Our natural satellite is the moon. The orbit of the moon. The Moon's own motion. The visible orbit of the moon

The moon is a satellite of our planet, attracting the eyes of scientists and just curious people from time immemorial. In the ancient world, both astrologers and astronomers dedicated impressive treatises to her. Poets did not lag behind them. Today, little has changed in this sense: the orbit of the Moon, the features of its surface and interior are carefully studied by astronomers. Horoscope compilers also do not take their eyes off her. The influence of the satellite on the Earth is studied by both. Astronomers study how the interaction of two cosmic bodies is reflected in the movement and other processes of each. During the study of the moon, knowledge in this area has increased significantly.

Origin

According to research by scientists, the Earth and the Moon were formed at about the same time. Both bodies are 4.5 billion years old. There are several theories about the origin of the satellite. Each of them explains individual features of the moon, but leaves several unresolved questions. The theory of a giant collision is considered the closest to the truth today.

According to the hypothesis, a planet similar in size to Mars collided with the young Earth. The impact hit on a tangent and caused the ejection into space of most of the substance of this cosmic body, as well as a certain amount of terrestrial "material". A new object was formed from this substance. The radius of the Moon's orbit was originally sixty thousand kilometers.

The giant collision hypothesis explains well many of the structural features and chemical composition satellite, most of the characteristics of the Moon-Earth system. However, if we take the theory as a basis, some facts still remain incomprehensible. Thus, the iron deficiency on the satellite can only be explained by the fact that by the time of the collision, differentiation of the inner layers had taken place on both bodies. To date, there is no evidence that this was the case. And nevertheless, despite such counterarguments, the hypothesis of a giant collision is considered to be the main one all over the world.

Parameters

The moon, like most other satellites, has no atmosphere. Found only traces of oxygen, helium, neon and argon. The surface temperature between illuminated and shaded areas is therefore very different. On the sunny side, it can rise to +120 ºС, and on the dark side it can drop to -160 ºС.

The average distance between the Earth and the Moon is 384 thousand km. The satellite is almost a perfect ball in shape. The difference between the equatorial and polar radii is small. They are 1738.14 and 1735.97 km, respectively.

A complete revolution of the Moon around the Earth takes just over 27 days. For the observer, the movement of a satellite across the sky is characterized by a phase change. The time from one full moon to another is slightly longer than the indicated period and is approximately 29.5 days. The difference arises because the Earth and the satellite also move around the Sun. The moon, in order to be in its original position, has to overcome a little more than one circle.

System "Earth-Moon"

The moon is a satellite that is somewhat different from other similar objects. Its main feature in this sense is mass. It is estimated at 7.35 * 10 22 kg, which is approximately 1/81 of that of the Earth. And if the mass itself is not something out of the ordinary in space, then its relationship with the characteristics of the planet is atypical. As a rule, the mass ratio in satellite-planet systems is somewhat less. Only Pluto and Charon can boast of a similar ratio. These two cosmic bodies some time ago began to be characterized as a system of two planets. It seems that this designation is also true in the case of the Earth and the Moon.

Moon movement in orbit

The satellite makes one revolution around the planet relative to the stars per sidereal month, which lasts 27 days, 7 hours and 42.2 minutes. The Moon's orbit is elliptical in shape. V different periods the satellite is located either closer to the planet, then further from it. The distance between the Earth and the Moon varies from 363 104 to 405 696 kilometers.

Another piece of evidence is associated with the trajectory of the satellite in favor of the assumption that the Earth with the satellite should be considered as a system consisting of two planets. The orbit of the Moon is not located near the equatorial plane of the Earth (as is typical for most satellites), but practically in the plane of rotation of the planet around the Sun. The angle between the ecliptic and the satellite's trajectory is just over 5º.

The Moon's orbit around the Earth is influenced by many factors. In this regard, determining the exact trajectory of a satellite is not an easy task.

A bit of history

The theory that explains how the moon moves was laid back in 1747. The author of the first calculations, which brought scientists closer to understanding the features of the satellite's orbit, was the French mathematician Clairaut. Then, in the distant eighteenth century, the rotation of the moon around the earth was often put forward as an argument against Newton's theory. The calculations made with the use were strongly at variance with the apparent movement of the satellite. Clairaud solved this problem.

