The search for definite answers to this question gives an interesting cross section of the history of classical physics. Around the year 265 bce, Samos, the Greek thinker Aristarchus maintained that the Earth rotates.
He had measured the parallax of theMoon (today known to be up to 0.95°) and of the Sun (today known to be 8.8').**
The parallax is an interesting effect; it is the angle describing the difference between the directions of a body in the sky when seen by an observer on the surface of the Earth and when seen by a hypothetical observer at the Earth’s centre. (See Figure 89.)
FIGURE 89 The parallax – not drawn to scale
Aristarchus noticed that the Moon and the Sun wobble across the sky, and this wobble has a period of 24 hours. He concluded that the Earth rotates. It seems that Aristarchus received death threats for his result.
Aristarchus’ observation yields an evenmore powerful argument than the trails of the stars shown in Figure 90. Can you explain why? (And how do the trails look at the most populated places on Earth?)
FIGURE 90 The motion of the stars during the night, observed on 1 May 2012 from the South Pole, together with the green light of an aurora australis (© Robert Schwartz).
Measurements of the aberration of light also show the rotation of the Earth; it can be detected with a telescope while looking at the stars.The aberration is a change of the expected light direction, which we will discuss shortly. At the Equator, Earth rotation adds an angular deviation of 0.32' , changing sign every 12 hours, to the aberration due to the motion of the Earth around the Sun, about 20.5' . In modern times, astronomers have found a number of additional proofs, but none is accessible to theman on the street.
Furthermore, the measurements showing that the Earth is not a sphere, but is flattened at the poles, confirmed the rotation of the Earth. Figure 91 illustrates the situation.
FIGURE 91 Earth’s deviation from spherical shape due to its rotation (exaggerated).
Again, however, this eighteenth centurymeasurement byMaupertuis*** is not accessible to everyday observation.
Then, in the years 1790 to 1792 in Bologna, Giovanni Battista Guglielmini (1763–1817) finally succeeded in measuring what Galileo and Newton had predicted to be the simplest proof for the Earth’s rotation. On the Earth, objects do not fall vertically, but are slightly deviated to the east. This deviation appears because an object keeps the larger horizontal velocity it had at the height fromwhich it started falling, as shown in Figure 92.
FIGURE 92 The deviations of free fall towards the east and towards the Equator due to the rotation of the Earth.
Guglielmini’s result was the first non-astronomical proof of the Earth’s rotation. The experiments were repeated in 1802 by Johann Friedrich Benzenberg (1777–1846). Using metal balls which he dropped from theMichaelis tower in Hamburg – a height of 76m – Benzenberg found that the deviation to the east was 9.6mm. Can you confirm that the value measured by Benzenberg almost agrees with the assumption that the Earth turns once every 24 hours? There is also a much smaller deviation towards the Equator, not measured by Guglielmini, Benzenberg or anybody after them up to this day; however, it completes the list of effects on free fall by the rotation of the Earth.
Both deviations from vertical fall are easily understood if we use the result (described Page 180 below) that falling objects describe an ellipse around the centre of the rotating Earth. The elliptical shape shows that the path of a thrown stone does not lie on a plane for an observer standing on Earth; for such an observer, the exact path thus cannot be drawn on a piece of paper.
In 1798, Pierre Simon Laplace explained how bodies move on the rotating Earth and showed that they feel an apparent force. In 1835, Gustave-Gaspard Coriolis then reformulated the description. Imagine a ball that rolls over a table. For a person on the floor, the ball rolls in a straight line. Now imagine that the table rotates. For the person on the floor, the ball still rolls in a straight line. But for a person on the rotating table, the ball traces a curved path. In short, any object that travels in a rotating background is subject to a transversal acceleration.The acceleration, discovered by Laplace, is nowadays called Coriolis acceleration or Coriolis effect. On a rotating background, travelling objects deviate from the straight line.The best way to understand the Coriolis effect is to experience it yourself; this can be done on a carousel, as shown in Figure 93.
FIGURE 93 A typical carousel allows observing the Coriolis effect in its most striking appearance: if a person lets a ball roll with the proper speed and direction, the ball is deflected so strongly that it comes back to her.
Watching films on the internet on the topic is also helpful. You will notice that on a rotating carousel it is not easy to hit a target by throwing or rolling a ball.
Also the Earth is a rotating background. On the northern hemisphere, the rotation is anticlockwise. As the result, any moving object is slightly deviated to the right (while the magnitude of its velocity stays constant). On Earth, like on all rotating backgrounds, the Coriolis acceleration a results from the change of distance to the rotation axis. Can you deduce the analytical expression for the Coriolis effect?
* ‘And yet she moves’ is the sentence about the Earth attributed, most probably incorrectly, to Galileo since the 1640s. It is true, however, that at his trial he was forced to publicly retract the statement of a moving Earth to save his life. For more details of this famous story, see the section on page 311.
** For the definition of the concept of angle, see page 66, and for the definition of the measurement units for angle see Appendix B.
*** Pierre LouisMoreau deMaupertuis (1698–1759), French physicist andmathematician.He was one of the key figures in the quest for the principle of least action, which he named in this way. He was also founding president of the Berlin Academy of Sciences.Maupertuis thought that the principle reflected the maximization of goodness in the universe.This idea was thoroughly ridiculed by Voltaire in this Histoire du Docteur Akakia et du natif de Saint-Malo, 1753.Maupertuis (www.voltaire-integral.com/Html/23/08DIAL.htm) performed his measurement of the Earth to distinguish between the theory of gravitation of Newton and that of Descartes, who had predicted that the Earth is elongated at the poles, instead of flattened.
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