. It's so simple.

In light propagating in aether, speed of light waves and speed of rays (photons) to an observer will be different (usually). In light propagating according to the emission theory, it will be the same.

For light that is propagated in aether, speed of light waves and ray (photons) relative to an observer will be different (usually). And,for light that is propagated according to emission theory, above will be the same.

There are two mirrors. One is on the ground, one is 22.6m above. These are facing each other. A laser beam is emitted downward from the left end of the upper mirror, forming letter W, and reaches the upper right (beam is in vacuum). Frequency at five points will be the same. There will be no time dilation due to difference of gravity.

Note) A few translations say that, when the distance between two points on the light path remains the same, the frequency of two points are the same (assuming frequency of the light source is constant).

Major aberrations observable on the moon’s surface are four. Two are corresponding to daily, annual aberrations of earth. Two are annual, secular aberrations of earth themselves (in common). These four aberrations show that aberration are caused by the motion of the telescope on the moon’s surface relative to aether. Qualitatively, quantitatively. Motion of telescope is motion relative to aether.

On the moon’s surface, a water-filled telescope will show what Airy imaged (but if light receiving surface is glass, it will follow the refractive index of the glass). Also on the moon’s surface, picture of tilted umbrella and rain drops (raindrops are photons) will be valid (invalid on earth).

In all areas of a free-falling elevator, formula F = ma ≠ 0 (but, = is almost) will consist. So, there will be no inertial frame, even locally.

In a free-falling elevator (assumed to be a rigid body), coexistence of inertial frame and accelerated frame will be impossible, even locally.

1) Rotary motion: Two same disks are rotating. If the rotary speed is the same, the same inertial force will appear. Regardless of the direction of plane of rotation. It must be because of aether (homogeneous and isotropic).
2) Curvilinear motion: Two same spheres move in curvilinear motion. Two curves are the same in size and shape. If two spheres move at the same uniform speed (from the same starting point), the same inertial force will appear. Regardless of the direction of curve. It must be because of aether (homogeneous and isotropic).
3) Accelerated motion on straight lines: Two same spheres move on two straight lines. If motions are the same accelerated motion, the same inertial force will appear. Regardless of the direction of the straight line. It must be because of aether (homogeneous and isotropic).
4) Uniform linear motion: Two same spheres move in uniform linear motion. Inertial forces do not appear. Regardless of the direction of straight line. It must be because of aether (homogeneous and isotropic).

Gravity acts on everything equally. And if there is action, there is reaction. As stated by Newton's third law of motion. Below are some examples.
F = mg (free fall)
F = normal reaction
F = air resistance (falling at terminal speed)
F = air resistance + inertial force (falling before terminal speed)

Is F in F = mg fictitious ? The claim of fictitious will not hold.

A body of mass m is suspended from ceiling by a string. From below, this body is pulled by another string. Tension of this string is 2 mg. So, the tension of upper string is 3 mg. That is, action-reaction of upper string is both 3 mg. Mass of the body is basically irrelevant.

On a plane (no friction), there is a body mass 3m. It is pulled by a string from the left and is accelerated. Tension of the string F is 3ma. Now, suppose there is another body to the right of this body. Two bodies are tied with a string. Also suppose the mass of the left body be 2m and the mass of the right body be m. The force F that pulls the left string is the same. So, tension on the left string will be 3ma and tension on the right string will be ma.

Formula, F = ma, is well-known formula. Now, dividing both sides by m. It gives F/m = a. F on the left side is the force (external force) in "Newton". Both F and m are physical quantities. Both will not be fictitious. Therefore, a and inertial force ma will not be fictitious also. Is there anything wrong with the above ?

In previous lost (170), both sides of formula F = ma are divided by m. Now, alternatively, F = ma are divided by a. Then, formula F/a = m is given. This will also show that a and ma will not be fictitious.

Also, two formulas F = ma and F = mg may not be compatible with the assertion of gravitational mass and inertial mass (“Both are completely different phenomena” on Wikipedia “mass” in Japanese. Also, not be compatible with existence of two idioms).

Let's review formulas, F = ma and F = mg.
Dividing both sides by m gives a = F/m and g = F/m. Therefore, a = g.

Thus, mass acting as gravity and mass acting as inertial force are (assumed to be) the same. Also, quantitatively as m. This is also guaranteed by Newton's third law of motion.