Such famous scientists as D'Alembert and Laplace, Euler, Hill, Puiseau and others were engaged in the study of the issue. The modern theory of the Moon's revolution actually began with the work of Brown (1923). Research by a British mathematician and astronomer helped bridge the gap between calculation and observation.

Difficult task

The Moon's movement consists of two main processes: rotation around its axis and rotation around our planet. It would not be so difficult to derive a theory explaining the movement of a satellite if its orbit were not influenced by various factors. This is the attraction of the Sun, and the features of the shape of the Earth and other planets. Such influences disturb the orbit and it becomes difficult to predict the exact position of the Moon at a particular period. In order to understand what is the matter here, let us dwell on some parameters of the satellite's orbit.

Ascending and descending node, line of apses

As mentioned, the Moon's orbit is tilted towards the ecliptic. The trajectories of movement of two bodies intersect at points called ascending and descending nodes. They are located on opposite sides of the orbit relative to the center of the system, that is, the Earth. The imaginary straight line that connects these two points is designated as a line of nodes.

The satellite closest to our planet is at the point of perigee. The maximum distance separates two cosmic bodies when the moon is at its apogee. The straight line connecting these two points is called the line of the apses.

Orbit disturbances

As a result of the influence on the movement of the satellite at once by a large number of factors, in fact, it is the sum of several movements. Let us consider the most noticeable of the arising perturbations.

The first is knot line regression. The straight line connecting the two points of intersection of the plane of the lunar orbit and the ecliptic is not fixed in one place. It moves very slowly in the opposite direction (hence called regression) to the satellite's motion. In other words, the plane of the Moon's orbit rotates in space. It takes 18.6 years for one complete revolution.

The line of apses is also moving. The movement of the straight line connecting the apocenter and periapsis is expressed in the rotation of the orbital plane in the same direction as the Moon is moving. This happens much faster than in the case of a line of nodes. A full turnaround takes 8.9 years.

In addition, the lunar orbit experiences fluctuations of a certain amplitude. Over time, the angle between its plane and the ecliptic changes. Values ​​range from 4 ° 59 "to 5 ° 17". As in the case of the knot line, the period of such fluctuations is 18.6 years.

Finally, the moon's orbit changes shape. It stretches a little, then returns to its original configuration. In this case, the eccentricity of the orbit (the degree of deviation of its shape from the circle) changes from 0.04 to 0.07. Change and return to original position take 8.9 years.

Not so simple

Basically, the four factors that need to be taken into account during the calculations are not so many. However, they do not exhaust all perturbations of the satellite's orbit. In fact, each parameter of the moon's motion is constantly influenced by a large number of factors. All this complicates the task of predicting the exact location of a satellite. Taking into account all these parameters is often the most important task. For example, the calculation of the Moon's trajectory and its accuracy affects the success of a spacecraft mission sent to it.

The influence of the moon on the earth

The satellite of our planet is relatively small, but its effect is clearly visible. Perhaps everyone knows that it is the Moon that forms the tides on Earth. Here you need to make a reservation right away: the sun also causes a similar effect, but due to the much greater distance, the tidal effect of the star is not very noticeable. In addition, the change in the water level in the seas and oceans is associated with the peculiarities of the rotation of the Earth itself.

The gravitational effect of the Sun on our planet is about two hundred times greater than the analogous parameter of the Moon. However, tidal forces primarily depend on the field inhomogeneity. The distance separating the Earth and the Sun smoothes them out, so the impact of the Moon close to us is more powerful (twice as significant as in the case of a star).

A tidal wave forms on the side of the planet that is this moment facing the night star. The tide also occurs on the opposite side. If the Earth were stationary, then the wave would move from west to east, located exactly under the moon. Its full turnover would be completed in over 27 days, that is, in a sidereal month. However, the period around the axis is slightly less than 24 hours. As a result, the wave travels along the planet's surface from east to west and completes one revolution in 24 hours and 48 minutes. Since the wave constantly meets the continents, it moves forward in the direction of the Earth's motion and outstrips the satellite of the planet in its run.

Removing the Moon's orbit

The tidal wave causes the movement of a huge body of water. This directly affects the movement of the satellite. An impressive part of the planet's mass is displaced from the line connecting the two bodies, and attracts the moon to itself. As a result, the satellite experiences a moment of force, which accelerates its movement.

At the same time, the continents running on a tidal wave (they move faster than the waves, since the Earth rotates at a higher speed than the Moon turns), are affected by a force that slows them down. This leads to a gradual slowdown in the rotation of our planet.

