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And also while analysing Earth's spinning motion about its center? Do we have to care about the forces from the giant Black Hole at the center of Milky way?

I guess we would have to take the Black Hole force into account, as it is an external force on every single particle of the system? Switching to the CoM frame may nullify the overall linear acceleration of the system, but the torque from the external forces would still be there, right?

If the black hole force (and also the external forces from billions of other star systems) matters even in the CoM frame, how does analysing things from the CoM frame make anything simpler? Also, when we say that Earth's angular momentum is conserved while it revolves around the sun, we make that statement only based on the force from the sun (this statement is made in the CoM frame, right?). Does the torque from the supermassive black hole not matter?

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    $\begingroup$ The gravitational acceleration of Sagittarius A* is pretty weak where we are. I calculate around 1.09e-18 m/s/s (which has got to be wrong, like, c'mon, man, that's weak). Nearby stars might have a greater influence than it. $\endgroup$
    – BMF
    Commented Aug 24, 2020 at 16:17
  • $\begingroup$ @BMF Is the force from nearby stars any significant? Can we treat the Solar system CoM frame as almost an inertial frame? $\endgroup$
    – Ryder Rude
    Commented Aug 25, 2020 at 3:57
  • $\begingroup$ Nearby stars? Not really sure. Probably not, no. Probably not even when they briefly pass in proximity, like through the Oört Cloud (to the Planets, anyway). Maybe over obnoxious timescales solar-distant objects could be affected. Their effect is probably biased by rotation around the galaxy. $\endgroup$
    – BMF
    Commented Aug 25, 2020 at 10:39

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Accurate predictions of solar system orbital dynamics can be obtained by ignoring our galaxy's central black hole, because despite its mass, it is too far away to produce any measurable effects here.

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the solar system is falling in free fall as it orbits the galaxy, as such this interaction has no effect (other than tidal forces that are negligible) on the interaction between the solar system and its planets

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