Not a few explanations of law of action and reaction begins with two bodies. Misleading explanation. This law is the law at point of action of force. And, it is the law that action and reaction are equal, and direction of force is opposite.

A body is pulled by a string. At every point on the string, tension is the same. That is, action and reaction have the same magnitude and opposite directions. This is the same when the body is uniformly accelerated by the string. Both forces are true forces. It is Impossible that one (inertial resistance) is fictitious.

A large number of particles are floating in vacuum space. To our eyes, these are visible as a cube or an elevator cabin. Suddenly, a gravity source appears below and the elevator-like thing starts free-falling. As time passes, the elevator-like thing gradually changes its shape.

The above can be explained by Newtonian mechanics.

A homogenous disk is rotating vertically. Gravity from below. Therefore, inertial force (centrifugal force) and gravity act on each mass point of the disk. When the rotation speed of the disk exceeds a certain magnitude, a mass point appears where vector of inertial force and gravity are canceled (as total). But it is only natural.It seems to not be note worthy.

Mass point where vector of inertial force and gravity are canceled (as total) also appears in free-falling elevator. Physically, it would be the same phenomenon as a rotating disk.

On a plane (no friction), a body is pulled by a string and is moving in a uniform linear acceleration. Magnitude of inertial force and a force originating from the tension of the string (acting on each mass point of the body) are equal. This body is not inertial frame.

However, in free-falling elevator, there is local area where magnitude of gravity and inertial force are equal. And, it is considered to be local inertial frame.

A body is in free fall. Assume that this body is a homogeneous rectangular body. Inertial force is acting on every local area. Therefore, there can be no local inertial frame for this body.

Inertial force and gravity are canceled each other partially and sometimes totally. But it is action not existence, that is canceled.

For gravity and inertial force in free-falling elevator, acceptable explanation will be Newton's law of action and reaction. Equivalence principle should be forgotten.

The same five bodies (mass m) are lined up sideways on a horizontal plane. Five bodies are tied with four strings. Assume that horizontal plane is zero friction, and mass of strings is zero. On right most body, force of 5ma is acting to the right and five bodies start a uniform linear accelerating motion toward the right. Tension acting on four strings are, from right to left, 4ma, 3ma, 2ma, and 1ma.

Tension in the string above will be the same to an observer of any frame of motion. Inertial force (accelerated motion) is not fictitious.

◎　Michelson-Morley Experiment

It (done in air) is nonsense. In air, light is propagated at c/n. So, the result of M-M experiment (done in air) is only natural.

In a book “Theory of Relativity” by Pauli, W 1958, it’s written as follows (quoted from English version ; in 1-6). “Rather should one say that for an observer moving with medium, light is propagated as usual with velocity c/n in all directions”.

◎　Speed of Light

The defined value of speed of light is based on measurements (with wavelength and frequency) done by Evenson et al. in 1973. Error is 1.1 m / s in pramai. Now measuring instrument is separated into a measuring part and a light source part. When one of them is moved at a constant speed higher than above error (in the direction of light path), different value will be obtained.

◎　Propagation of Light
　　　　　　　　　　　　
In outer space, a starlight is reflected by a mirror. There is a formula c = f λ. Now, the mirror is stationary. In comparing of incident light and reflected light, f is the same. And usually, c & λ are different. 　　　　　　　　　　　　　　　　　　
Now, the mirror moves in the direction of the light path of incident light. In the formula on incident light, λ is constant. And c & f will be variables. And in the formula on reflected light, c is constant. And f & λ will be variables.

1. In outer space, a star light is reflected by a mirror. Speed of incident light is constant relative to aether.
2. In outer space, a star light is reflected by a mirror. Speed of reflected light is constant relative to the mirror (the emission theory).

In two pictures sbove each, speed of light to a moving observer follows Galilean transformation.

◎　Aether

All kinds of aberration are caused by motion of Earth. Qualitatively, quantitatively. For example, cycle of annual aberration is 365 days. It is reflection of motion of Earth. On the other hand, any motion of star’s side has no influence. Only position on the celestial sphere is valid. These facts will be explainable only by aether.

