Define inertial frame and non-inertial frame. Is earth an inertial frame of reference?

In physics, an inertial frame of reference is a coordinate system in which Newton's first law of motion holds true. According to this law, an object at rest will remain at rest, and an object in motion will continue to move at a constant velocity unless acted upon by an external force. In an inertial frame, the laws of physics are consistent and do not require any additional forces or accelerations to explain the motion of objects.

On the other hand, a non-inertial frame of reference is a coordinate system that is accelerating or rotating relative to an inertial frame. In a non-inertial frame, fictitious or pseudo-forces, such as the centrifugal force or Coriolis force, may arise due to the acceleration or rotation of the frame. These forces appear to act on objects within the non-inertial frame, even though no actual physical forces are acting on them.

Now, considering the Earth, it is not strictly an inertial frame of reference. Although the Earth's rotational motion is relatively uniform and the deviation from uniform motion is generally small, it is not completely free from acceleration. The Earth undergoes a variety of accelerations and motions, including rotation around its axis, revolution around the Sun, and small irregularities in its rotation.

However, for many practical purposes, such as studying the motion of objects on the surface of the Earth or in its vicinity, we can often treat the Earth as an approximately inertial frame of reference. This approximation is valid in situations where the effects of the Earth's non-inertial motion are negligible compared to the scale of the problem being analyzed.