a story about special relativity,who can explain it？

How do you see this gravitational Doppler Effect working?

The sun is not changing its mass or position wrt the solar system, therefore it does not emit gravitational waves. The gravitational field in the solar system is constant, so there's no Doppler Effect.

 

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Assume that the earth speed v0 = 0. Star began to approach the earth at the speed of v. Star came to position B, and the elapsed time was T seconds. The gravitational changes experienced by the earth are as follows:
T = 0s: F = G * M * m / R^2
T = 1s: F = G * M * m / (R + 1000)^2 ≈ G * M * m / R^2
According to the law of conservation of momentum:
F * T = mv1-mv0 = mv1, then v1 = F * T / m = T * G * M / R^2
T = 0s: v1 = 2 * G * M / R^2
T = 1s: v1 = 1 * G * M / R^2
Because of the speed v of the star, the earth obtained a different speed v1. The larger v is, the larger v1 will be, but the gravitational force on the planet from the star has hardly changed. If the star's v = X * cos(wt), then the speed change of earth will also show volatility.
The relative speed between them really affects the speed of the earth. Do you still think there is no Doppler effect between them? If you understand the Doppler effect, you will know that it exists anywhere.

 

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Assume that the earth speed v0 = 0. Star began to approach the earth at the speed of v. Star came to position B, and the elapsed time was T seconds. The gravitational changes experienced by the earth are as follows:
A: F = G * M * m / R^2
B: F = G * M * m / (R + 1000)^2 ≈ G * M * m / R^2
According to the law of conservation of momentum:
F * T = mv1-mv0 = mv1, then v1 = F * T / m = T * G * M / R^2
T = 2s: v1 = 2 * G * M / R^2
T = 1s: v1 = 1 * G * M / R^2
Because of the speed v of the star, the earth obtained a different speed v1. The larger v is, the larger v1 will be, but the gravitational force on the planet from the star has hardly changed. If the star's v = X * cos(wt), then the speed change of earth will also show volatility.
The relative speed between them really affects the speed of the earth. Do you still think there is no Doppler effect between them? If you understand the Doppler effect, you will know that it exists anywhere.
T: elapsed time

 

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Planetary precession data under the Doppler effect:
Mercury: e = 0.205608, Precession per century = 568.075883 "
Venus: e = 0.006811, Precession per century = 277.589395 "
Earth: e = 0.016780, Precession per century = 240.844614 "
Mars: e = 0.093332, Precession per century = 216.645123 "
Jupiter: e = 0.048700, Precession per century = 112.550073 "

Observed precession data:
Mercury -------------- 5.75 ------------- 575 "per century
Venus ---------------- 2.04 ------------- 204 "per century
Earth ----------------- 11.45 ----------- 1145 "per century
Mars ----------------- 16.28 ----------- 1628 "per century
Jupiter --------------- 6.55 ------------- 655 "per century
Saturn ------------- 19.50 ------------ 1950 "per century
Uranus --------------- 3.34 ------------- 334 "per century
Neptune ------------- 0.36 ------------- 36 "per century

Except for Mercury 575 "PK 568" and Venus 204 "PK 277", the precessions of the other planets differ greatly. But we all know that Mercury's precession is the largest, so I suspect there is a problem with the observation data.

 

We study a physical force situation, often by observing its speed change. Then under the Doppler effect of the gravitational field, the speed change of the object will also be different from the change under the ordinary gravitational field (non-Doppler effect).
I wrote the planetary orbit precession under the action of the Doppler effect of the gravitational field. I found that if I remove this effect, there will be no precession in the planetary orbit, and with the Doppler effect, you can see that there is precession.

Precession under the Doppler effect of gravitational field:
Planet -------- Perihelion precession ------------ Afar precession (per century)
------------------------------------------------------------------------------------------
Mercury********** 58.404"***************** 32.938"
Venus********** 38.004"****************** 38.466"
Earth********** 33.073"****************** 32.392"
Mars********** 27.609"****************** 24.686"
Jupiter********** 14.524"****************** 13.042"
Saturn********** 10.831"****************** 9.519"
Uranus********** 7.446"****************** 6.992"
Neptune********** 6.064"***************** 5.929"

Precession under the normal gravitational field: (non-Doppler effect)
Planet -------- Perihelion precession ---- Afar precession per century
-----------------------------------------------------------------------
Mercury********** 0.000"****************** 0.000"
Venus********** 0.000"****************** 0.000"
Earth********** 0.000"****************** 0.000"
Mars********** 0.000"****************** 0.000"
Jupiter********** 0.000"****************** 0.000"
Saturn********** 0.000"****************** 0.000"
Uranus********** 0.000"****************** 0.000"
Neptune********** 0.000"****************** 0.000"

 

Planet -------- Perihelion precession ---- Afar precession per century under the Doppler effect
---------------------------------------------------------------------------------------------------
Mercury********** 58.404"****************** 32.938"*******meanArc= 43.053"
Venus********** 38.004"****************** 38.466"*******meanArc= 38.236"
Earth********** 33.073"****************** 32.392"*******meanArc= 32.726"
Mars********** 27.609"****************** 24.686"*******meanArc= 26.075"
Jupiter********** 14.524"****************** 13.042"*******meanArc= 13.747"
Saturn********** 10.831"****************** 9.519"*******meanArc= 10.138"
Uranus********** 7.446"****************** 6.992"*******meanArc= 7.209"
Neptune********** 6.064"****************** 5.929"*******meanArc= 5.996"

 

Mercury********** 58.404"****************** 32.938"*******meanArc= 43.053"
Mercury Precession Deviation 43" comes from the Doppler effect of the gravitational field.

 

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