◎　Lorentz Contraction

Plane waves of starlight (wavelength is constant) is arriving from upper left 45 degrees. Two spacecrafts are sailing in the right and left directions. Number of waves hitting the front and rear ends (A and B) of each spacecraft is the same. Therefore, number of waves existing between A and B is invariant (for both spacecrafts, regardless of lateral motion). Lorentz contractions will be impossible.

Relativity of simultaneity will be impossible also.

◎　Aberration

Aberration is caused by various motions of Earth relative to stationary aether (uniform isotropic). Light that enters upper air of Earth (from aether) is bent in the direction of motion of Earth. As a phenomenon, aberration is completed in the upper air. The same as refraction.

Therefore, illustration of raindrops and an umbrella is NG. Result of Airy’s experiment with a water-filled telescope is only natural. It is said that apparent displacement of stars is displaced in the direction of Earth’s motion, but in fact, it will be the opposite. You can check this by drawing light bending (in upper air) on a paper.

◎　Inertial Force is not Fictitious.

The same five bodies (mass m) are lined up sideways on a horizontal plane. Five bodies are tied with four strings. Assume that horizontal plane is zero friction, and mass of strings is zero. On right most body, force of 5ma is acting to the right and five bodies start a uniform linear accelerating motion toward the right. Tension acting on four strings are, from right to left, 4ma, 3ma, 2ma, and 1ma.

Tension in the string above will be the same to an observer of any frame of motion. Inertial force (accelerated motion) is not fictitious.

◎　Equivalence Principle

For gravity and inertial force in free-falling elevator, acceptable explanation will be Newton’s law of action and reaction. Equivalence principle should be forgotten.

◎ Light Clock

A light clock is working in a moving passenger car. In books or in other illustrations, light travels back and forth vertically, but this light clock slightly leans to the right or left. So, the zigzag (sawtooth) of light path seen by an observer on the ground warps. Two kinds of dilations ? And how about if two light clocks with different lean work ?

◎ Time Dilation

In outer space, a spaceship is sailing horizontally. Plane wave of light (wavelength is constant) of the first-magnitude star Sirius is coming from directly above. Phenomenon of time dilation can not be valid.

◎ Relativity of Simultaneity

On the Moon's surface, a passenger car is moving to the right. From the center of the ceiling of the car, light rays are emitted to directly below and diagonally downward to left and right at 45 degrees. And three points of light are reflected on the floor. Three points are symmetrical to observer on the Moon's surface also. Relativity of simultaneity will be invalid.

◎　Perihelion　Shift of Mercury

The perihelion shift moves in one direction and its speed seems to be almost constant. Like the hands of a clock. Main cause of the shift seems not to be gravity of other planets. Main cause will be two-body problem of Mercury and Sun. Not as points, but as spheres.

◎ Speed of Light
For speed of light, the constant speed, and the formula c = fλ seem to be all. But is it really that simple?

A beam of light is propagating through aether. An observer is in uniform linear motion at various angles relative to this beam. The speed of the observer relative to aether also varies. Observer's motion can be accelerated motion, jerk motion, or curvilinear motion. Also, speed of light wave and light ray (photon) will generally be different.

No, to light, special treatment must not be given. Then, all must be simple.

◎ Aether
In outer space, frequency and wavelength of two stars light are being measured. Two stars are in opposite directions (antipodal point) on the celestial sphere, and the measurements are done simultaneously. The sum of the two values will be 2c or a constant close to 2c.

The above will show the motion of the observer relative to aether.

◎ Accelerated Motion and Aether
Accelerated motion will be absolute motion against aether. Accelerated motion and inertial force are two sides of the same coin. Gravity is not involved and is irrelevant.

That is, we are surrounded by aether.

◎ Acceleration and Non-Acceleration
The passenger car is accelerating uniformly to the right. In this car, a ray of light (frequency is constant) is emitted from the rear to the front. The number of light waves existing inside the car will be higher than when the car is stationary. That is, there will be apparent difference between non-acceleration and acceleration.

Ray of light is emitted from the ceiling of the passenger car downward. If the passenger car is accelerating, the ray draw a parabola. That is, there will be apparent difference between non-acceleration and acceleration.

◎ Local Inertial Frame
An elevator-like but homogeneous rectangular body is in free falling. Suppose this body consists of many local area of mass m. So, inertial force acting on each local area is mg. That is, local inertial frame will be impossible.

Gravity and inertial force are cancelled out partially or sometimes totally. But, it is action that cancelled out, not existence.

