In our daily lives, we are accustomed to standing on solid ground and not feeling the rotation of the earth. But in fact, the Earth is rotating from west to east on its axis at a speed of about 1,670 kilometers per hour, and it takes a full 24 hours to complete a rotation. This law of nature has a profound impact on every living thing we live on the earth.
Imagine a scenario: an airplane is suspended in the air at an altitude of 100 meters above the ground, and if air resistance is ignored, it will move with the rotation of the earth. But the question is, in 12 hours, will the plane reach the other side of the planet because of the rotation of the earth? To answer this question, we need to delve into the principle of the Earth's rotation and the relative motion of objects on the Earth.
First of all, the rotation of the Earth does not mean that all objects on the Earth will move in a circle along the surface at the same speed. Due to the huge size of the Earth and the centrifugal force generated during rotation, the rotation speed at different latitudes of the Earth's surface is different. At the equator, the rotation speed is the fastest, while at the pole, the rotation speed drops to zero. This means that even if the aircraft is suspended in the air at an altitude of 100 meters, it will participate in the rotation of the Earth at different speeds along with the surface.
The Collision of Historical Cosmology: Geocentrism and Heliocentrism
In discussing the question of whether the plane will reach the other side of the Earth in 12 hours, we cannot but mention two main historical views on the structure of the universe: geocentrism and heliocentrism. Geocentrism was put forward by the ancient Greek philosopher Ptolemy, who believed that the earth is the center of the universe, and the sun, moon and stars revolve around the earth. This view dominated the Western scientific community for nearly two thousand years, and it was not until Copernicus's heliocentric theory that revolutionized the cosmology.
Copernicus' heliocentric theory held that the Sun was the center of the universe and that the Earth was a planet revolving around the Sun. Although this theory described celestial motion more precisely, it was not immediately widely accepted at the time, in part because of its conflict with people's everyday experience and its challenge to conventional wisdom. In particular, if the Earth is indeed rotating at high speed, why can't we feel the motion? Why can't objects on Earth be thrown out?
These questions became the focus of scientific discussion in Galileo's time. Galileo provided strong support for the principle of relativity through a series of subtle experiments and observations, especially his example of Salviti's large ship. He pointed out that if a person is inside a large, closed ship that moves at a constant speed, he cannot tell whether the boat is moving by any phenomenon inside the ship. This principle means that the state of inertial motion of an object is constant, whether on a ship or on Earth. Therefore, even if the earth is rotating and the plane is stationary relative to the ground, it will move with the earth and will not suddenly appear on the other side of the earth because of the rotation.
The Principle of Relativity: Exploring the Truth of the Suspension of Airplanes
Galileo's principle of relativity plays a central role in solving the question of whether an airplane will move to the other side of the Earth due to the rotation of the Earth. This principle states that the mathematical form of the laws of classical mechanics is invariant in any frame of inertia. In simple terms, this means that in a frame of reference without acceleration, the state of motion of the object does not change.
An inertial frame is an idealized concept that requires the frame of reference itself to move in a uniform linear motion without being affected by any external force. Although the Earth's surface is not a strict inertial frame due to its rotation, we can approximate it as an inertial frame when analyzing low-velocity moving objects. In this case, when the aircraft is suspended in the air at an altitude of 100 meters, its velocity is 0 with respect to the ground, so when there is no other external force acting on it, the displacement of the aircraft is the same as the ground, i.e., it will stay in place.
When the airplane rotates with the earth, as described by Galileo's principle of relativity, there is no relative acceleration between the airplane and the ground, so the relative position of the airplane and the ground remains the same. This means that although the Earth is rotating, the plane does not move to the other side of the Earth as a result. The plane is always relatively stationary from where it took off, which is consistent with what we experience in our daily lives. For example, when we are stationary on the ground, we do not feel that we are moving because of the rotation of the earth, which is a direct manifestation of Galileo's principle of relativity.
From the above analysis, we can conclude that the plane is suspended in the air at an altitude of 100 meters, and even after 12 hours, it will not reach the other side of the earth because of the rotation of the earth. The aircraft will remain in place, in relation to the ground. This phenomenon is the practical application of Galileo's principle of relativity.
Beyond the Inertial Frame: Foucault's Pendulum and the Proofs of the Earth's Rotation
Although according to Galileo's principle of relativity, an airplane suspended on the surface of the Earth does not move to the other side of the Earth because of the Earth's rotation, this does not mean that the Earth's rotation does not exist. In fact, the fact of the Earth's rotation has been confirmed by numerous experiments and observations, one of the most famous of which is the Foucault pendulum experiment.
The Foucault pendulum is a huge single pendulum that is able to keep the direction of the swing constant for a long time. When a Foucault pendulum is released at rest at a certain point on the earth's surface, the oscillating plane will gradually deflect relative to the ground due to the rotation of the earth. This deflection phenomenon proves that the Earth is indeed rotating, and it provides direct experimental evidence for the Earth's rotation.
The deflection angle of the Foucault pendulum is related to the speed of rotation of the earth and the latitude of the place of the swing. At the equator, the angle of deflection of the Foucault pendulum is also the largest due to the maximum rotation speed of the Earth. Whereas, at the poles, the Foucault pendulum does not deflect due to the zero rotation speed of the Earth. This phenomenon shows that even if we cannot directly feel the rotation of the earth, we can still conclusively confirm this natural phenomenon through precise scientific experiments.
In summary, although the plane is suspended at an altitude of 100 meters, it will not reach the other side of the Earth after 12 hours, which demonstrates the validity of Galileo's principle of relativity. However, through experiments such as Foucault's pendulum, we were able to prove that the Earth is indeed rotating. Together, these experiments and theories have constructed our modern understanding of the motion of the universe and provided an important building block for the development of physics.
In the long history of science, behind every seemingly simple problem, there may be a profound physical principle hidden. Through continuous exploration and experimentation, we are able to uncover the mysteries of the natural world and further understand the world we live in.