An inertial reference frame is a coordinate system in which an object at rest remains at rest and an object in uniform motion continues to move in a straight line at a constant speed, unless acted upon by an external force. In other words, an inertial reference frame is a frame of reference where Newton's first law of motion (the law of inertia) holds true.
The Earth can be considered an inertial reference frame under certain conditions:
Non-accelerating frame: When we neglect the Earth's acceleration due to its rotation and revolution around the Sun, the Earth can be approximated as an inertial reference frame over short periods of time. On relatively small spatial and temporal scales, the Earth's motion is approximately uniform and rectilinear.
Local reference frame: For many practical purposes and observations conducted within a limited region on Earth, the Earth can be treated as an inertial reference frame. This is because the deviations from inertial motion caused by the Earth's rotation and orbital motion are relatively small over small distances and short time intervals.
Geostationary frame: If we consider a point on the Earth's surface that is in geostationary orbit (an orbit that matches the Earth's rotational period), the reference frame at that point can be treated as approximately inertial with respect to distant objects in space.
However, it's essential to note that the Earth is not a perfectly inertial reference frame over large scales or for highly precise measurements. Over extended periods of time and large distances, the Earth's motion must be taken into account for accurate calculations. To conduct high-precision experiments or make precise measurements, corrections for the Earth's rotation, revolution, and gravitational effects may be necessary.
In summary, the Earth can be considered an inertial reference frame for many everyday observations and practical purposes, especially within small regions and short time intervals. But for more precise and global applications, the Earth's non-inertial effects must be considered to obtain accurate results.