What explains the rotation of the starry sky. Rotation of the starry sky

Regarding the celestial sphere (Earth).

All experimental evidence of the rotation of the Earth around its axis comes down to the proof that the reference system associated with the Earth is a non-inertial reference system of a special type - a reference system that performs rotational motion relative to inertial reference systems.

Unlike inertial motion (that is, uniform rectilinear motion relative to inertial frames of reference), to detect non-inertial motion of a closed laboratory it is not necessary to make observations of external bodies - such motion is detected using local experiments (that is, experiments carried out inside this laboratory). In this (precisely this!) sense of the word, non-inertial motion, including the rotation of the Earth around its axis, can be called absolute.

Inertia forces

Centrifugal force on a rotating Earth.

Effects of centrifugal force

Dependence of free fall acceleration on geographic latitude. Experiments show that the acceleration of gravity depends on geographic latitude: the closer to the pole, the greater it is. This is explained by the action of centrifugal force. Firstly, points on the earth's surface located at higher latitudes are closer to the rotation axis and, therefore, when approaching the pole, the distance from the rotation axis decreases, reaching zero at the pole. Secondly, with increasing latitude, the angle between the centrifugal force vector and the horizon plane decreases, which leads to a decrease in the vertical component of the centrifugal force.

This phenomenon was discovered in 1672, when the French astronomer Jean Richet, while on an expedition in Africa, discovered that pendulum clocks near the equator were running slower than in Paris. Newton soon explained this by saying that the period of oscillation of a pendulum is inversely proportional to the square root of the acceleration due to gravity, which decreases at the equator due to the action of centrifugal force.

Oblateness of the Earth. The influence of centrifugal force leads to the oblateness of the Earth at the poles. This phenomenon, predicted by Huygens and Newton at the end of the 17th century, was first discovered in the late 1730s as a result of processing data from two French expeditions specially equipped to solve this problem in Peru and Lapland.

Coriolis force effects: laboratory experiments

Foucault pendulum at the North Pole. The axis of rotation of the Earth lies in the plane of oscillation of the pendulum.

This effect should be most clearly expressed at the poles, where the period of complete rotation of the pendulum plane is equal to the period of rotation of the Earth around its axis (sidereal day). In general, the period is inversely proportional to the sine of geographic latitude; at the equator, the plane of oscillation of the pendulum is unchanged.

Gyroscope- a rotating body with a significant moment of inertia retains its angular momentum if there are no strong disturbances. Foucault, who was tired of explaining what happens to a Foucault pendulum not at the pole, developed another demonstration: a suspended gyroscope maintained its orientation, which means it turned slowly relative to the observer.

Deflection of projectiles during gun firing. Another observable manifestation of the Coriolis force is the deflection of the trajectories of projectiles (to the right in the northern hemisphere, to the left in the southern hemisphere) fired in a horizontal direction. From the point of view of the inertial reference system, for projectiles fired along the meridian, this is due to the dependence of the linear speed of rotation of the Earth on geographic latitude: when moving from the equator to the pole, the projectile retains the horizontal component of the speed unchanged, while the linear speed of rotation of points on the earth's surface decreases , which leads to a displacement of the projectile from the meridian in the direction of the Earth’s rotation. If the shot was fired parallel to the equator, then the displacement of the projectile from parallel is due to the fact that the trajectory of the projectile lies in the same plane with the center of the Earth, while points on the earth's surface move in a plane perpendicular to the Earth's rotation axis. This effect (for the case of shooting along the meridian) was predicted by Grimaldi in the 40s of the 17th century. and first published by Riccioli in 1651.

Deviation of freely falling bodies from the vertical. ( ) If the speed of a body has a large vertical component, the Coriolis force is directed to the east, which leads to a corresponding deviation of the trajectory of a body freely falling (without initial speed) from a high tower. When considered in an inertial reference frame, the effect is explained by the fact that the top of the tower relative to the center of the Earth moves faster than the base, due to which the trajectory of the body turns out to be a narrow parabola and the body is slightly ahead of the base of the tower.

The Eötvös effect. At low latitudes, the Coriolis force, when moving along the earth's surface, is directed in the vertical direction and its action leads to an increase or decrease in the acceleration of gravity, depending on whether the body is moving west or east. This effect is called the Eötvös effect in honor of the Hungarian physicist Loránd Eötvös, who experimentally discovered it at the beginning of the 20th century.

Experiments using the law of conservation of angular momentum. Some experiments are based on the law of conservation of angular momentum: in an inertial reference frame, the magnitude of angular momentum (equal to the product of the moment of inertia and the angular velocity of rotation) does not change under the influence of internal forces. If at some initial moment of time the installation is stationary relative to the Earth, then the speed of its rotation relative to the inertial reference system is equal to the angular speed of rotation of the Earth. If you change the moment of inertia of the system, then the angular speed of its rotation should change, that is, rotation relative to the Earth will begin. In a non-inertial reference frame associated with the Earth, rotation occurs as a result of the Coriolis force. This idea was proposed by the French scientist Louis Poinsot in 1851.

The first such experiment was carried out by Hagen in 1910: two weights on a smooth crossbar were installed motionless relative to the surface of the Earth. Then the distance between the loads was reduced. As a result, the installation began to rotate. An even more demonstrative experiment was carried out by the German scientist Hans Bucka in 1949. A rod approximately 1.5 meters long was installed perpendicular to a rectangular frame. Initially, the rod was horizontal, the installation was motionless relative to the Earth. Then the rod was brought into a vertical position, which led to a change in the moment of inertia of the installation by approximately a factor and its rapid rotation with an angular velocity several times higher than the speed of rotation of the Earth.

Funnel in the bath.

Because the Coriolis force is very weak, it has a negligible effect on the direction of swirl of water when draining a sink or bathtub, so in general the direction of rotation in the funnel is not related to the rotation of the Earth. However, in carefully controlled experiments, it is possible to separate the effect of the Coriolis force from other factors: in the northern hemisphere the funnel will spin counterclockwise, in the southern hemisphere - vice versa.

Coriolis force effects: phenomena in the surrounding nature

Baer's law. As St. Petersburg academician Karl Baer first noted in 1857, rivers erode the right bank in the northern hemisphere (the left bank in the southern hemisphere), which consequently turns out to be steeper (Baer's law). The explanation for the effect is similar to the explanation for the deflection of projectiles when firing in a horizontal direction: under the influence of the Coriolis force, the water hits the right bank harder, which leads to its blurring, and, conversely, retreats from the left bank.

Cyclone over the southeast coast of Iceland (view from space).

Winds: trade winds, cyclones, anticyclones. Atmospheric phenomena are also associated with the presence of the Coriolis force, directed to the right in the northern hemisphere and to the left in the southern hemisphere: trade winds, cyclones and anticyclones. The phenomenon of trade winds is caused by the uneven heating of the lower layers of the earth's atmosphere in the equatorial zone and in the middle latitudes, leading to air flow along the meridian to the south or north in the northern and southern hemispheres, respectively. The action of the Coriolis force leads to the deflection of air flows: in the northern hemisphere - towards the northeast (northeast trade wind), in the southern hemisphere - towards the southeast (southeast trade wind).