As a result of the tidal interaction of two bodies, as well as the action and angular momentum, the satellite moves to a higher orbit. At the same time, the speed of the moon decreases. In orbit, it starts to move more slowly. Something similar is happening with the Earth. It slows down, resulting in a gradual increase in the length of the day.

The moon is moving away from the Earth by about 38 mm per year. Research by paleontologists and geologists confirms the astronomers' calculations. The process of gradual slowing down of the Earth and the removal of the Moon began about 4.5 billion years ago, that is, from the moment of the formation of two bodies. The researchers' data support the assumption that earlier the lunar month was shorter, and the Earth rotated at a higher speed.

A tidal wave occurs not only in the waters of the world's oceans. Similar processes take place in the mantle and in the earth's crust. However, they are less noticeable because these layers are not as malleable.

The removal of the Moon and the slowing down of the Earth will not last forever. In the end, the period of rotation of the planet will be equal to the period of rotation of the satellite. The moon will "hover" over one area of ​​the surface. The earth and the satellite will always be facing the same side to each other. It is appropriate to remember here that part of this process has already been completed. It was the tidal interaction that led to the fact that the same side of the moon is always visible in the sky. In space, there is an example of a system in such equilibrium. These are already called Pluto and Charon.

The moon and earth are in constant interaction. It cannot be said which of the bodies influences the other more. In this case, both are also exposed to the influence of the sun. Other, more distant, cosmic bodies also play a significant role. Taking into account all such factors makes it quite difficult to accurately construct and describe the model of the satellite's orbital motion around our planet. However, a huge amount of accumulated knowledge, as well as constantly improving equipment, make it possible to more or less accurately predict the position of the satellite at any time and predict the future that awaits each object individually and the Earth-Moon system as a whole.

Why doesn't the moon rotate and we only see one side? June 18th, 2018

As many have already noticed, the Moon is always turned to the Earth by the same side. The question arises: is the rotation around their axes of these celestial bodies synchronous relative to each other?

Although the Moon rotates around its axis, it always faces the Earth with the same side, that is, the Moon's rotation around the Earth and rotation around its own axis is synchronized. This synchronization is caused by the friction of the tides that the Earth produced in the lunar shell.

Another mystery: does the moon rotate on its axis at all? The answer to this question lies in the solution of the semantic problem: who is at the forefront - an observer on Earth (in this case, the Moon does not rotate around its axis), or an observer in extraterrestrial space (then the only satellite of our planet rotates around its axis).

Let's do this simple experiment: draw two circles of the same radius, touching each other. Now imagine them as discs and mentally roll one disc along the edge of the other. In this case, the rims of the discs must be in continuous contact. So, how many times, in your opinion, the rolling disk will turn around its axis, making a full revolution around the static disk. Most will say once. To test this assumption, take two coins of the same size and repeat the experiment in practice. And what is the bottom line? The rolling coin has time to rotate twice on its axis before it makes one revolution around the stationary coin! Are you surprised?

On the other hand, does the rolling coin rotate? The answer to this question, as in the case of the Earth and the Moon, depends on the observer's frame of reference. The moving coin makes one revolution relative to the starting point of contact with the static coin. In relation to an outside observer, in one revolution around a stationary coin, the rolling coin turns twice.

Following the publication of this coin problem in Scientific American in 1867, the editorial board was literally inundated with letters from indignant readers who held the opposite opinion. They almost immediately drew a parallel between the paradoxes with coins and celestial bodies (the Earth and the Moon). Those who adhered to the point of view that a moving coin in one revolution around a stationary coin once manages to turn around its own axis, were inclined to think about the inability of the moon to rotate around its axis. Readers' activity regarding this problem has increased so much that in April 1868 it was announced that the controversy on this topic was stopped in the pages of Scientific American. It was decided to continue the controversy in the magazine The Wheel, specially devoted to this "great" problem. One issue at least came out. In addition to illustrations, it contained a variety of drawings and diagrams of intricate devices created by readers in order to convince editors that they were wrong.

Various effects generated by the rotation of celestial bodies can be detected using devices like Foucault's pendulum. If it is placed on the Moon, it turns out that the Moon, revolving around the Earth, makes revolutions around its own axis.