◎　Doppler Effect of Light

Frequency of incoming light varies with the motion of an observer. In the formula c = fλ, it is clear that the speed of light (for the observer) cannot be constant.

Effect of Mercury's size on perihelion shift will be centrifugal force < gravity. Also, effect of Sun's size will be greater than when it is a point. Both effects will be acceleration of Mercury's orbital motion, especially near perihelion.

Shift of perihelion is in the direction of Mercury's own revolution, and speed of shift is constant. Like hands of clock. Main reason will be two-body problem.

How is Sun's gravity acting on Mercury calculated ? Will be by Newton's spherical shell theorem. But is this theorem right ? Has anyone raised any objection ?

Gravity of Sun acting on Mercury depends on square of the distance between them. On the other hand, centrifugal force due to orbital motion of Mercury depends on distance between them. Therefore, the size of Mercury and Sun will also play a role. But it is contrary to the spherical shell theorem.

If the above is right, because the two bodies are close, size of Mercury and Sun will increase the magnitude of gravity. And orbital motion of Mercury will be accelerated.

A homogeneous sphere, the source of gravity, and a line of action of gravity extending horizontally through the center of the sphere are drawn. At a fixed point, on left side of the line of action, not far apart, magnitude of gravity is calculated. Now, let the gravity source be the left and right hemispheres, and the gravity originating from the two hemispheres is calculated. Magnitude of gravity depends on the square of the distance. Therefore, sum of the gravity originating from the two hemispheres will differ from the magnitude calculated by the spherical shell theorem.

The above is on the Sun's gravity only.

Here is a figure of Mercury. Mercury is drawn as a circle. Plus, the center of it and an arc are drawn. This arc passes through the center and is extending symmetrically upward and downward. This arc is part of circle centered at the center of Sun that is located on the right of this figure. Therefore, the size of Mercury divided by the arc is left > right. Thus, actual magnitude of centrifugal force of Mercury due to its orbital motion will exceed the magnitude calculated as a point. Probably, this will be the reason for perihelion shift of Mercury.

Note: For planets with satellites, perihelion shif seems to be larger. This will be due to centrifugal force.
Note) There must be more unknowns in perihelion shift.

There are two figures A and B that draw Sun and Mercury. A shows Mercury on the line of action of gravity of Sun extending from the left. Distance between two stars is 50. In B, Mercury is divided into two hemispheres, left and right. The distance between center of sphere (of A) and the center of gravity of two hemispheres each is 1. In B, denominators of formula for magnitude of gravity are 49 and 51. And squared are 2401 and 2601.

Magnitude of gravity is 2500 in A and 2501 in B. Size of sphere seems to be related to magnitude of gravity. Spherical shell theorem will not be valid. Main reason for perihelion shift of Mercury will be its size.

Note) In this post, only gravity of Sun is under consideration.

Allow me to add below to my March 14 post.

Actual magnitude of centrifugal force due to Mercury's orbital motion will exceed magnitude calculated as a point. This will cause Mercury to rotate long and short axes of its elliptical orbit.
Note: Closeness of Mercury to Sun and size (mass distribution) of Mercury also play a role.

Story will be started from aphelion. And returns to aphelion. It is repeated. Beginning is addition of centrifugal force(because of the size of Mercury), which causes orbit to be outside the original orbit. Then, very slight rotation of long axis and short axis, i.e., the elliptical orbit, will continue.

Is gravity involved ? Is spherical shell theorem right ? Let me hold off on this post.

I said earlier that this story should start from aphelion, not perihelion. Yes, size of Mercury will increase centrifugal force and will rotate the orbit of Mercury in the direction of revolution. It will also increase size of orbit and increase momentum of Mercury.

Moon is said to be receding away from Earth. Although it is on order of a few centimeters per year. There are not a few sites on web. Many of them say that reason is slowing down of rotation of Earth. And total angular momentum of Earth and Moon must be conserved. But is relationship between Earth and Moon still the same today ? I guess what I said in the first half of this post applies to Moon as well.

Size (mass distribution) of Mercury will slightly increase magnitude of actual centrifugal force (due to its orbital motion). As a result, direction of ellipse of Mercury will be shifted in the direction of Mercury's orbital motion around Sun (that is axis). In other words, long and short axes of ellipse will continue to shift its direction like hands of clock. This phenomenon, also known as apsidal precession is a phenomenon that exists widely (not only on Mercury).