Optical experiments

A number of experiments demonstrating the rotation of the Earth are based on the Sagnac effect: if a ring interferometer performs a rotational motion, then due to relativistic effects a phase difference appears in the oncoming beams

where is the area of projection of the ring onto the equatorial plane (the plane perpendicular to the axis of rotation), is the speed of light, and is the angular velocity of rotation. To demonstrate the rotation of the Earth, this effect was used by the American physicist Michelson in a series of experiments carried out in 1923-1925. In modern experiments using the Sagnac effect, the rotation of the Earth must be taken into account to calibrate ring interferometers.

There are a number of other experimental demonstrations of the Earth's diurnal rotation.

Uneven rotation

Precession and nutation

However, virtually nothing is known about Hicetas and Ecphantes, and even their very existence is sometimes questioned. According to the opinion of most scientists, the Earth in the Philolaus world system did not perform a rotational, but a translational movement around the Central Fire. In his other works, Plato follows the traditional view that the Earth is immobile. However, numerous evidence has reached us that the idea of the rotation of the Earth was defended by the philosopher Heraclides of Pontus (IV century BC). Probably, another assumption of Heraclides is associated with the hypothesis of the Earth’s rotation around its axis: each star represents a world, including earth, air, ether, and all this is located in infinite space. Indeed, if the daily rotation of the sky is a reflection of the rotation of the Earth, then the prerequisite for considering the stars to be on the same sphere disappears.

About a century later, the assumption of the rotation of the Earth became part of the first, proposed by the great astronomer Aristarchus of Samos (3rd century BC). Aristarchus was supported by the Babylonian Seleucus (2nd century BC), as well as Heraclides of Pontus, who considered the Universe to be infinite. The fact that the idea of the daily rotation of the Earth had its supporters back in the 1st century AD. e., evidenced by some statements of the philosophers Seneca, Dercyllidas, and the astronomer Claudius Ptolemy. The vast majority of astronomers and philosophers, however, did not doubt the immobility of the Earth.

Arguments against the idea of the Earth's motion are found in the works of Aristotle and Ptolemy. So, in his treatise About Heaven Aristotle justifies the immobility of the Earth by the fact that on a rotating Earth, bodies thrown vertically upward could not fall to the point from which their movement began: the surface of the Earth would shift under the thrown body. Another argument in favor of the immobility of the Earth, given by Aristotle, is based on his physical theory: the Earth is a heavy body, and heavy bodies tend to move towards the center of the world, and not rotate around it.

From the work of Ptolemy it follows that supporters of the hypothesis of the rotation of the Earth responded to these arguments that both air and all earthly objects move together with the Earth. Apparently, the role of air in this argument is fundamentally important, since it is implied that it is its movement together with the Earth that hides the rotation of our planet. Ptolemy objects to this:

bodies in the air will always seem to lag behind... And if the bodies rotated with the air as one whole, then none of them would seem to be ahead of or behind the other, but would remain in place, in flight and throwing it would not make deviations or movements to another place, like those that we personally see taking place, and they would not slow down or accelerate at all, because the Earth is not motionless.

Middle Ages

India

The first medieval author to suggest that the Earth rotates around its axis was the great Indian astronomer and mathematician Aryabhata (late 5th - early 6th centuries). He formulates it in several places in his treatise Aryabhatiya, For example:

Just as a man on a forward-moving ship sees fixed objects moving backward, so an observer... sees the fixed stars moving in a straight line to the west.

It is not known whether this idea belongs to Aryabhata himself or whether he borrowed it from ancient Greek astronomers.

Aryabhata was supported by only one astronomer, Prthudaka (9th century). Most Indian scientists defended the immobility of the Earth. Thus, the astronomer Varahamihira (6th century) argued that on a rotating Earth, birds flying in the air could not return to their nests, and stones and trees would fly off the surface of the Earth. The outstanding astronomer Brahmagupta (6th century) also repeated the old argument that a body that fell from a high mountain could sink to its base. At the same time, he, however, rejected one of Varahamihira’s arguments: in his opinion, even if the Earth rotated, objects could not come off it due to their gravity.

Islamic East

The possibility of rotation of the Earth was considered by many scientists of the Muslim East. Thus, the famous geometer al-Sijizi invented the astrolabe, the operating principle of which is based on this assumption. Some Islamic scholars (whose names have not reached us) even found a correct way to refute the main argument against the rotation of the Earth: the verticality of the trajectories of falling bodies. Essentially, the principle of superposition of movements was put forward, according to which any movement can be decomposed into two or more components: in relation to the surface of the rotating Earth, a falling body moves along a plumb line, but a point that is a projection of this line onto the surface of the Earth would be transferred by it rotation. This is evidenced by the famous encyclopedist al-Biruni, who himself, however, was inclined to the immobility of the Earth. In his opinion, if some additional force acts on the falling body, then the result of its action on the rotating Earth will lead to some effects that are not actually observed.

Among scientists of the 13th-16th centuries associated with the Maragha and Samarkand observatories, a discussion arose about the possibility of an empirical substantiation of the immobility of the Earth. Thus, the famous astronomer Qutb ad-Din al-Shirazi (XIII-XIV centuries) believed that the immobility of the Earth could be verified by experiment. On the other hand, the founder of the Maragha Observatory, Nasir ad-Din al-Tusi, believed that if the Earth rotated, then this rotation would be divided by a layer of air adjacent to its surface, and all movements near the surface of the Earth would occur exactly the same as if the Earth was motionless. He substantiated this with the help of observations of comets: according to Aristotle, comets are a meteorological phenomenon in the upper layers of the atmosphere; however, astronomical observations show that comets take part in the daily rotation of the celestial sphere. Consequently, the upper layers of air are carried away by the rotation of the sky, therefore the lower layers can also be carried away by the rotation of the Earth. Thus, the experiment cannot answer the question of whether the Earth rotates. However, he remained a supporter of the immobility of the Earth, since this was in accordance with the philosophy of Aristotle.

Most Islamic scholars of later times (al-Urdi, al-Qazwini, an-Naysaburi, al-Jurjani, al-Birjandi and others) agreed with al-Tusi that all physical phenomena on a rotating and stationary Earth would occur in the same way. However, the role of air was no longer considered fundamental: not only air, but also all objects are transported by the rotating Earth. Consequently, to justify the immobility of the Earth it is necessary to involve the teachings of Aristotle.

A special position in these disputes was taken by the third director of the Samarkand Observatory, Ala ad-Din Ali al-Kushchi (15th century), who rejected the philosophy of Aristotle and considered the rotation of the Earth physically possible. In the 17th century, the Iranian theologian and encyclopedist Baha ad-Din al-Amili came to a similar conclusion. In his opinion, astronomers and philosophers have not provided sufficient evidence to refute the rotation of the Earth.

