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By Newton's gravity equations, 5557 out of 5600 arcsec Mercury perihelion advancement due to other planets gravitational attraction. is it possible that regular asteroids striking forces could explain the remaining 43 arcsec?

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    $\begingroup$ Please, try to be more specific at your questions. 5 out of 6 of your questions have been closed or on-hold and you're still asking unclear questions. $\endgroup$ – G K Sep 17 '18 at 12:46
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    $\begingroup$ Has anybody measured such asteroids? is there a valid model, have you put down the numbers, number and mass of asteroids, momentum of asteroids needed, ? , $\endgroup$ – anna v Sep 17 '18 at 13:26
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    $\begingroup$ Three comments: (1) To first order, general relativity changes neither the shape nor size of Mercury's orbit. Asteroid strikes will in general affect both the size and shape. (2) Very few asteroids hit Mercury. The amount by which a typical asteroid strike would affect Mercury's orbit is miniscule. (3) The MESSENGER spacecraft traveled from the Earth to Mercury, with several gravity assists to help it. General relativity was used to plan MESSENGER's trajectory, making MESSENGER a test of general relativity. It was not hit by asteroids along the way. $\endgroup$ – David Hammen Sep 17 '18 at 13:43
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    $\begingroup$ Related: physics.stackexchange.com/q/26408/2451 , physics.stackexchange.com/q/814/2451 and links therein. $\endgroup$ – Qmechanic Sep 17 '18 at 13:49
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The perihelion advance of Mercury is rather small, but it was one of the very small number of things we could observe well enough a century or so ago to actually test GR.

Even if this advance could be explained within Newtonian gravitation by impacts on Mercury (I suspect it can't: other orbital parameters would change as well) you would need to account for its regularity: you need to account for $43''$ per century occurring as a tiny per-orbit change, So you'd need some stream of impacting objects hitting Mercury in some suitably asymmetric way, essentially all the time. Where are these objects? Presumably the impacts would be visible as they would, at least locally, cause significant heating: we don't observe this.

Apart from this, GR predicts much smaller rates of perihelion advance for other planets, notably Venus & Earth. These have now been measured and compared with the GR prediction (figures from Relativistic Perihelion Precession of Orbits of Venus and the Earth, Abhijit Biswas, Krishnan R. S. Mani, 2008):

$$ \begin{array}{rll} \text{Planet}&\text{Measured}&\text{Predicted by GR}\\ \text{Venus}&8.6247 \pm 0.0005&8.6247\\ \text{Earth}&3.8387 \pm 0.0004&3.8387 \end{array} $$

(Figures are seconds of arc / century.)

I think it's pretty convincing that the GR figures explain the results. It should also be convincing that Earth is not experiencing this strange rain of meteorites: we'd know if it was.

An alternative approach might be to look for other objects, preferably with much larger advances, and see if GR makes the right predictions for them as well.

And indeed we know of such objects. A famous example is the Hulse-Taylor binary. The Periastron advance of this system is about $4.2^\circ$ per year: the advance of this system in a day is about as much as Mercury's in a century.

Well, famously GR very nicely explains this and other characteristics of the orbit of the Hulse-Taylor system.

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