This problem could be discribed as a problem in which Mercury's elliptical orbit rotates slightly in the direction of Mercury's orbital motion. Like hands of a clock. Reason for rotation may be due to the fact that Mercury is not a point but a sphere that has a size (mass distribution). But beyond that, it is a labyrinth for me.

Is the reason for rotation lies in perihelion or in aphelion ? Or is it in neither ? And, if the reason lies in aphelion, is it due to addition of centrifugal force ? Or is it due to weakening of gravitational pull of Sun ?

As mentioned before, the size of Mercury as a sphere would be core to this problem. Allow me to reconfirm.

Divide Mercury into two the same spheres (two are contacted). Two centers of sphere lie on the line of action of Sun's gravity. Distance between Sun and centers of two spheres are 49 and 51. Magnitude of Sun's gravity is F=GM/r^2. Therefore, the denominators of magnitude of Sun's gravity acting on the two spheres are 2401 and 2601.

In laboratory experiment, inertial force is something that we can control. Even in laboratory of thought experiment, we can control falling of an elevator also. On the other hand, gravity will be beyond our reach. In other words, inertial force and gravity will be different things.

Inertial force and gravity will be different even outside laboratory (not concerned it is in our reach or not).

In laboratory experiment, inertial force is something that we can control. In laboratory where thought experiments are done, we can control falling of an elevator. On the other hand, it can be said that gravity is beyond our reach. In other words, inertial force and gravity will be different things.

Even outside laboratory (whether within our reach or not), inertial force and gravity will be different thing.

Two laps of elliptical orbit of Mercury is drawn. Ellipse B after perihelion must be drawn outside previous ellipse A. However, in many figures such as web, it is inside. Ellipse is rotating around Sun. Many figures must be wrong.

In other words, state of ellipse nearby perihelion must be the same as that of nearby aphelion (that same qualitatively). Nearby these two points, Mercury will be affected by excessive acceleration due to its size. Acceleration will be caused by centrifugal force or gravity or by both.

In many figures, Mercury's new orbit is outside the previous orbit for some extent after aphelion, and inside for some extent after perihelion. Unacceptable.

Long axis of Mercury's orbit is slowly rotating. That is, Mercury will follow an orbit outside its previous orbit for some extent after passing either perihelion or aphelion. This is not so for perihelion in many figures.

In laboratory experiment, inertial force is something that we can control. In a laboratory called thought experiment, we can control falling of an elevator cabin also. On the other hand, it seems that gravity is beyond our reach. In other words, inertial force and gravity will be different things.

Even outside laboratory (whether within our reach or not), inertial force and gravity may be different thing.

Two bodies of the same mass m tied by a fairly long string are in free fall to Jupiter. Two bodeies are back and forth, and increasing tension of the string is informed to Earth. Inertial force and gravity are different things.

Comet Shoemaker-Levy, which fell to Jupiter in 1994. It was broken into at least 21 pieces in a line, before it fell.

Annual aberration of Mars is based on its revolution period of 1.881 years and average orbital speed of 28.07 km/sec. That is, aberration is mainly caused by motion of observer relative to the aether. Qualitatively and quantitatively. Needless to explain.

Other aberrations of Mars are also.

In outer space, three pinhole cameras are pointed in X, Y and Z directions (these are in uniform linear motion, the same as Sun). Cameras are pretty large. In the camera, on the inner wall, on the opposite side of the pinhole, disks rotate once and receiving position of star lights are recorded.

Recorded position of star lights on three disks will not be true circle. These may indicate motion of the pinhole cameras relative to aether.

Otherday's my post was misunderstanding. Sorry.

In outer space, three pinhole cameras are moving at different constant speed in X direction. Size of celestial sphere reflected on the receiving surface in the camera will be slightly different. This will be due to the different speed of the cameras relative to aether.

My recent postst 204 and 205 seem to be invalid. Sorry.

In outer space, a starlight is coming from the right. This ray enters the pinhole of a pinhole camera and is reflected upward by a mirror set at 45 degrees upwards in the camera.

As I wrote before, when the camera moves to the right or left (at a uniform speed), the position where reflected light hits the inner wall of upper part of the camera will move (angle of lincident light and rleflected light relative to the mirror is generally different). Incident light is propagated in aether, and reflected light follows the emission theory.