Latin West

A detailed discussion of the possibility of the Earth's motion is widely contained in the writings of the Parisian scholastics Jean Buridan, Albert of Saxony, and Nicholas of Oresme (second half of the 14th century). The most important argument in favor of the rotation of the Earth rather than the sky, given in their works, is the smallness of the Earth compared to the Universe, which makes attributing the daily rotation of the sky to the Universe highly unnatural.

However, all of these scientists ultimately rejected the rotation of the Earth, although on different grounds. Thus, Albert of Saxony believed that this hypothesis was not capable of explaining the observed astronomical phenomena. Buridan and Oresme rightly disagreed with this, according to whom celestial phenomena should occur in the same way regardless of whether the rotation is made by the Earth or the Cosmos. Buridan was able to find only one significant argument against the rotation of the Earth: arrows fired vertically upward fall down a vertical line, although with the rotation of the Earth they, in his opinion, should lag behind the movement of the Earth and fall west of the point of the shot.

Nikolai Orem.

But even this argument was rejected by Oresme. If the Earth rotates, then the arrow flies vertically upward and at the same time moves east, being captured by the air rotating with the Earth. Thus, the arrow should fall in the same place from where it was fired. Although the enthralling role of air is again mentioned here, it does not really play a special role. The following analogy speaks to this:

Likewise, if the air were closed in a moving ship, then to a person surrounded by this air it would seem that the air was not moving... If a person were in a ship moving at high speed to the east, unaware of this movement, and if he extended his hand in a straight line along the mast of the ship, it would seem to him that his hand was making a linear movement; in the same way, according to this theory, it seems to us that the same thing happens to an arrow when we shoot it vertically up or vertically down. Inside a ship moving at high speed to the east, all kinds of motion can take place: longitudinal, transverse, down, up, in all directions - and they appear exactly the same as when the ship is stationary.

I conclude, therefore, that it is impossible to demonstrate by any experiment that the heavens have a diurnal movement and that the earth does not.

However, Oresme's final verdict on the possibility of the Earth's rotation was negative. The basis for this conclusion was the text of the Bible:

However, so far everyone supports and I believe that it is [Heaven] and not the Earth that moves, for “God made the circle of the Earth, which will not be moved,” despite all the arguments to the contrary.

The possibility of the daily rotation of the Earth was also mentioned by medieval European scientists and philosophers of later times, but no new arguments were added that were not contained in Buridan and Oresme.

Thus, almost none of the medieval scientists accepted the hypothesis of the rotation of the Earth. However, during its discussion, scientists of the East and West expressed many deep thoughts, which would later be repeated by scientists of the New Age.

Renaissance and Modern Times

Nicolaus Copernicus.

In the first half of the 16th century, several works were published that argued that the cause of the daily rotation of the sky was the rotation of the Earth around its axis. One of them was the treatise of the Italian Celio Calcagnini “On the fact that the sky is motionless and the Earth rotates, or on the perpetual motion of the Earth” (written around 1525, published in 1544). He did not make much of an impression on his contemporaries, since by that time the fundamental work of the Polish astronomer Nicolaus Copernicus “On the Rotations of the Celestial Spheres” (1543) had already been published, where the hypothesis of the daily rotation of the Earth became part of the heliocentric system of the world, like Aristarchus of Samos . Copernicus previously outlined his thoughts in a small handwritten essay Small Comment(not earlier than 1515). Two years earlier than the main work of Copernicus, the work of the German astronomer Georg Joachim Rheticus was published First narration(1541), where Copernicus' theory was popularly expounded.

In the 16th century, Copernicus was fully supported by astronomers Thomas Digges, Rheticus, Christoph Rothmann, Michael Möstlin, physicists Giambatista Benedetti, Simon Stevin, philosopher Giordano Bruno, and theologian Diego de Zuniga. Some scientists accepted the rotation of the Earth around its axis, rejecting its translational motion. This was the position of the German astronomer Nicholas Reimers, also known as Ursus, as well as the Italian philosophers Andrea Cesalpino and Francesco Patrizi. The point of view of the outstanding physicist William Gilbert, who supported the axial rotation of the Earth, but did not speak out about its translational motion, is not entirely clear. At the beginning of the 17th century, the heliocentric system of the world (including the rotation of the Earth on its axis) received impressive support from Galileo Galilei and Johannes Kepler. The most influential opponents of the idea of earth motion in the 16th and early 17th centuries were the astronomers Tycho Brahe and Christopher Clavius.

The hypothesis of the rotation of the Earth and the development of classical mechanics

Essentially, in the XVI-XVII centuries. the only argument in favor of the axial rotation of the Earth was that in this case there is no need to attribute enormous rotation rates to the stellar sphere, because even in antiquity it was already reliably established that the size of the Universe significantly exceeds the size of the Earth (this argument was also contained in Buridan and Oresme) .

Considerations based on the dynamic concepts of that time were expressed against this hypothesis. First of all, this is the verticality of the trajectories of falling bodies. Other arguments also appeared, for example, equal firing range in the eastern and western directions. Answering the question about the unobservability of the effects of daily rotation in terrestrial experiments, Copernicus wrote:

Not only does the Earth rotate with the water element connected to it, but also a considerable part of the air and everything that is in any way akin to the Earth, or the air closest to the Earth, saturated with earthly and watery matter, follows the same laws of nature as The Earth, or has acquired motion, which is imparted to it by the adjacent Earth in constant rotation and without any resistance

Thus, the main role in the unobservability of the Earth’s rotation is played by the entrainment of air by its rotation. The majority of Copernicans in the 16th century shared the same opinion.

Galileo Galilei.

Proponents of the infinity of the Universe in the 16th century also included Thomas Digges, Giordano Bruno, Francesco Patrizi - they all supported the hypothesis that the Earth rotates around its axis (and the first two also around the Sun). Christoph Rothmann and Galileo Galilei believed that stars were located at different distances from the Earth, although they did not explicitly speak out about the infinity of the Universe. On the other hand, Johannes Kepler denied the infinity of the Universe, although he was a supporter of the rotation of the Earth.

Religious context for the Earth's rotation debate

A number of objections to the rotation of the Earth were associated with its contradictions with the text of Holy Scripture. These objections were of two types. Firstly, some places in the Bible were cited to confirm that it is the Sun that makes the daily movement, for example:

The sun rises and the sun sets, and hastens to its place where it rises.

In this case, the axial rotation of the Earth was affected, since the movement of the Sun from east to west is part of the daily rotation of the sky. A passage from the book of Joshua has often been quoted in this connection:

Jesus cried to the Lord on the day that the Lord delivered the Amorites into the hands of Israel, when he defeated them in Gibeon, and they were beaten before the children of Israel, and said before the Israelites: Stand, O sun, over Gibeon, and the moon, over the valley of Avalon. !

