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My book states that:

A reference frame attached to earth is not inertial because it is revolving around the sun and it is rotating about its own axis.

Don't we need a specified observer's frame to comment on other frames? If the observer's frame was on Earth won't Earth be inertial?

I have read other answers to questions based on inertial and non-inertial on this site. I just want to clarify if what I am thinking is right.

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Don't we need a specified observer's frame to comment on other frames? If the observer's frame was on Earth won't Earth be inertial?

No, being inertial frame is a property of the frame, not a relative state dependent on the observer.

Frame being inertial is an idealization that is never perfectly realized in practice. A real frame may be pronounced to be inertial if the non-inertial effects in the space and time region of interest are negligible.

Thus Earth can be assumed to be inertial frame if we study motion of ping-pong ball in a common table tennis exchange, because any non-inertial effect is negligible compared to effective gravity and aerodynamic forces. But Earth cannot be assumed to be inertial frame if we study motion of a cannon ball moving across long distances (miles) in Earth's atmosphere, because the Coriolis force due to Earth's rotation has measurable manifestations on such long ballistic trajectories.

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  • $\begingroup$ Okay. So if i take 2 accelerating frames(with same acceleration) A and B, then both are non-inertial frames, and it is not like ,from A ,B is inertial or anything.Am I right? $\endgroup$
    – Vaishakh Sreekanth Menon
    Commented Mar 19, 2019 at 1:40
  • $\begingroup$ @VaishakhSreekanthMenon yes. $\endgroup$
    – Ján Lalinský
    Commented Mar 19, 2019 at 18:47
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Don't we need a specified observer's frame to comment on other frames? If the observer's frame was on Earth won't Earth be inertial?

I don't understand why you need an observer in one from to talk about another frame. An inertial frame is simply a frame where Newton's laws hold. A frame moving with the Earth certainly does not meet this criteria. Centrifugal and Coriolis effects are certainly present on the surface of Earth. i.e. objects accelerate without forces acting on them. Therefore the frame is not inertial.

Perhaps you are thinking inertial means "non-accelerating", but in order to talk about acceleration you need to have an "outside frame" specified? Certainly that is one way to think about non-inertial frames, but the above discussion is a fine way of doing it too that does not reference "outside frames"

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  • $\begingroup$ Let me take an instance where I am inside an accelerating elevator , won't newton's laws hold fine for objects inside the elevator for me but not for someone observing from outside? $\endgroup$
    – Vaishakh Sreekanth Menon
    Commented Mar 18, 2019 at 15:20
  • $\begingroup$ @VaishakhSreekanthMenon It's the other way around. In the accelerating frame objects in the elevator have an additional "force" acting on them that is not coming from any sort of interaction. $\endgroup$
    – BioPhysicist
    Commented Mar 18, 2019 at 15:21
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Well you can get the answer to this question by reading fundamental laws of mechanics by I.E IRODOV. His book has given a complete discussion on reference frames in his 2nd chapter Basic equation of dynamics.

In that chapter he stated that we have a 'heliocentric' reference frame which is assumed to be inertial and is attached to the reference frame of sun.All reference frames are classified with respect to this frame.

He also gave a beautiful and a graspy definition of inertial reference frame in which he explained that a frame in which a body experiences no force due to the frame itself and all the forces on that body are due to its interaction with other bodies is called an inertial reference frame.

EDIT:-

Much like our solar system is in a stable orbit around the sun, the vast majority of a galaxy is in a stable orbit around the black hole, with no real reason to go plunging towards the very centre of the galaxy. The book defines it in such a way to assume that heliocentric reference frame is inertial so that we can observe nature in our solar system. But this fact is not universal.

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    $\begingroup$ Isn't the solar system revolving around a black hole at the galaxy's centre? This leads to same problem as with selecting earth as an inertial frame. $\endgroup$
    – drake01
    Commented Mar 18, 2019 at 15:19
  • $\begingroup$ Much like our solar system is in a stable orbit around the sun, the vast majority of a galaxy is in a stable orbit around the black hole, with no real reason to go plunging towards the very centre of the galaxy. Your query is quite correct but book defines it the same way for observing nature in our solar system. $\endgroup$
    – user213933
    Commented Mar 18, 2019 at 16:20

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