There is optical path of triangle ∆ABC with top A of tall tower and mirror BC placed on the ground (as vertices). Laser light emitted from light source set at A (frequency is constant) is reflected by BC and returns to A. Frequencies of laser light at ABC will be the same. There will be no time dilation due to gravity.

Plane waves of Sunlight are arriving horizontally from above to two passenger cars on Moon's surface. There is a small pinhole at the center of ceiling of two passenger cars, and on the floor, there is a spot of light that passed through pinhole.

The two passenger cars are moving on the Moon's surface at different speeds (in x direction). For an observer inside the passenger car, position of light spot on the floor will be different. This difference in position will be the same for an observer stands on the Moon's surface.

Compare propagation of light with propagation of sound waves. Neither time nor space will require any transformation in our understanding of propagation of sound waves (in air or other medium). In this respect, there will be no difference between propagation of light and propagation of sound waves (if we accept aether as medium for light propagation).

First formula, v=fλ: It is speed of light relative to aether. Area is where light follows aether frame. That is, more than a few light seconds away from light source.
Second formula, c=fλ; It is speed of light relative to light source. Area is where light follows emission theory. That is, within a few light seconds from light source.

Note) First formula is the same as formula for the speed of sound in air (depending on f and λ).
Note) In outer space, a starlight is passing through a tube. In the center of the tube, a plate of glass is placed. The starlight in front of the glass follows aether frame, and in the back of it, starlight follows emission theory.
Note) A starlight is moving in aether. It is possible that v and c move at the same speed. Many of c will be below v.
Note) For a moving observer, speed of light must be reconsidered (starting with the Doppler effect).

A starlight > A light source

Every mass point is either in an inertial (unaccelerated) frame or accelerated frame. If a rigid homogeneous cuboid is in free-falling, every mass point is in accelerated frame. In this cuboid, there can be no inertial frame even locally.

P.S. This difference is not fictitious but absolute.

1) For inertial force, space is homogeneous isotropic. Gravity is not.
2) For inertial force, every position in space is the same. Gravity is not.

An elevator cabin is in free falli　　　ng. Let's assume that every local frame of this cabin is the same (mass m). There can be no local inertial frame.

A homogeneous cuboid made of atomic silver (atomic weight 107.9) is in free calling. Magnitude of inertial force acting on every silver atom is the same. There can be no local inertial frame.

◎ Inertia Force
1) Between inertial force and motion of a mass point in space, there will be direct connection.
2) Position in space has no meaning. Space is homogeneous isotropic.
3) Absolute space is required.
◎ Gravity
1) Between gravity and motion of a mass point in space, there will be no direct connection.
2) Position in space has meaning. As a gravitational field. Space is not homogeneous isotropic.
3) Absolute space is not required.

It is argued that inertial force and gravity are equivalent. However, in light of the followings, the two will not be equivalent. Even if vectors as action cancel each other out, vectors as existence do not disappear. Qualitatively, quantitatively. These are composing and decomposing of forces.
◎ Inertial force corresponds to accelerated motion of a mass point in homogeneous isotropic space.
◎ Gravity corresponds to position of a mass potint in space modified by gravitational fields.

In light of the followings, inertial force and gravity will not be equivalent.
◎ Inertial force: It is emerged in an accelerated motion (of a mass point) in space.
◎ Gravity: It does not emerge in an accelerated motion (of a mass point) in space.

If magnitude of vector of gravity and another force (e.g. tension) is the same, body will show the same vector of acceleration. On idiom (compound word) "gravitational acceleration", sense of incongruity cannot be wiped out.

Idiom "gravitational acceleration" seems to be meaningful only limited situationon. Free fall, gravity at the surface of Earth, etc. Is it an idiom of physics ?

If gravity and inertial force are different things, gravity and acceleration are also different things. Will there be qualification of idiom ?

Well, "gravitational acceleration" is "magnitude of gravity on the surface of Earth ?" said an Alien 👽

Gravity acts on a body as a vector. At a local area in free falling elevator, vector of gravity and vector of inertial force (vector of action, not of existence) will cancel each other. In that case, inertial force will not be fictitious.

