Is the surface of Earth a global inertial frame?

Question

I understand that a reference frame attached to an observer standing on the surface of non-rotating Earth is not a locally inertial frame but I wonder it can taken as a globally inertial frame because Newton's laws and other laws of physics are satisfied.

I asked my professor today about this and he quickly replied "no, the concept of global inertial frames only applies to flat spacetime." So it means a reference frame attached to an observer standing on the surface of non-rotating Earth is neither locally or globally inertial frame?

Suppose Earth is instead an infinite sheet with uniform gravitational field with strength $g$. In this case, a frame of an observer standing on it is not a local inertial frame but is a global inertial frame. Is that right?

Answer 1

You might get different answers, depending on which physics class you ask in. The best answer might be No, but it is often close enough if you ignore the vertical direction.

There are different versions of physics that treat gravity in different ways.

In classical physics, an inertial frame is a coordinate system where an object without forces acting on it stays at rest or moves at constant velocity. At the surface of the Earth, gravity acts of everything. So no. A skydiver doesn't stay at rest.

But an object sitting on a level ice skating rink does stay at rest. So the surface of the Earth is often treated as a inertial for two dimensional problems.

Unless the problems are big enough that the rotation of the Earth matters. For example, a wind blows north from the equator. The rotation of the Earth carries it sideways at about 1000 MPH. If it blows to a northerly latitude, the sideways motion of the earth is slower. But the wind keeps its original velocity. It blows sideways over the surface. From the viewpoint of the Earth, it has accelerated sideways. This is called the Coriolis force. It shows that the surface is not inertial.

The Coriolis force deflects me if I walk north. But it is small enough that I ignore it and think of the surface as inertial.

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In special relativity, spacetime is flat. That is, special relativity only applies where there is no gravity. We use it for thought experiments on the surface of the earth involving trains and barns-and-ladders and such. We ignore gravity the same way we do for classical physics.

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In general relativity, gravity is an effect of curved spacetime. An inertial frame of reference is a region of flat spacetime, at least locally where you don't look outside the falling elevator. A skydiver in the elevator does stay at rest.

The surface of the Earth does not stay at rest from the frame of the falling elevator. It is accelerated upward. So the surface of the Earth is not inertial.

It is worth noting that spacetime at the surface of the Earth is pretty close to flat on a scale that goes up to black holes. The radius of curvature of spacetime is about 1 light year.

Answer 2

No, because Earth exists in a strong gravitational field. It's non inertial In every context.

If you try to escape into an inertial frame, even in your house alone in a field, as far away from physics class as you can think of, objects still jump out of your hand and slam against the surface of the Earth.

Answer 3

No, it isn't because it rotates around its axis and has a gravitational field (apply the equivalence principle). A freefalling body like a satellite can be considered an inertial frame but not the Earth's surface. Also, note that its revolution around the Sun doesn't make our reference frame more accelerated because it is in freefall (basically, gravitational acceleration by the Sun is cancelled due to centrifugal force, not perfectly because Earth's orbit is not perfectly spherical).