Can these physical considerations act as an argument confirming the rotation of the Moon around its axis, regardless of the observer's frame of reference? Oddly enough, from the point of view of general relativity, probably not. In general, we can assume that the Moon does not revolve at all, it is the Universe that revolves around it, creating gravitational fields like the Moon revolving in a stationary space. Of course, it is more convenient to take the Universe as a stationary frame of reference. However, if you think objectively, with regard to the theory of relativity, the question of whether this or that object really rotates or is at rest is generally meaningless. Only relative motion can be "real".
To illustrate, imagine that the Earth and the Moon are connected by a barbell. The rod is fixed on both sides rigidly in one place. This is a situation of mutual synchronization - one side of the Moon is visible from the Earth, and one side of the Earth is visible from the Moon. But this is not the case with us, this is how Pluto and Charon rotate. And we have a situation - one end is fixed rigidly on the Moon, and the other moves along the surface of the Earth. Thus, one side of the Moon is visible from the Earth, and different sides of the Earth from the Moon.

Instead of a barbell, gravity acts. And her " rigid mount"causes tidal phenomena in the body, which gradually either slow down or speed up the rotation (depending on whether the satellite is rotating too quickly or too slowly).

Some other bodies in the solar system are already in this synchronization too.

Thanks to photography, we can still see more than half of the Moon's surface, not 50% - one side, but 59%. There is a phenomenon of libration - the apparent oscillatory motion of the moon. They are caused by irregularities in orbits (not ideal circles), tilts of the axis of rotation, and tidal forces.

The moon is in tidal grip on the Earth. Tidal capture is a situation when the period of revolution of the satellite (Moon) around its axis coincides with the period of its revolution around the central body (Earth). In this case, the satellite always faces the central body with the same side, since it revolves around its axis for the same time it takes to orbit around its partner. Tidal capture occurs in the process of mutual motion and is characteristic of many large natural satellites of the planets of the solar system, and is also used to stabilize some artificial satellites. When observing a synchronous satellite from the central body, only one side of the satellite is always visible. When viewed from this side of the satellite, the central body "hangs" motionless in the sky. On the other side of the satellite, the central body is never visible.

Moon facts

There are moon trees on earth

Hundreds of tree seeds were brought to the moon during the 1971 Apollo 14 mission. Former American Forestry Officer (USFS) Stuart Roose took the seeds as personal cargo as part of the NASA / USFS project.

Upon their return to Earth, the seeds were germinated and the resulting moon seedlings were planted throughout the United States as part of the country's bicentennial celebration in 1977.

There is no dark side

Place your fist on the table, fingers down. You can see the back of it. Someone on the other side of the table will see knuckles. This is how we see the moon. Since it is tidally blocked in relation to our planet, we will always see it from the same point of view.
The notion of the "dark side" of the moon came out of popular culture - remember Pink Floyd's 1973 album "Dark Side of the Moon" and the thriller of the same name in 1990 - and really means the far, night side. The one that we never see and which is opposite to the side closest to us.

Over a period of time, we see more than half of the moon, thanks to libration

The moon moves along its orbital path and moves away from the Earth (at a rate of about one inch per year), accompanying our planet around the sun.
If you looked up at the Moon as it accelerated and slowed down on this journey, you would also see it wobble from north to south and west to east in a motion known as libration. As a result of this movement, we see part of the sphere, which is usually hidden (about nine percent).

However, we will never see another 41%.

Helium-3 from the Moon could solve the Earth's energy problems

The solar wind is electrically charged and from time to time collides with the Moon and is absorbed by the rocks of the lunar surface. One of the most valuable gases in this wind that is absorbed by the rocks is helium-3, a rare isotope of helium-4 (commonly used for balloons).

Helium-3 is perfect for meeting the needs of fusion reactors with subsequent energy generation.

One hundred tons of helium-3 could meet the energy needs of the Earth for a year, according to the calculations of Extreme Tech. The lunar surface contains about five million tons of helium-3, while there is only 15 tons on Earth.

The idea is this: we fly to the moon, extract helium-3 in the mine, collect it in tanks and send it to Earth. True, this may not happen very soon.

Is there some truth in the myths about full moon madness?

Not really. The assumption that the brain, one of the most watery organs of the human body, is influenced by the moon, is rooted in legends that are several thousand years old, even in the time of Aristotle.