Since the command to stop was given to the Sun, and not to the Earth, it was concluded that it was the Sun that performed the daily movement. Other passages have been cited to support the immobility of the Earth, for example:

You have set the earth on firm foundations: it will not be shaken for ever and ever.

These passages were considered to contradict both the view that the Earth rotates on its axis and the revolution around the Sun.

Proponents of the rotation of the Earth (notably Giordano Bruno, Johannes Kepler, and especially Galileo Galilei) pursued a defense on several fronts. First, they pointed out that the Bible was written in a language understandable to ordinary people, and if its authors provided scientifically clear language, it would not be able to fulfill its main, religious mission. Thus, Bruno wrote:

In many cases it is foolish and inadvisable to make much reasoning according to truth rather than according to the given case and convenience. For example, if instead of the words: “The sun is born and rises, passes through noon and leans toward Aquilon,” the sage said: “The earth goes in a circle to the east and, leaving the sun, which sets, leans toward the two tropics, from Cancer to the South, from Capricorn to Aquilon,” then the listeners would begin to think: “How? Does he say the earth moves? What kind of news is this? In the end they would consider him a fool, and he would indeed be a fool.

This kind of answer was given mainly to objections concerning the diurnal movement of the Sun. Secondly, it was noted that some passages of the Bible should be interpreted allegorically (see the article Biblical allegorism). Thus, Galileo noted that if Holy Scripture is taken literally in its entirety, it will turn out that God has hands, is subject to emotions such as anger, etc. In general, the main idea of the defenders of the doctrine of the movement of the Earth was that science and religion have different goals: science examines the phenomena of the material world, guided by the arguments of reason, the goal of religion is the moral improvement of man, his salvation. Galileo in this regard quoted Cardinal Baronio that the Bible teaches how to ascend to heaven, not how heaven works.

These arguments were considered unconvincing by the Catholic Church, and in 1616 the doctrine of the rotation of the Earth was prohibited, and in 1631 Galileo was convicted by the Inquisition for his defense. However, outside Italy, this ban did not have a significant impact on the development of science and contributed mainly to the decline in the authority of the Catholic Church itself.

It must be added that religious arguments against the movement of the Earth were given not only by church leaders, but also by scientists (for example, Tycho Brahe). On the other hand, the Catholic monk Paolo Foscarini wrote a short essay “Letter on the views of the Pythagoreans and Copernicus on the mobility of the Earth and the immobility of the Sun and on the new Pythagorean system of the universe” (1615), where he expressed considerations close to those of Galileo, and the Spanish theologian Diego de Zuniga even used Copernican theory to interpret some passages of Scripture (although he later changed his mind). Thus, the conflict between theology and the doctrine of the movement of the Earth was not so much a conflict between science and religion as such, but a conflict between old (already outdated by the beginning of the 17th century) and new methodological principles underlying science.

The significance of the hypothesis about the rotation of the Earth for the development of science

Understanding the scientific problems raised by the theory of the rotating Earth contributed to the discovery of the laws of classical mechanics and the creation of a new cosmology, which is based on the idea of the boundlessness of the Universe. Discussed during this process, the contradictions between this theory and the literalist reading of the Bible contributed to the demarcation of natural science and religion.

Notes

Poincare, About science, With. 362-364.
This effect was first observed by Vincenzo Viviani (a student of Galileo) back in 1661 (Grammel 1923, Hagen 1930, Guthrie 1951).
Foucault's theory of the pendulum is described in detail in General physics course Sivukhin (T. 1, § 68).
Under Soviet rule, a 98 m long Foucault pendulum was demonstrated in St. Isaac's Cathedral (Leningrad).
Grammel 1923.
Kuhn 1957.
For more details, see Mikhailov 1984, p. 26.
Graney 2011.
For calculation of the effect, see General physics course Sivukhin (Vol. 1, § 67).
The angular velocity of the base and the apex is the same, but the linear velocity is equal to the product of the angular velocity and the radius of rotation.
A slightly different but equivalent explanation is based on Kepler's II law. The sectoral speed of a body moving in a gravitational field, proportional to the product of the radius vector of the body by the square of the angular velocity, is a constant value. Let's consider the simplest case, when the tower is located on the earth's equator. When the body is at the top, its radius vector is maximum (the radius of the Earth plus the height of the tower) and the angular velocity is equal to the angular velocity of the Earth's rotation. When a body falls, its radius vector decreases, which is accompanied by an increase in the angular velocity of the body. Thus, the average angular velocity of the body turns out to be slightly greater than the angular velocity of the Earth's rotation.
Koyre 1955, Burstyn 1965.
Armitage 1947, Mikhailov and Filonovich 1990.
Grammel 1923, p. 362.
Grammel 1923, p. 354-356
Schiller, Motion Mountain, pp. 123, 374. See also de:Erdrotation.
Surdin 2003.
For a detailed explanation, see Aslamazov and Varlamov (1988).
G. B. Malykin, “Sagnac effect. Correct and incorrect explanations”, Advances in Physical Sciences, volume 170, No. 12, 2000.
Grammel 1923, Rigge 1913, Compton 1915, Guthrie 1951, Schiller, Motion Mountain .
Precession- article from (3rd edition)
APOD: 2010 November 25 - Spherical Astronomy
Nutation (physical)- article from the Great Soviet Encyclopedia (3rd edition)
Veselovsky, 1961; Zhitomirsky, 2001.
“He [the Demiurge] determined for the earth, our nurse, to rotate around an axis passing through the Universe.”
They are sometimes considered characters in the dialogues of Heraclides of Pontus.
This evidence is collected in an article by Van der Waerden, 1978.
Evidence of the daily rotation of the Earth from Aristarchus: Plutarch, About the face visible on the disk of the Moon(excerpt 6); Sextus Empiricus, Against scientists; Plutarch, Platonic questions(question VIII)
Plutarch testifies to this.
Heath 1913, pp. 304, 308; Ptolemy, Almagest, book 1, chapter 7.
Aristotle, About Heaven, book II.14.
Ptolemy, Almagest, book 1, chapter 7.
Right there.
Chatterjee 1974, p. 51.
According to some historians, Aryabhata's theory is a reworking of the heliocentric theory of Greek astronomers (Van der Waerden, 1987).
Chatterjee 1974, p. 54.
Rosenfeld et al. 1973, p. 94, 152-155.
Biruni, Canon of Mas'ud, book 1, chapter 1
Ragep, 2001. See also Dzhalalov, 1958.
The Biographical Encyclopedia of Astronomers, p. 42.
Jean Buridan on the diurnal rotation of Earth; see also Lanskoy 1999.
Lupandin, Lecture 11.
Nicole Oresme on the Book of the Heavens and the world of Aristotle; see also Dugas 1955 (p. 62-66), Grant 1974, Lanskoy 1999 and Lupandin, Lecture 12.
Lupandin, Lecture 12.
Grant 1974, p. 506.
Lanskoy 1999, p. 97. It should be noted, however, that not all religious arguments against the rotation of the Earth were considered convincing by Oresme (Dugas 1955, p. 64)).
At the end of his life, however, Zuniga rejected the Earth's daily rotation as an "absurd assumption." See Westman 1986, p. 108.
Many articles are devoted to the history of this argument and various attempts to overcome it (Mikhailov and Filonovich 1990, Koyre 1943, Armitage 1947, Koyre 1955, Ariotti 1972, Massa 1973, Grant 1984).
Copernicus, On the rotations of the celestial spheres, Russian translation 1964, p. 28.
Mikhailov and Filonovich 1990, Ariotti 1972.
Galileo G. Selected works in two volumes. - T. 1. - P. 333.
In ancient times, supporters of the infinity of the Universe were Heraclides of Pontus and Seleucus, who assumed the rotation of the Earth.
This refers to the daily rotation of the celestial sphere.
Koyre, 2001, p. 46-48.
Ecclesiastes 1:5.
Bible, Book of Joshua, chapter 10.
Psalm 103:5.
Rosen 1975.
This is the subject of his letters to his student, the priest Benedetto Castelli and the Grand Duchess Christina of Lorraine. Extensive extracts from them are given in Fantoli 1999.
Oresme spoke about this in the 14th century.
J. Bruno, Feast on the ashes, dialogue IV.
Howell 1998.

