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  1. Can someone explain to me what I put in bold?

Inertial frame definition:

When the coordinate axes are stationary with respect to the mean position of the "fixed" stars or if they move with uniform linear velocity, without rotation, with respect to the stars.

  1. When the author says the following (see bold text), what makes this frame "slightly not inertial"?

Of course, it should be noted that measurements made with great precision could show that the frame of "fixed stars" is slightly not inertial.

  1. The reason why a frame of reference on earth, both on the surface and at its center, is not inertial is because of its acceleration of circular motion? Doesn't it matter that the angular velocity of the earth is constant 360°/24h (daily rotation) and 360°/365days (annual rotation)?
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Now consider the definition of inertial frame here:-

A frame in which acceleration of a body solely arises due to its interaction with other bodies is known as inertial frame of reference.

While in non inertial frame of reference the acceleration of a body arises not only due to its interaction with other bodies but also due to the frame itself.

The earth's angular velocity may be constant but it still rotates about its axis which is caused by a centripetal force which produces centripetal acceleration and that's why it is a non inertial reference frame.

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  • $\begingroup$ How could we know if the observed acceleration solely arises due to its interaction with other bodies? $\endgroup$ Jun 1, 2019 at 14:50
  • $\begingroup$ @GiorgioP Well the answer to this question would be equivalent to the fact that we can never find a complete inertial frame of reference. $\endgroup$ Jun 1, 2019 at 17:08

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