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At the Wikipedia about an aberration, there is the phrase:

a recommended galactocentric aberration constant of 5.8 µas/yr

What is the galactocentric aberration? How is it calculated correctly? An attempt to calculate it gives a different value.

Mean distance from Sun to Milky Way core is ~26,660 light-years. Galactic period is ${\text{2}}{\text{.25}} \ldots 2.50 \cdot 10^8$ years. Velocity of the Solar system orbit is ~251 km/s around the center of the Milky Way.

At the opposite points of the orbit the difference of the gravitational deflection of light is approximately $\Delta\theta = 2\frac{1}{2}\frac{4 \cdot G \cdot M}{R \cdot c^2} \approx 4\frac{v^2}{c^2} \approx 2.8 \cdot 10^{-6}\approx 0.58 \text{ arcsec} $. It is the value about $0.005 \text{ µas/yr}$. That is a thousand times less than above written the galactocentric aberration.

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  • $\begingroup$ Of what? What is the context of your question? I don;t understand what it is about at all. I make the centripetal accelation of the Sun (assuming a circular orbit) $2.4\times 10^{-10}$ m s$^{-2}$. $\endgroup$
    – ProfRob
    Jan 7, 2023 at 15:50
  • $\begingroup$ Ok, I have rewritten question and deleted wrong acceleration. $\endgroup$
    – Imyaf
    Jan 7, 2023 at 16:17

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