Four the same spheres connected to the ends of two rods are rotating on a plane (no friction). Asuume the bar as a cross and the whole as a disk. At any point on the rod, the magnitudes of the centrifugal force and centripetal force are equal, as shown by Newton's third law of motion. That is, centrifugal force (and centripetal) is not fictitious to an observer in any frame.

Original text of the third law is said, it is not on two bodies, but on every point of action of force. Two bodies seem to be example.

A mass point is placed in aether frame, but when it is forced to move other than uniform linear motion (including zero speed) relative to aether frame, it shows resistance called inertial resistance. Inertial resistance is commonly said to be inertial force. Inertial force will correspond to motion of the mass in aether frame, qualitatively, quantitatively.

Allow me to alter some of previous post. Previous setting was four spheres and two rods. Now,on two spheres and one rod (in X direction only), mass is two times (without deflection). Then,at close to the center, magnitude of centrifugal force and centripetal force will be about two times. Also, magnitude of centrifugal force and centripetal force will correspond to rotational speed.

Speed of gravity propagation is said to be the same to speed of light. But is it true ? Something can't be found in thought experiments ? How about Sun and Mercury ? Solar system is said to move in the direction called sun facing point (on the celestial sphere). So position from which gravitational force of Sun acting Mercury will be the position some back in time. If so, this effect will slightly acuumlate (like free falling).

In Encyclopaedia Britannica 1969, there is a passage as follows (in item "Gravitation" ; original text). "If the action of gravitation were not absolutely instantaneous"(omission)"All experiments and observations were, however, consistent with the law, from the short distances employed in laboratory experiments to the long ranges used in interplanetary calculations". It says, action will be instantaneous.

This is supplement to the former post 47 (Speed of Light). Half of measurement results of speed of light waves will exceed c.

Uniform linear motion (ether can be emerged in an optical way), uniform circular motion, inertial force, action and reaction are all existence graspable qualitatively and quantitatively. These are not fictitious.

In my previous post (189), Mercury is divided into two spheres. But this thought experiment doesn't seem to hold. Surprising ! It does not disprove Newton's spherical shell theorem. So, my hope is shifted in another thought experiment on centrifugal force.

◎　But this thought experiment (see 189) doesn’t seem to explain perihelion shift of Mercury. Because, m/49^2 + m/51^2 = 2m/50^2. Surprising !
◎　Another thought experiment is on centrifugal force (see also 188).

In a figure, Mercury is shown as a circle. Plus, the center and an arc that through the center and extending upward and downward (that is a part of orbit) are shown. This arc divides Mercury into left and right, and the area is left > right. This figure will show that actual magnitude of centrifugal force exceeds that calculated for Mercury as a point (see formula of centrifugal force). Perihelion shift of Mercury may be due to Mercury's size.

Constant tension is acting on a rope extending from a passenger car to the left, and passenger car is decelerating. Even if the ground speed of passenger car becomes zero due to deceleration, tension of the rope is constant. So passenger car starts accelerating to the left. But, there will be no difference in situation in before and after of passenger car. And, there will be no point significant in the ground speed of passenger car.

Moon is said to be moving away from Earth by several centimeters per year. I proposed formally (in 68), size of orbiting celestial body increases its centrifugal force (compared to calculated as a point). And so, it moves forward the long axis of elliptical orbit, and also it increases the length of long axis a little ? Is Mercury moving away from Sun too ?

From a passenger car moving to the right, a rope is extending to left, and on it, constant tension is acting. Then, the passenger car is decelerating. And, when the ground speed of passenger car falls in zero, tension of the rope is still constant. So passenger car starts accelerating to the left. But, there will be no difference in situation in before and after in the passenger car. There will not be much meaning in the ground speed of passenger car.

As written above, everything is accelerated motion and decelerated motion does not exist. But "counter-jerk motion" where degree of accelerated motion withdraws may be possible.

Size of Mercury will increase gravity and increase centrifugal force quolitatively also. Of the two, gravity is probably the main factor. Because, increase in gravity shift aphelion in the direction of revolution. On the other hand, increase in centrifugal force shift aphelion in the opposite direction of revolution.

The formula for gravity F = mM/r^2 probably shows that magnitude of gravity is related to the size of Mercury (but surprisingly small).

There is one more problem. Size of Mercury receives surplus force. But where does this surplus force go ?