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During the day, the Sun moves across the sky. It rises, rises higher and higher, then begins to fall and sets. It is not difficult to see that the stars also move across the sky.

Choose a place for observation from where the sky is clearly visible, and note from it over which objects visible on the horizon (houses or trees) the Sun is visible in the morning, at noon and in the evening. Come to this place after sunset, notice the brightest stars in the same directions of the sky and mark the time of observation on the clock. If you come to the same place an hour or two later, make sure that all the stars you noticed have moved from left to right. So, the star that was in the direction of the morning Sun rose in the sky, and the star that was in the direction of the evening Sun sank.

Do all the stars move across the sky? It turns out, everything, and at the same time. We can say that the entire sky with the stars in it seems to revolve around us every day.

The side of the sky where the Sun is visible at noon is called the southern side, and the opposite side is called the northern side. Look in the northern sky, first at the stars close to the horizon, and then at the higher ones. You will see that the higher the stars are from the horizon, the less noticeable their movement. You can also find a star in the sky whose movement throughout the night is almost imperceptible, and the closer other stars are to this star, the less noticeable their movement is. This star was called Polar, we already know how to find it from the stars of Ursa Major.

When we look at the North Star, or more precisely, at a fixed point next to it - at the north pole of the world, the direction of our gaze coincides with the direction of the axis of the starry sky. The axis of rotation of the starry sky itself is called the axis of the world.

The rotation of the sky around the Earth is an apparent phenomenon. The reason for this is the rotation of the Earth. Just as a person spinning around a room seems as if the whole room is spinning around him, so to us, who are on a rotating Earth, it seems that the sky is spinning. In ancient times, observing the daily rotation of the sky, people made a deeply erroneous conclusion that the stars, the Sun and the planets revolve around the Earth every day. In fact, as it was established in the 16th century. Copernicus, the apparent rotation of the starry sky is only a reflection of the daily rotation of the Earth around its axis. However, the stars still move. Not so long ago, astronomers found that all the stars of our Galaxy move at different speeds around its center (the Galaxy is described in the article “3 Stars and the Depths of the Universe”).

The imaginary axis around which the globe rotates intersects the Earth's surface at two points. These points are the North and South geographic poles. If we continue the direction of the earth's axis, it will pass near the North Star. This is why the North Star seems almost motionless to us.

In the southern starry sky, which in our northern hemisphere is only partially visible due to the spherical shape of the Earth, there is a second fixed point in the sky - the south celestial pole. The stars of the southern hemisphere revolve around this point.

Let's take a closer look at the apparent daily motion of stars. Turn your face to the southern side of the horizon and watch the movements of the stars. To make observations more convenient, imagine a semicircle that passes through the zenith (the point directly above your head) and the celestial pole. This semicircle (celestial meridian) will intersect with the horizon at the point of the north (under the North Star) and at the opposite point of the south. It divides the sky into eastern and western halves. Observing the movement of stars in the southern part of the sky, we will notice that the stars located to the left of the celestial meridian (i.e., in the eastern part of the sky) rise above the horizon. Having passed through the celestial meridian and entering the western part of the sky, they begin to descend towards the horizon. This means that when the stars pass through the celestial meridian, they reach their greatest height above the horizon. Astronomers call the passage of a star through its highest position above the horizon the upper culmination of that star.

If you turn your face to the north and begin to observe the movements of the stars in the northern part of the sky, you will notice that the stars passing through the celestial meridian below the North Star at this moment occupy the lowest position above the horizon. Moving

from left to right, they, having passed the celestial meridian, begin to rise. When a star passes through its lowest possible position above the horizon, astronomers say the star is at its lowest climax.

Among the constellations visible in our country, there are those that, moving around the celestial pole, never go beyond the horizon. This is easy to verify by observation: in the winter months, the constellation Ursa Major is visible above the horizon at its lowest position during the day.

But not only the Big Dipper turns out to be a non-setting constellation for the inhabitants of the USSR. The stars Ursa Minor, Cassiopeia, Draco, Cepheus, located close to the north pole of the world, also never go, for example, beyond the Moscow horizon. These are never setting stars.

Along with the stars that never set, there are also those that never rise over our country. These include many stars in the southern hemisphere of the sky.

The sky, like the globe, is mentally divided into two hemispheres by an imaginary circle, all points of which are at the same distance from the poles of the world. This circle is called the celestial equator. It crosses the horizon at the east and west points.

All stars during the day describe paths parallel to the celestial equator. The hemisphere of the sky in which the North Star is located is called the northern hemisphere, and the other hemisphere is called the southern hemisphere.

View of the starry sky in different places on Earth

The sky looks different in different places around the world. It turns out that the appearance of the starry sky depends on what parallel the observer is at, in other words, what is the geographic latitude of the observation site. The angular elevation of the celestial pole (or, approximately, the North Star) above the horizon is always equal to the geographic latitude of the place.

If you take a trip to the North Pole from Moscow, you will notice as you go that the North Star (or celestial pole) is getting higher and higher above the horizon. Therefore, more and more stars turn out to be non-setting.

Finally, you have arrived at the North Pole. Here the arrangement of stars is not at all the same as in the Moscow sky.

The geographic latitude of the North Pole of the globe is 90°. This means that the celestial pole (and the North Star) will be directly overhead - at the zenith. It is not difficult to imagine that the celestial equator will coincide with the horizon here at the North Pole. Thanks to this, at the North Pole you will see an unusual picture of the movement of stars: always moving along paths parallel to the celestial equator, the stars move parallel to the horizon. Here all the stars in the northern hemisphere of the sky will be non-setting, and all the stars in the southern hemisphere will be non-rising.

