Question

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

Answer 1

Inertial frame

1. The term "inertial reference frame" is a relative term.
2. If there is no reference, we cannot define an inertial frame when two objects accelerate in opposite directions.
3. We can label one as inertial and the other as non-inertial, but we can't pick which one is inertial.
4. Inertial reference frames are subjective ideas. We begin by assuming that the reference frame is inertial.
5. Then, with regard to the reference frame, we can define a new frame that is at rest or has a constant velocity.
6. Assume you're looking at something that's moving at a constant speed relative to you. Then you may use Newton's equations of motion to calculate the motion of any object within the automobile.
7. The frame will be an inertial frame if we consider a coordinate system for a moving automobile moving at constant velocity.

Earth an inertial frame

1. The Earth rotates and accelerates with respect to the Sun, a coordinate system tied to the Earth is not an inertial reference frame.
2. We know that the earth rotates around its axis and also revolves around the sun. In both these motions, centripetal acceleration is present. Therefore, earth or any frame of reference fixed on earth cannot be taken as an inertial frame.

Hence, the earth cannot be considered an inertial frame of reference.