In figure of perihelion shift of Mercury,its destination seems not to be found. Ah, perhaps the same phenomenon as Moon's retreat (Moon's orbit is expanding) will be destination. This surplus force probably turns and expands Mercury's elliptical orbit each time.

[Size of Mercury increases gravity during orbital motion]
Mm/r^2 is formula for gravity. There are models for Mercury and Sun. When, 2Mm is 100 and r is 50, gravity is 0.04. Next, two half spheres of Mercury are lined up on the line of action of Sun's gravity. Mm is 50, r is 49 and 51. Then, gravity is 0.0400479.
[Size of Mercury increases centrifugal force during orbital motion]
See my post posted on March 15, 2023 (or around).

There is a figure of Mercury and its orbit. Mercury is drawn as a single point. But actually, Mercury has a size, and this size will slightly increase magnitude of gravity and centrifugal force of Mercury. Now, limit our consideration to half of orbit from perihelion to aphelion. Increase in gravity will shift aphelion in the direction of revolution. On the other hand, increase in centrifugal force will shift aphelion in the opposite direction of revolution. In increase, gravity will exceed.

Size of Mercury will cause the difference in its gravity and in its orbit. It will rotate long axis and shift perihelion (in the direction of revolution).

But, will size of Mercury cause difference in its centrifugal force ? This difference probably correspond to the difference in motion that is caused by difference in gravity.

Size of Mercury will increase Mercury's gravity. The main result will be slight expansion of orbit, and followed by shift in perihelion. Therefore, centrifugal force also increases. Newton's third law of motion will be inviolable.

Allow me to rewrite my previous post (Sep 29 and around).

Shift of perihelion is constant. Then, a doubt arises. What is momentum of Mercury ? Is it increasing ? Is it decreasing ? Is there no increase or decrease ? I'd like to hear even hypothesis.

Two Mercurys are revolving. One is in the orbit of Mercury and the other is in the orbit of Venus. In the former, magnitude of shift of perihelion seems to be larger. This is probably because effect of Mercury's size is greater in the former.

Imagine Mercury is revolving in the orbit of Neptune. Size of Mercury seen from Sun is close to a single point. So, magnitude of perihelion shift as two-body problem will be slight. And are perturbations outstanding ?

Imagine that two Mercurys are revolving in the orbit of Venus and Neptune. At two perihelions, Mercury moves in the same vector (direction and speed) as Venus and Neptune. Magnitude of Mercury's shift of perihelion will be smaller than that of the two. Because size of Mercury is smaller than that of the two.

Towards Earth, two bodies with the same mass are in free fall. One is assumed to be a single point (with no size), and the other is a long pole (falling vertically). Also assumed that gravity of Earth is constant at g. As posted formerly, magnitude of gravity of Earth acting on two bodies will be former < latter slightly. As example, in my former post, it was 0.04 < 0.04000479. So latter continues to fall in advance. In a broad sense, orbital motion is considered to be free fall. It seems that the shift of perihelion of Mercury is caused by its size.

Value of perihelion shift of Mercury is 5.75 seconds/year (observed). Of this value, 5.32 seconds/year is said to be caused by gravity (perturbation) of other planets. And remaining 0.43 seconds/year is attributed to general relativity. Here, a question arises. Why is perihelion shift (of each orbiting) the same regardless of the direction and distances of other planets that exert gravity on Mercury ?

In a site in English "Perihelion Precession of the Planets", there are tables on observed values and on theoretical values for perihelion shift on planets (of solar system). The same question arises.

If one centroid is an approximation, two centroids are also approximation. But an inequality 0.04 < 0.0400479 will be a problem presentation for Newton

A drawing shows Sun, Earth, and orbit of Earth. It also shows shift of perihelion of Earth (in the direction of revolution, annually) and shift of vernal equinox (in the opposite direction of revolution, annually). Shift of vernal equinox is said to be caused by precession of rotation axis (of Earth). Precession of rotation axis ? Really ? Shift of vernal equinox seems to be caused by extra centrifugal force due to size of the Earth. There is no other reason than that it seems to fit well.
Note: Perihelion is said to take about 110,000 years, and vernal equinox takes about 26,000 years to complete one revolution.

A question arises. Aren't shift of perihelion and vernal equinox (of Earth) in the same direction and magnitude ? To me, it is probable but not certain. I'll leave it to the physicists.