Avi asked: The Earth turns around its axis at a speed of around 1,800km/h. A commercial flight flies at a speed of about half of this. If we fly to a destination located on the opposite side of the Earth and the direction of the flight is the same as that of the Earth’s rotation, we will not be able to reach our destination since the speed of the Earth is greater than that of the plane. If so, how do we still manage to reach our destination?

Hi Avi,

For hundreds of years humans believed that Earth was the center of the Solar System and that the moon, sun, planets and all the other stars revolved around it. This view was based upon the fact that the ground below us is stable and stationary, and when people looked up to the sky they saw the rest of the celestial objects moving and revolving around Earth. Nowadays, we know that this notion was incorrect. In order to understand the true nature of the Earth’s rotation along with the motion of a plane, we need to first understand what a ‘frame of reference’.

When we wish to describe the motion of an object we first need to choose our frame of reference, namely a point to reference from where we want to measure (the coordinates of the origin), as well as the directions to which we are referring to in space (up,down or to the side). In addition, we need to choose the velocity of the system relative to another object (e.g., the ground). There are an infinite number of possibilities for choosing the frame of reference in any physics problem. However, the laws of physics will apply in all frames of reference, and no one is better than the other.

Let’s assume that a person is standing on a platform at the train station and a train passes by at a velocity of 200km/h in an easterly direction, and a bicycle rider passes by at a velocity of 10km/h in the same direction. One frame of reference is the person at rest, while the train is moving east at 200km/h and the bicycle is moving east at 10km/h. The second frame of reference is moving with the train. In this frame of reference the train is at rest, the person on the platform is moving west at 200km/h relative to it, and the bicycle is moving west at 190km/h. We could also define another frame of reference that is moving with the bicycle rider. In this frame of reference, the train is moving east at 190km/h and the person on the platform is moving west at 10km/h. Even though it seems the correct answer is that in which the person is at rest since this is the frame of reference of the ground, all three are equally good.

We can understand from this that in order to state that an object is moving at a certain velocity, we need to define in reference to what point in space it is moving or in what frame of reference it is moving. When stating velocities in a physics problem, it is important to pay attention to what the frame of reference is. In your question, you claimed that the velocity of the Earth’s rotation is 1,800km/h and that the velocity of the plane is half of this, but this is not true – since both velocities are being measured according to different frames of reference.

Plane. Speed is relative. | Photograph by: Oyoyoy, Wikipedia

The rotation time of the Earth is measured compared to the stars being fixed, i.e. stars which move very slowly in the sky, and therefore serve as a good reference point that almost does not move relative to Earth. In this frame of reference, we will observe the Earth rotating east at 1,800km/h at the Equator. This means the ground of the Earth and everything attached to it also rotates at this speed. From this point of view, the plane standing on the ground will also be moving east at 1,800km/h.

A plane ascending and flying east at 800km/h relative to the ground will appear, relative to the fixed stars, to be moving east at 2,600km; while a plane flying west at the same speed of 800km/h relative to the ground, will appear to the fixed stars to be moving east at 1,000km/h. In both cases the ground moves east at 1,800km/h. Therefore, the speed of the plane relative to the ground is 800km/h, and it is able to reach its destination.

Boomerang – question back at you
In the 19th century it was thought that there is one unique frame of reference termed “aether” in which light  travels at the familiar speed of 299,792,458 m/s, and that all other frames of reference move relative to it. What famous experiment was performed in order to disprove this claim, and what theory in physics developed following it?

Hagai Edri
Department of Physics of Complex Systems
Weizmann Institute of Science

Article translated from Hebrew by Elee Shimshoni, PhD student at the Weizmann Institute of Science.