Is Earth an inertial frame of reference? Is the sun? Justify your response.

Both the Earth and the Sun are in motion relative to each other and other celestial bodies. Earth revolves around the Sun in an elliptical orbit, and also rotates on its own axis. The Sun, at the center of the solar system, exerts gravitational force on Earth and other planets, but it is also in motion around the center of the Milky Way galaxy.

Since Earth is revolving around the Sun and also rotating on its own axis, it is undergoing both translational and rotational motion. The centripetal acceleration experienced by an object at the Earth's surface due to its rotation is given by the equation \( a_c = r\omega^2 \), where \(r\) is the distance from the rotation axis and \(\omega\) is the angular velocity of Earth's rotation. Due to the centripetal acceleration, objects on the Earth's surface are subject to a small apparent force (the Coriolis force) that causes the objects to deviate slightly from a straight-line path, which does not meet the criteria of an inertial frame of reference. Therefore, the Earth cannot be considered an inertial frame of reference.

The Sun, although massive and exerting gravitational force on the planets in the solar system, is also in motion within the Milky Way galaxy. This motion makes the Sun an accelerating frame of reference. In this frame, objects are subject to apparent forces (e.g., centrifugal and Coriolis forces) that affect their motion, which violates the conditions for an inertial frame of reference. Therefore, the Sun also cannot be considered an inertial frame of reference.

Both the Earth and the Sun are not inertial frames of reference because they are subject to acceleration due to their respective motions. Consequently, objects within these frames experience apparent forces, which does not meet the criteria of an inertial frame of reference.