Trap experiments to prove the earth's rotation

The tower of the main church St. Michaelis in Hamburg. Benzenberg carried out his measurements in the tower of the previous building.

Trap experiments to prove the rotation of the earth are physical experiments with which the rotation of the earth around its own axis could be empirically demonstrated for the first time from around 1800 . The rotation of the earth causes freely falling bodies to deflect eastwards from the perpendicular , which was predicted by Galileo and Newton , calculated by Carl Friedrich Gauß and measured by Guglielmini , Benzenberg and Reich . In today's physics system, it is treated as a partial aspect of the Coriolis effect.

appraisal

The eastward deflection is a consequence of the higher rotation speed of the earth at the dropping height compared to the rotation speed at the earth's surface. There is a deflection to the east in the direction of rotation of the earth, which can be estimated as follows.

The fall time without taking air resistance into account is and the difference in rotation speeds between the start and end of the fall ${\ displaystyle t = {\ sqrt {2h / g}}}$

{\ displaystyle \ Delta v = {\ frac {v} {r}} \, \ cos (\ varphi) \, h}

.

Because of the quadratic course of the speed, the actual difference is twice as large.

Are there

${\ displaystyle h}$ : Height of fall in meters
${\ displaystyle g}$ : Acceleration due to gravity in m / s² (between 9.780 m / s² at the equator and 9.832 m / s² at the poles)
${\ displaystyle \ varphi}$ : latitude
${\ displaystyle v = 463 \; {\ text {m / s}}}$ : Speed of rotation at the equator
${\ displaystyle r = 6,378,136.6 \; {\ text {m}}}$ : equatorial earth radius

It results z. B. at and latitude (Hamburg) with a fall time of a deflection from to the east. ${\ displaystyle s = 120 \; {\ text {m}}}$ ${\ displaystyle \ varphi = 53 ^ {\ circ}}$ ${\ displaystyle 4 {,} 9 \; {\ text {s}}}$ ${\ displaystyle 2 {,} 6 \; {\ text {cm}}}$

{\ displaystyle d _ {\ text {ost}} = {\ frac {2} {3}} {\ frac {v} {r}} \, \ cos (\ varphi) \, h \, {\ sqrt {\ frac {2h} {g}}}}

The deflection is due to the vertical Coriolis effect .

Experiments

The crooked Torre degli Asinelli in Bologna, on which Guglielmini experimented

Even Galileo and Newton (1679, letter to Hooke) proposed such experiments. The experiment requires extremely careful performance in order to shield against interference and a certain minimum height.

Robert Hooke (1635–1703) carried out tests from a height of 8.2 m, but did not come up with clear results (theoretical value: 0.5 mm).
A first experiment with a sufficient height of fall was carried out in 1791 by the Italian Giovanni Battista Guglielmini on one of the city towers (that of the Asinelli) of Bologna . With a drop height of around 78 m and 15 attempts, it received an average deviation of 16 mm to the east (theoretical value: 10.7 mm).
In Hamburg, the experiment was repeated in 1802 in the Hamburg Michel by the surveyor and astronomer Johann Friedrich Benzenberg (the Michel had intermediate floors with trap doors, which made the experiment possible). The height of fall of the lead balls was 76.3 m, and in 31 tests over four months an average deviation of 8.7 mm was measured in an easterly direction, which corresponded almost exactly to the calculations of Carl Friedrich Gauß (Benzenberg had written to Wilhelm Olbers , who Gauss contacted). However, there was also a mean deflection to the south that could not be explained at the time.
Benzenberg repeated the experiments in 1804 in a coal mine of the Trappe colliery . He dropped 29 bullets over 80.4 m, with a result that differed little from Gauss's prediction of 9.9 mm. He accurately measured a mean deviation of 5.1 Paris lines (11.4 mm) to the east and 0.7 lines (1.5 mm) to the south.
Ferdinand Reich received a deviation of 27.4 mm (theoretical value: 28.1 mm) with a drop of 158.5 m in the Drei-Brüder-Schacht near Freiberg in 1831. An important point was “letting go” of the balls as undisturbed as possible before the fall, which was achieved with pliers or by Reich by cooling heated lead balls over a precisely fitting hole.
Around the middle of the 19th century, the observed southern deflection, which could not be explained at the time, was the subject of heated debates. WW Rundell from the Royal Cornell Polytechnic therefore carried out the experiment again in 1848 in the deeper mining mines of Cornwall , which were two to three times deeper than Reich's mine shaft in Freiberg. The result was a clear deflection to the south. Also Florian Cajori presented an overview of 1901 established an undoubted Südablenkung, but could find no explanation.
In repeating the experiment in 1903 in the Paris Pantheon, Camille Flammarion used a holding device with an electromagnet.

A similar device was used in a repetition of the experiments in 2003 at the drop tower in Bremen as part of an experiment by students from the Free University of Berlin . There, at a height of fall of 119 m in a vacuum tube, an average deviation of 26 mm eastward was measured (theoretical value: 16.9 mm). Here, too, not all disruptive factors could be eliminated (e.g. there was also a mean deviation of 14 mm to the south).