If you now mentally transport yourself from the North Pole to the earth's equator, you will see a completely different picture.

As you move south, the latitude of the place and therefore the height of the celestial pole (and Polaris) will begin to decrease, i.e. Polaris will approach the horizon.

When you find yourself on the earth's equator, the geographic latitude of any point of which is zero, you will see the following picture: the north pole of the world will find itself at the north point, and the celestial equator will become perpendicular to the horizon. At the south point there will be the south celestial pole, located in the constellation Octantus.

All stars on the earth's equator describe paths perpendicular to the horizon during the day. If there were no Sun, because of which it is impossible to see the stars during the day, then during the day at the earth's equator it would be possible to observe all the stars of both hemispheres of the sky.

At different times of the year, different constellations can be observed in the evenings. Why is this happening?

To understand this, make some observations. Shortly after sunset, notice a star in the western sky low above the horizon and remember its position in relation to the horizon. If about a week later at the same hour of the day you try to find this star, you will notice that it has now become closer to the horizon and is almost hidden in the rays of the evening dawn. This happened because the Sun approached this star. And in a few weeks the star will completely disappear in the sun’s rays and will no longer be visible in the evenings. When another 2-3 weeks have passed, the same star will become visible in the morning, shortly before sunrise, in the eastern part of the sky. Now the Sun, continuing its movement from west to east, will be east of this star.

Such observations show that the Sun not only moves along with all the stars, rising in the east and setting in the west during the day, but also slowly moves among the stars in the opposite direction (i.e. from west to east), moving from constellation to constellation.

Of course, you will not be able to observe the constellation in which the Sun is currently located, since it rises along with the Sun and moves across the sky during the day, that is, when the stars are not visible. The sun with its rays extinguishes the stars not only of the constellation where it is located, but also of all others. Therefore, they cannot be observed.

The path along which the Sun moves among the stars throughout the year is called the ecliptic. It passes through twelve so-called zodiacal constellations, in each of which the Sun appears for approximately one month each year. The zodiac constellations are called: Pisces (March), Aries (April), Taurus (May), Gemini (June), Cancer (July), Leo (August), Virgo (September), Libra (October), Scorpio (November),

Constellations visible at mid-latitudes in the southern half of the sky in spring.

Sagittarius (December), Capricorn (January), Aquarius (February). The months when the Sun is in these constellations are indicated in brackets.

The annual movement of the Sun among the stars is apparent. In fact, the observer himself moves along with the Earth around the Sun. If we observe the stars in the evenings throughout the year, we will discover a gradual change in the starry sky and become familiar with all the constellations that are visible at different times of the year.

FUNDAMENTALS OF SPHERICAL AND PRACTICAL ASTRONOMY

CHAPTER 1

The meaning of astronomy

Astronomy and its methods are of great importance in the life of modern society. Issues related to the measurement of time and providing humanity with knowledge of the exact time are now being resolved by special laboratories - time services, organized, as a rule, at astronomical institutions.

Astronomical orientation methods, along with others, are still widely used in navigation and aviation, and in recent years - in astronautics.

The calculation and compilation of the calendar, which is widely used in the national economy, is also based on astronomical knowledge.

Drawing up geographical and topographic maps, pre-calculating the onset of sea tides, determining the force of gravity at various points on the earth's surface in order to detect mineral deposits - all this is based on astronomical methods.

Studies of processes occurring on various celestial bodies allow astronomers to study matter in states that have not yet been achieved in earthly laboratory conditions. Therefore, astronomy, and in particular astrophysics, which is closely related to physics, chemistry, and mathematics, contributes to the development of the latter, and they, as we know, are the basis of all modern technology.

Astronomy, by studying celestial phenomena, exploring the nature, structure and development of celestial bodies, proves that the Universe is subject to the uniform laws of nature and, in accordance with them, develops in time and space. Therefore, the conclusions of astronomy have deep philosophical significance.

No matter where we are on the earth’s surface, it always seems to us that all celestial bodies are located at the same distance from us on the inner surface of a certain sphere, which is colloquially called firmament , or simply sky .

During the day, the sky, if it is not covered by clouds, is blue, and we see the brightest celestial body on it - the Sun. Sometimes, simultaneously with the Sun, the Moon is visible during the day and very rarely some other celestial bodies, for example, the planet Venus.

On a cloudless night in the dark sky we see stars, the Moon, planets, nebulae, sometimes comets and other bodies. The first impression from observing the starry sky is the countless number of stars and the randomness of their arrangement in the sky. In reality, there are not as many stars visible to the naked eye as it seems, only about 6 thousand in the entire sky, and in one half of it, which is currently visible from any point on the earth’s surface, no more than 3 thousand.

Stars have two properties: 1) they differ in brightness from each other; 2) relatively motionless. These properties make it possible to distinguish star figures in the sky, called constellations.

The system of constellations in our sky was created 500 years BC. by the ancient Greeks.

The constellations were designated by the names of animals ( Ursa Major, Leo, Dragon etc.), names of heroes of Greek mythology ( Cassiopeia, Andromeda, Perseus etc.) or simply the names of those objects that resembled the figures formed by the bright stars of the group ( Northern Crown, Triangle, Arrow, Libra and so on.).

Since the 17th century individual stars in each constellation began to be designated by letters of the Greek alphabet, and, as a rule, in descending order of their brightness. Somewhat later, numerical numbering was introduced, which is currently used mainly for faint stars. In addition, bright stars (about 130) received their own names. For example: a Canis Major is called Sirius, a Auriga - Capella, a Lira - Vega, a Orion - Betelgeuse, b Orion - Rigel, b Perseus - Algolem etc. These names and designations of stars are still used today. However, the boundaries of the constellations, outlined by ancient astronomers and representing winding lines, were changed at the astronomical congress in 1922, some large constellations were divided into several independent constellations, and constellations began to be understood not as figures of stars, but as sections of the starry sky. Now the entire sky is conventionally divided into 88 separate sections - constellations.

The brightest stars in the constellations serve as good guides for locating fainter stars or other celestial objects in the sky.

If you observe the starry sky for several hours on a clear night, it is easy to notice that the vault of heaven, as one whole, with all the luminaries located on it, smoothly rotates around some imaginary axis, one end of which passes through the place of observation, and the other is very close near Polar stars. This rotation of the firmament and luminaries is called daily movement of the starry sky , since one complete circulation is completed per day. Due to daily rotation, stars and other celestial bodies continuously change their position relative to the sides of the horizon and describe circles around the axis of rotation.

Moreover, the period of this rotation is equal to a sidereal day - the period of a complete revolution of the celestial sphere relative to the Earth.

Inertia forces

Centrifugal force on a rotating Earth.

Effects of centrifugal force

Coriolis force effects: laboratory experiments

Foucault pendulum at the North Pole. The axis of rotation of the Earth lies in the plane of oscillation of the pendulum.

