Question

Is earth an inertial frame if you consider the acceleration due to gravity?

Answer 1

In a theoretical sense, the physics of a system in an inertial frame have no external sources. With respect to one another, all inertial frames are in a condition of constant, rectilinear motion; an accelerometer moving with any of them would record zero acceleration.

Complete answer:
The Earth rotates and accelerates with respect to the Sun, a coordinate system tied to the Earth is not an inertial reference frame. A free-falling object is one that is falling only due to gravity's impact. A free-falling object has an acceleration of $9.8m.{s^{ - 1}}$ , downward.
Because the earth revolves around the sun, it experiences some acceleration. However, there are two forces at work for all bodies on the earth's surface: the gravitational force and the pseudo force caused by the earth's acceleration. Since the gravitational force nearly cancels out the pseudo force, there is no influence of the earth's movement on the earth's bodies due to the gravitational force. That is why the earth is considered an inertial frame of reference.
Or in other words, the Earth circles around the Sun at a constant speed, it is an inertial reference frame. A centripetal acceleration, on the other hand, causes the Earth to rotate while spinning at a constant speed. As a result, we might deduce that Earth is a Non Inertial Reference Frame in relation to the Sun.
Hence, the earth is an inertial frame if we consider the acceleration due to gravity.

Note:
For the same reason that we may calculate instantaneous slopes of a function, an accelerating frame still has inertial frames. Even though an accelerating frame is continually changing inertial frames, it is nonetheless an inertial frame at any given time.