Another experiment was carried out by Edwin Hall at Harvard University in 1902 . He dropped 948 bullets from a height of 23 m, with a mean deviation of 1.8 mm to the east (according to Gauss, 1.79 mm was expected), and 0.05 mm to the south. Inspired by Hall's experiment, mining experiments were tried again, this time in the very deep (4250 feet , i.e. 1,295.4 m) copper mine shafts on Lake Superior , which, however, turned out to be too narrow.

In 1851, Léon Foucault carried out a more precise and easily evaluable experiment on the rotation of the earth with a pendulum experiment in the Panthéon in Paris, which, however, is based on the horizontal Coriolis effect.

literature

JF Benzenberg: Experiments on the law of fall, the resistance of the air and the rotation of the earth. Dortmund 1804, 2nd edition Hamburg 1824
W. Brunner: Is the earth turning? Mathem.-Physical. Library, Volume 17, Leipzig, Berlin 1915
Richard Grammel : The mechanical evidence for the rotation of the earth , Julius Springer Verlag 1922
Philipp Furtwängler : The mechanics of the simplest physical apparatus and test arrangements , Chapter III: Experiments for the mechanical proof of the earth's rotation , Encyclopedia of Mathematical Sciences , IV, Part 2, 1904

Web links

Individual evidence

↑ Galileo, however, only in one argument that aimed at the non-observability of the effect ( dialogue about the two main world systems ). Newton suggested an alternative approach to the Coriolis effect, in which he found that the movement of a falling body in a fixed, non-rotating frame of reference, mentally continued into the interior of the earth, would be an elliptical orbit with the center of the earth in one of the focal points of the ellipse. So he did not find the Coriolis force directly, but in a certain way the beginnings of his theory of gravity. See Persson: "The Coriolis Effect - a conflict between common sense and mathematics" ( Memento of the original from April 11, 2014 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. (English, PDF). Gauss started from a similar point of view as Newton. @1@ 2

^ CF Gauß: Works. Volume 5, p. 496.

↑ The exact equations of motion are given in the article Coriolis force . They also show that (in the northern hemisphere) there is a small southerly deflection effect ( 2nd order Coriolis effect ), which, however, is too small to play a role in the experiments mentioned.

^ Benzenberg, Johann Friedrich. Experiments on the law of fall, on the resistance of the air and on the rotation of the earth. 1804. p. 264

↑ Gauss received 3.951 Paris lines with an air resistance of 3.86, Benzenberg measured an average of 4 lines

↑ A south deviation was observed in almost all experiments, starting with Hooke.

^ Benzenberg trial .. , p. 425.

↑ he interpreted this to mean that no deviation to the south was measured, in accordance with Gauss's calculation. During the drop tests, there were always large "escapes", which Benzenberg attributed to a collision with drops from the atomization of water flowing down the shaft walls.

↑ Presentation of Rundell's Experiment, Mechanics Magazine, May 1849 , and a letter from Oersted to Herschel in the reports of the British Association for the Advancement of Science, 1846.

↑ Cajori, The unexplained southerly deviation of falling bodies, Science, Vol 14, November 29, 1901 S. 853-855

^ Hall: Do falling bodies move south? , Physical Review, Series 1, Vol. 17, 1903, p. 179.

↑ McNair report, 1906 . Abstract in Science, Vol. 23, 1906, p. 415 (PDF file)

[1] Galileo, however, only in one argument that aimed at the non-observability of the effect ( dialogue about the two main world systems ). Newton suggested an alternative approach to the Coriolis effect, in which he found that the movement of a falling body in a fixed, non-rotating frame of reference, mentally continued into the interior of the earth, would be an elliptical orbit with the center of the earth in one of the focal points of the ellipse. So he did not find the Coriolis force directly, but in a certain way the beginnings of his theory of gravity. See Persson: "The Coriolis Effect - a conflict between common sense and mathematics" ( Memento of the original from April 11, 2014 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. (English, PDF). Gauss started from a similar point of view as Newton. @1@ 2

[2] CF Gauß: Works. Volume 5, p. 496.

[3] The exact equations of motion are given in the article Coriolis force . They also show that (in the northern hemisphere) there is a small southerly deflection effect ( 2nd order Coriolis effect ), which, however, is too small to play a role in the experiments mentioned.

[4] Benzenberg, Johann Friedrich. Experiments on the law of fall, on the resistance of the air and on the rotation of the earth. 1804. p. 264

[5] Gauss received 3.951 Paris lines with an air resistance of 3.86, Benzenberg measured an average of 4 lines

[6] A south deviation was observed in almost all experiments, starting with Hooke.

[7] Benzenberg trial .. , p. 425.

[8] terpreted this to mean that no deviation to the south was measured, in accordance with Gauss's calculation. During the drop tests, there were always large "escapes", which Benzenberg attributed to a collision with drops from the atomization of water flowing down the shaft walls.

[9] Presentation of Rundell's Experiment, Mechanics Magazine, May 1849 , and a letter from Oersted to Herschel in the reports of the British Association for the Advancement of Science, 1846.

[10] Cajori, The unexplained southerly deviation of falling bodies, Science, Vol 14, November 29, 1901 S. 853-855

[11] Hall: Do falling bodies move south? , Physical Review, Series 1, Vol. 17, 1903, p. 179.

[12] McNair report, 1906 . Abstract in Science, Vol. 23, 1906, p. 415 (PDF file)