There are a number of other experiments with pendulums used to prove the rotation of the Earth. For example, Bravais' experiment (1851) used a conical pendulum. The rotation of the Earth was proven by the fact that the periods of oscillations clockwise and counterclockwise were different, since the Coriolis force in these two cases had a different sign. In 1853, Gauss proposed using not a mathematical pendulum, like Foucault, but a physical one, which would reduce the size of the experimental setup and increase the accuracy of the experiment. This idea was realized by Kamerlingh Onnes in 1879.

Deflection of projectiles during gun firing. Another observable manifestation of the Coriolis force is the deflection of the trajectories of projectiles (to the right in the northern hemisphere, to the left in the southern hemisphere) fired in a horizontal direction. From the point of view of the inertial reference system, for projectiles fired along the meridian, this is due to the dependence of the linear speed of rotation of the Earth on geographic latitude: when moving from the equator to the pole, the projectile maintains the horizontal component of the speed unchanged, while the linear speed of rotation of points on the earth's surface decreases , which leads to a displacement of the projectile from the meridian in the direction of the Earth's rotation. If the shot was fired parallel to the equator, then the displacement of the projectile from parallel is due to the fact that the trajectory of the projectile lies in the same plane with the center of the Earth, while points on the earth's surface move in a plane perpendicular to the Earth's rotation axis.

Deviation of freely falling bodies from the vertical. If the velocity of a body has a large vertical component, the Coriolis force is directed to the east, which leads to a corresponding deviation in the trajectory of a body freely falling (without initial velocity) from a high tower. When considered in an inertial reference frame, the effect is explained by the fact that the top of the tower relative to the center of the Earth moves faster than the base, due to which the trajectory of the body turns out to be a narrow parabola and the body is slightly ahead of the base of the tower.

The Eötvös effect. At low latitudes, the Coriolis force when moving along the earth's surface is directed in the vertical direction and its action leads to an increase or decrease in the acceleration of gravity, depending on whether the body is moving west or east. This effect is called the Eötvös effect in honor of the Hungarian physicist Roland Eötvös, who experimentally discovered it at the beginning of the 20th century.

Funnel in the bath. Because the Coriolis force is very weak, it has a negligible effect on the direction of swirl of water when draining a sink or bathtub, so in general the direction of rotation in the funnel is not related to the rotation of the Earth. However, in carefully controlled experiments, it is possible to separate the effect of the Coriolis force from other factors: in the northern hemisphere the funnel will spin counterclockwise, in the southern hemisphere - vice versa.

Coriolis force effects: phenomena in the surrounding nature

Cyclone over the southeast coast of Iceland (view from space).

Optical experiments

where is the area of the ring, is the speed of light, and is the angular velocity of rotation. To demonstrate the rotation of the Earth, this effect was used by the American physicist Michelson in a series of experiments carried out in 1923-1925. In modern experiments using the Sagnac effect, the rotation of the Earth must be taken into account to calibrate ring interferometers.

There are a number of other experimental demonstrations of the Earth's diurnal rotation.

Uneven rotation

Precession and nutation

Change of pole position

Slowdown of rotation over time

Origin of the Earth's rotation

History of the idea of the Earth's daily rotation

Antiquity

The explanation of the daily rotation of the sky by the rotation of the Earth around its axis was first proposed by representatives of the Pythagorean school, the Syracusans Hicetus and Ecphantus. According to some reconstructions, the rotation of the Earth was also confirmed by the Pythagorean Philolaus of Croton (5th century BC). A statement that can be interpreted as an indication of the rotation of the Earth is contained in Plato's dialogue Timaeus .

However, virtually nothing is known about Hicetas and Ecphantes, and even their very existence is sometimes questioned. According to the majority of scientists, the Earth in Philolaus’ world system did not perform a rotational, but a translational motion around the Central Fire. In his other works, Plato follows the traditional view that the Earth is immobile. However, numerous evidence has reached us that the idea of the rotation of the Earth was defended by the philosopher Heraclides of Pontus (IV century BC). Probably, another assumption of Heraclides is associated with the hypothesis about the rotation of the Earth around its axis: each star represents a world, including earth, air, ether, and all this is located in infinite space. Indeed, if the daily rotation of the sky is a reflection of the rotation of the Earth, then the prerequisite for considering the stars to be on the same sphere disappears.

About a century later, the assumption of the rotation of the Earth became part of the first, proposed by the great astronomer Aristarchus of Samos (3rd century BC). Aristarchus was supported by the Babylonian Seleucus (2nd century AD), as well as Heraclides of Pontus, who considered the Universe to be infinite. The fact that the idea of the daily rotation of the Earth had its supporters back in the 1st century AD. e., evidenced by some statements of the philosophers Seneca, Dercyllidas, and the astronomer Claudius Ptolemy. The vast majority of astronomers and philosophers, however, did not doubt the immobility of the Earth.

Aryabhata was supported by only one astronomer, Prthudaka (9th century). Most Indian scientists defended the immobility of the Earth. Thus, the astronomer Varahamihira (6th century) argued that on a rotating Earth, birds flying in the air could not return to their nests, and stones and trees would fly off the surface of the Earth. The outstanding astronomer Brahmagupta (6th century) also repeated the old argument that a body that fell from a high mountain could sink to its base. At the same time, he rejected one of Varahamihira’s arguments: in his opinion, even if the Earth rotated, objects could not come off it due to their gravity.

Islamic East. The possibility of rotation of the Earth was considered by many scientists of the Muslim East. Thus, the famous geometer al-Sijizi invented the astrolabe, the operating principle of which is based on this assumption. Some Islamic scholars (whose names have not reached us) even found a correct way to refute the main argument against the rotation of the Earth: the verticality of the trajectories of falling bodies. Essentially, the principle of superposition of movements was put forward, according to which any movement can be decomposed into two or more components: in relation to the surface of the rotating Earth, the falling body moves along a plumb line, but the point that is the projection of this line onto the surface of the Earth would be transferred by it rotation. This is evidenced by the famous encyclopedist al-Biruni, who himself, however, was inclined to the immobility of the Earth. In his opinion, if some additional force acts on the falling body, then the result of its action on the rotating Earth will lead to some effects that are not actually observed.

Latin West. A detailed discussion of the possibility of the Earth's motion is widely contained in the writings of the Parisian scholastics Jean Buridan, Albert of Saxony, and Nicholas of Oresme (second half of the 14th century). The most important argument in favor of the rotation of the Earth rather than the sky, given in their works, is the smallness of the Earth compared to the Universe, which makes attributing the daily rotation of the sky to the Universe highly unnatural.

Nikolai Orem.