Since the gravitational pull of the Moon controls the tides of the Earth's oceans, and humans are 60% water (and 73% brain), Aristotle and the Roman scientist Pliny the Elder believed that the Moon should have a similar effect on ourselves.

This idea gave rise to the terms "lunar madness", "transylvanian effect" (which became widespread in Europe during the Middle Ages) and "lunar madness". Films of the 20th century added fuel to the fire, linking the full moon to psychiatric disorders, car accidents, murders and other incidents.

In 2007, the government of the British seaside town of Brighton ordered additional police patrols to be sent during full moons (and on payday too).

Yet science says there is no statistical link between human behavior and a full moon, according to several studies, one of which was conducted by American psychologists John Rotton and Ivan Kelly. It is unlikely that the Moon affects our psyche, rather, it simply adds light, in which it is convenient to commit crimes.

Lost moonstones

In the 1970s, the Richard Nixon administration distributed stones brought from the lunar surface during the Apollo 11 and Apollo 17 missions to leaders of 270 countries.

Unfortunately, more than a hundred of these stones have gone missing and are believed to have gone to the black market. While at NASA in 1998, Joseph Gutheinz even conducted a covert operation called Lunar Eclipse to end the illegal sale of these stones.

What was all this hype about? A pea-sized lump of moonstone was valued at $ 5 million on the black market.

The moon belongs to Dennis Hope

At least he thinks so.

In 1980, exploiting a loophole in the 1967 UN Space Property Treaty that "no country" could claim the solar system, Nevada resident Dennis Hope wrote to the UN and announced the right to private property. He was not answered.

But why wait? Hope opened a lunar embassy and began selling one-acre plots for $ 19.99 each. For the UN solar system is almost the same as the world's oceans: outside the economic zone and owned by every inhabitant of the Earth. Hope claimed to have sold extraterrestrial real estate to celebrities and three former presidents USA.

It is unclear whether Dennis Hope really does not understand the wording of the treaty or is trying to force the legislature to make a legal assessment of its actions so that the development of heavenly resources begins under a more transparent legal environment.

Sources:

The natural satellite of the Earth is the Moon - a non-luminous body that reflects sunlight.

The study of the moon began in 1959, when the Soviet apparatus "Luna-2" first landed on the moon, and images were taken from space for the first time from the apparatus "Luna-3" back side The moon.

In 1966, the Luna-9 spacecraft landed on the moon and established a solid soil structure.

The first to visit the moon were the Americans Neil Armstrong and Edwin Aldrin. This happened on July 21, 1969. For further study of the moon, Soviet scientists preferred to use automatic vehicles - lunar rovers.

General characteristics of the moon

Average distance from the Earth, km
a. e.	363 104 0,0024
a. e.	405 696 0,0027
Average distance between the centers of the Earth and the Moon, km
The inclination of the orbit to the plane of its orbit
Average orbital speed	1,022
Average radius of the Moon, km
Weight, kg
Equatorial radius, km
Polar radius, km
Average density, g / cm 3
Equator inclination, deg.

The mass of the Moon is 1/81 of the mass of the Earth. The position of the Moon in its orbit corresponds to a particular phase (Fig. 1).

Rice. 1. Phases of the Moon

Moon phases- different positions relative to the Sun - new moon, first quarter, full moon and last quarter. During the full moon, the illuminated disc of the Moon is visible, since the Sun and the Moon are on opposite sides from the Earth. On a new moon, the moon is on the side of the sun, so the side of the moon facing the earth is not illuminated.

The Moon is always facing the Earth with one side.

The line that separates the illuminated part of the moon from the unlit part is called terminator.

In the first quarter, the Moon is visible at an angular distance of 90 "from the Sun, and the sun's rays illuminate only the right half of the Moon facing us. In other phases, the Moon is visible to us in the form of a crescent. Therefore, in order to distinguish the growing Moon from the old one, we must remember: the old Moon resembles the letter "C", and if the moon is growing, then you can mentally draw a vertical line in front of the moon and get the letter "P".

Due to the closeness of the Moon to the Earth and its large mass, they form the "Earth-Moon" system. The moon and earth rotate on their axes in the same direction. The orbital plane of the Moon is tilted to the plane of the Earth's orbit at an angle of 5 ° 9 ".

The intersection of the orbits of the Earth and the Moon are called nodes of the lunar orbit.

