211 – Coriolis proves the Earth motionless

What is Coriolis acceleration? This is a physical phenomenon occurring to an object moving in a rectilinear way on a rotating surface. Look at the images below: in the first picture the ball is moving over a rectilinear line on a stationary platform. The ball isn’t affected by any lateral acceleration, insofar as the platform is motionless. When the platform starts rotating, the ball starts bending its trajectory and the result will prove to be a non rectilinear movement. This side acceleration is known as Coriolis acceleration.

It is an outstanding phenomenon that can be useful to prove that the Earth is not moving.
For example, let’s consider the ball as starting its linear movement exactly in the center of the circular platform. The platform rotates, let’s say, at the speed of 0.1 turn per second, that means 6 rpm i.e. 0,628 rad/sec (1 rpm is about 0,1 radiant per second and you should remember that 2π radians are 360°).

The ball is initially in the center of the platform, so it is not dragged anywhere due to the peripheral speed of the platform because, in the center, the speed is actually zero and it increases moving toward the periphery proportionally to the radius, according to the relation:
𝑉𝑝 = 𝜔 ∙ 𝑟
where Vp is the peripheral speed, ω is the angular speed and r is the radius describing the position of the ball on the platform; r can vary from zero in the center to R that is the outer radius.

Thus, when the ball starts its rectilinear movement from the center to the periphery of the platform, it is affected by that speed, that constantly increases, due to the increasing of the radius. The ball should start to have a lateral acceleration in the sense of rotation, in order to maintain its rectilinear movement. However, this is not possible unless it receives a
push from the outside. Thus, it starts to remain laterally backward due to inertia, and the trajectory bends as it is shown in the first picture.

Out of curiosity: the lateral acceleration that the ball should maintain, in order to keep its linear trajectory, could be expressed by this following formula:
𝐴𝑐 = 2 ∙ 𝑉 ∙ 𝜔
where Ac is the Coriolis acceleration, V is the speed of the ball in radial direction and ω is the angular speed. In this example, the ball is free to move in whatsoever direction. Thus, it stays behind and, when the platform starts its rotation, the ball keeps curving back, as a consequence of its inertia.

But now, consider the case when the ball is laterally guided on the platform, as you can see in the picture 1.3. The ball is forced to follow the platform and move in a rectilinear way toward the edge. The ball, this way, rotates with the same rotation speed ω of the platform.

To maintain this rectilinear movement of the ball on the platform, the guide has to impress the force of Coriolis:
𝐹𝑐 = 𝑚 ∙ 𝑎 = 𝑚 ∙ 2 ∙ 𝑉 ∙ 𝜔
where m is the mass of the ball. This is a real force, not an apparent one. The force of Coriolis is apparent for a fixed reference system, but is a real force if we consider a reference system rotating with the platform. Let’s apply now this idea to the globe and, more specifically, to airplanes that fly over the Earth.

An airplane, moving on a pure east–west direction, will not be affected by the Coriolis Effect, because the speed of the globe on fixed latitude doesn’t vary. But an airplane, taking off from A , will not arrive at point A’ (north–south direction as shown in the picture), unless its trajectory is readjusted by the aid of a suitable Coriolis acceleration, but it will reach point X.
When you make some research surfing the net, you will find that airplanes have some electronic system able to correct the trajectory in a suitable way. But is that actually true? Let’s investigate.
Consider now a helicopter able to fly at a maximum speed of 500 km/h and taking off from the North Pole.

The Earth wouldn’t drag it with its peripheral speed because the pole is on the axis, r=0, so Vp=0 where Vp is the peripheral speed. Let’s suppose the helicopter flies in an exclusively South direction and its speed has only one South component of 500 km/h. Now, something dangerous is happening under the airplane.

As it continues to fly southwards the Earth below continues to accelerate due to its rotation in east–west direction as an effect of the increase of the radius, because r increases. When the helicopter arrives at the equator, r=R i.e. 6371 km, it should keep a peripheral speed of about 1700 km/h.

Can the airplane correct its trajectory? Not at all, because, even if it starts to follow the earth along the equator, it can only reach 500 km/h. The fuel is finished, the helicopter tries to
land but it will be destroyed in the same instant of its landing.

To the average reader this situation could seem too much theoretical. So let’s give him an example taken from the everyday life. Imagine a man lying on his bed and ready to get up. Imagine a treadmill (tapis roulant) moving under the bed at the level of his feet at an amazing speed of 1000 km/hour. Could the man be able to get up and immediately start his activities? Absolutely not. He would be, with no doubt, hurtled away from his bed and splattered somewhere against the wall.

This is a clear demonstration of the fact the earth is not moving around its axis. A rotating earth would have to keep on moving faster at the equator and slower near the north and south poles. But there is no difference in speed at any point on the earth’s surface, whether north of, south of, or at the equator. Therefore the earth is not rotating around its polar axis.

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