Likewise, if the air were closed in a moving ship, then to a person surrounded by this air it would seem that the air was not moving... If a person were in a ship moving at high speed to the east, unaware of this movement, and if he extended his hand in a straight line along the mast of the ship, it would seem to him that his hand was making a linear movement; in the same way, according to this theory, it seems to us that the same thing happens to an arrow when we shoot it vertically upward or vertically downward. Inside a ship moving at high speed to the east, all kinds of motion can take place: longitudinal, transverse, down, up, in all directions - and they appear exactly the same as when the ship is stationary.

Oresme then gives a formulation that anticipates the principle of relativity:

I conclude, therefore, that it is impossible to demonstrate by any experiment that the heavens have a diurnal movement and that the earth does not.

However, Oresme's final verdict on the possibility of the Earth's rotation was negative. The basis for this conclusion was the text of the Bible:

However, so far everyone supports and I believe that it is [Heaven] and not the Earth that moves, for “God made the circle of the Earth, which will not be moved,” despite all the arguments to the contrary.

Renaissance and Modern Times

Nicolaus Copernicus.

In the 16th century, Copernicus was fully supported by astronomers Thomas Digges, Rheticus, Christoph Rothmann, Michael Möstlin, physicists Giambatista Benedetti, Simon Stevin, philosopher Giordano Bruno, and theologian Diego de Zuniga. Some scientists accepted the rotation of the Earth around its axis, rejecting its translational motion. This was the position of the German astronomer Nicholas Reimers, also known as Ursus, as well as the Italian philosopher Francesco Patrizi. The point of view of the outstanding physicist William Gilbert, who supported the axial rotation of the Earth, but did not speak out about its translational motion, is not entirely clear. At the beginning of the 17th century, the heliocentric system of the world (including the rotation of the Earth on its axis) received impressive support from Galileo Galilei and Johannes Kepler. The most influential opponents of the idea of Earth motion in the 16th and early 17th centuries were the astronomers Tycho Brahe and Christopher Clavius.

The hypothesis of the rotation of the Earth and the formation of classical mechanics. Essentially, in the XVI-XVII centuries. the only argument in favor of the axial rotation of the Earth was that in this case there is no need to attribute enormous rotation rates to the stellar sphere, because even in antiquity it was already reliably established that the size of the Universe significantly exceeds the size of the Earth (this argument was contained in Buridan and Oresme) .

Not only the Earth rotates with the water element connected to it, but also a considerable part of the air and everything that is in any way akin to the Earth, or the air closest to the Earth, saturated with earthly and watery matter, follows the same laws of nature as The Earth, or has acquired motion, which is imparted to it by the adjacent Earth in constant rotation and without any resistance

Thus, the main role in the unobservability of the Earth's rotation is played by the entrainment of air by its rotation. The majority of Copernicans in the 16th century shared the same opinion.

Galileo Galilei.

Jesus cried to the Lord on the day that the Lord delivered the Amorites into the hands of Israel, when he defeated them in Gibeon, and they were beaten before the children of Israel, and said before the Israelites: Stand, O sun, over Gibeon, and the moon, over the valley of Avalon. !

You have set the earth on firm foundations: it will not be shaken for ever and ever.

These passages were considered to contradict both the view that the Earth rotates on its axis and the revolution around the Sun.

Proponents of the rotation of the Earth (notably Giordano Bruno, Johannes Kepler, and especially Galileo Galilei) pursued a defense on several fronts. First, they pointed out that the Bible was written in language understandable to ordinary people, and if its authors were written in scientifically clear terms, it would not be able to fulfill its main, religious mission. Thus, Bruno wrote:

In many cases it is foolish and inadvisable to make much reasoning according to truth rather than according to the given case and convenience. For example, if instead of the words: “The sun is born and rises, passes through noon and leans toward Aquilon,” the sage said: “The earth goes in a circle to the east and, leaving the sun, which sets, leans toward the two tropics, from Cancer to the South, from Capricorn to Aquilon,” then the listeners would begin to think: “How? Does he say the earth moves? What kind of news is this? In the end they would consider him a fool, and he would indeed be a fool.

This kind of answer was given mainly to objections concerning the diurnal movement of the Sun. Secondly, it was noted that some passages of the Bible must be interpreted allegorically. Thus, Galileo noted that if Holy Scripture is taken literally in its entirety, it will turn out that God has hands, is subject to emotions such as anger, etc. In general, the main idea of the defenders of the doctrine of the movement of the Earth was that science and religion have different goals: science examines the phenomena of the material world, guided by the arguments of reason, the goal of religion is the moral improvement of man, his salvation. Galileo in this regard quoted Cardinal Baronio that the Bible teaches how to ascend to heaven, not how heaven works.

The significance of the hypothesis about the rotation of the Earth for the development of science

Notes

Poincare, About science, With. 362-364.
This effect was first observed by Vincenzo Viviani (a student of Galileo) back in 1661 (Grammel 1923, Hagen 1930, Guthrie 1951).
Foucault's theory of the pendulum is described in detail in General physics course Sivukhin (T. 1, § 68).
Under Soviet rule, a 98 m long Foucault pendulum was demonstrated in St. Isaac's Cathedral (Leningrad).
Grammel 1923.
For more details, see Mikhailov 1984, p. 26.
For calculation of the effect, see General physics course Sivukhin (Vol. 1, § 67).
The angular velocity of the base and the apex is the same, but the linear velocity is equal to the product of the angular velocity and the radius of rotation.
A slightly different but equivalent explanation is based on Kepler's II law. The sectoral speed of a body moving in a gravitational field, proportional to the product of the radius vector of the body by the square of the angular velocity, is a constant value. Let's consider the simplest case, when the tower is located on the earth's equator. When the body is at the top, its radius vector is maximum (the radius of the Earth plus the height of the tower) and the angular velocity is equal to the angular velocity of the Earth's rotation. When a body falls, its radius vector decreases, which is accompanied by an increase in the angular velocity of the body. Thus, the average angular velocity of the body turns out to be slightly greater than the angular velocity of the Earth's rotation.
See Armitage 1947 for historical overview.

What explains the rotation of the starry sky. Rotation of the starry sky

Inertia forces

Effects of centrifugal force

Coriolis force effects: laboratory experiments

Coriolis force effects: phenomena in the surrounding nature

Optical experiments

Uneven rotation

Precession and nutation

Middle Ages

India

Islamic East

Latin West

Renaissance and Modern Times

The hypothesis of the rotation of the Earth and the development of classical mechanics

Religious context for the Earth's rotation debate

The significance of the hypothesis about the rotation of the Earth for the development of science

Notes

Literature

Inertia forces

Effects of centrifugal force

Coriolis force effects: laboratory experiments

Coriolis force effects: phenomena in the surrounding nature

Optical experiments

Uneven rotation

Precession and nutation

Change of pole position

Slowdown of rotation over time

Origin of the Earth's rotation

History of the idea of ​​the Earth's daily rotation

Antiquity

Renaissance and Modern Times

The significance of the hypothesis about the rotation of the Earth for the development of science

Notes

History of the idea of the Earth's daily rotation