There's no single, definitive "proof" in the same way you'd prove a mathematical theorem. Instead, there's a vast body of evidence from different scientific fields that overwhelmingly points to the Earth's rotation. Here are some of the key pieces of evidence:

1. Observation of the Stars:

* Diurnal Motion: Stars appear to move in circles across the sky, rising in the east and setting in the west. This is caused by the Earth's rotation. If the Earth was stationary, we'd see stars in the same position all the time.

* Stellar Parallax: The apparent position of nearby stars shifts slightly over the year due to the Earth's orbit around the sun. This shift, known as parallax, is stronger for closer stars, and can only be explained by the Earth's motion.

2. Foucault's Pendulum:

* Rotating Pendulum: A Foucault pendulum, a long pendulum suspended freely, will slowly change its swing plane over time. This change is caused by the Earth's rotation and is noticeable at higher latitudes. It's a direct demonstration of the Earth's rotation.

3. Coriolis Effect:

* Deflection of Objects: The Coriolis effect causes objects in motion on the Earth's surface to be deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This is due to the Earth's rotation. This effect is noticeable in large-scale weather patterns like hurricanes and ocean currents.

4. Satellite Observations:

* Earth's Shape: Satellites have shown that the Earth is not perfectly spherical but slightly flattened at the poles and bulging at the equator. This shape is due to the Earth's rotation, which causes the equator to bulge outward.

* Earth's Gravity: Satellites also measure variations in Earth's gravity, which are influenced by the Earth's rotation.

5. Inertial Frames of Reference:

* Newton's Laws: Newton's laws of motion describe the behavior of objects in inertial frames of reference. An inertial frame is a non-accelerating frame. The Earth's rotation causes it to be a non-inertial frame, which is evident in phenomena like the Coriolis effect.

6. Historical Observations:

* Ancient Records: Ancient civilizations like the Greeks and Chinese observed the movement of the stars and developed theories about the Earth's rotation.

Conclusion:

The evidence for the Earth's rotation is vast and comes from various scientific disciplines. While no single experiment is definitive, the cumulative evidence overwhelmingly supports the idea that our planet is indeed rotating.