Sidereal(from Latin sideris - star) month is the period of rotation of the Earth around its axis and the same position of the Moon on the celestial sphere in relation to the stars. It is 27.3 Earth days.

Synodic(from the Greek synod - connection) a month is called a period of complete change lunar phases, that is, the period of the return of the moon to its original position relative to the moon and the sun (for example, from new moon to new moon). It averages 29.5 Earth days. The synodic month is two days longer than the sidereal month, since the Earth and the Moon rotate around their axes in the same direction.

The force of gravity on the moon is 6 times less strength gravity on Earth.

The relief of the Earth's satellite is well studied. Visible dark areas on the lunar surface are called “seas” - these are vast waterless low-lying plains (the largest is “Oksan Bury”), and light areas - “continents” - are mountainous, elevated areas. The main planetary structures of the lunar surface are ring craters up to 20-30 km in diameter and multi-ring circuses with a diameter of 200 to 1000 km.

The origin of the ring structures is different: meteorite, volcanic and shock-explosive. In addition, there are cracks, shears, domes, and fault systems on the lunar surface.

Investigations of the spacecraft "Luna-16", "Luna-20", "Luna-24" have shown that the surface clastic rocks of the Moon are similar to earthly igneous rocks - basalts.

The meaning of the moon in the life of the earth

Although the mass of the Moon is 27 million times less than the mass of the Sun, it is 374 times closer to the Earth and has a strong influence, causing water rises (high tides) in some places and low tides in others. This happens every 12 hours and 25 minutes, since the Moon makes a complete revolution around the Earth in 24 hours 50 minutes.

Due to the gravitational influence of the Moon and the Sun on the Earth, ebb and flow(fig. 2).

Rice. 2. Scheme of the occurrence of ebbs and flows on Earth

The most distinct and important in their consequences are tidal phenomena in a wave envelope. They represent periodic rises and falls in the level of the oceans and seas, caused by the forces of attraction of the Moon and the Sun (2.2 times less than the lunar).

In the atmosphere, tidal phenomena are manifested in semidiurnal changes in atmospheric pressure, and in the earth's crust - in deformation of the solid matter of the Earth.

On Earth, there are 2 high tides at the point closest and distant from the Moon and 2 low tides at points located at an angular distance of 90 ° from the Moon - Earth line. Allocate sigisial tides, which occur during the new moon and full moon and quadrature- in the first and last quarter.

In the open ocean, tidal events are small. Fluctuations in the water level reach 0.5-1 m. In the inland seas (Black, Baltic, etc.), they are almost not felt. However, depending on the latitude and outlines of the coastline of the continents (especially in narrow bays), the water during high tides can rise up to 18 m (Bay of Fundy in the Atlantic Ocean off the coast of North America), 13 m on the western coast of the Sea of ​​Okhotsk. In this case, tidal currents are formed.

The main meaning of tidal waves is that, mixing from east to west following the apparent motion of the Moon, they slow down the axial rotation of the Earth and lengthen the day, change the shape of the Earth by reducing the polar compression, cause pulsation of the Earth's shells, vertical displacements of the earth's surface, semidiurnal changes in atmospheric pressure, change the conditions of organic life in the coastal parts of the World Ocean and, finally, affect economic activity coastal countries. V whole line ports, seagoing vessels can only enter at high tide.

After a certain period of time on Earth repeat solar and lunar eclipses. You can see them when the Sun, Earth and Moon are in the same line.

Eclipse- an astronomical situation in which one celestial body blocks the light from another celestial body.

A solar eclipse occurs when the Moon gets between the observer and the Sun and obscures it. Since the Moon before the eclipse is facing us with its unlit side, there is always a new moon before the eclipse, that is, the Moon is not visible. One gets the impression that the Sun is covered by a black disk; the observer from the Earth sees this phenomenon as a solar eclipse (Fig. 3).

Rice. 3. Solar eclipse (relative sizes of bodies and distances between them are conditional)

A lunar eclipse occurs when the Moon, being in line with the Sun and the Earth, falls into a cone-shaped shadow cast by the Earth. The diameter of the Earth's shadow spot is minimum distance The Moon is 363,000 km from Earth, which is about 2.5 times the diameter of the Moon, so the entire Moon can be shaded (see Fig. 3).

Lunar rhythms are repetitive changes in the intensity and nature of biological processes. There are lunar-monthly (29.4 days) and lunar-diurnal (24.8 h) rhythms. Many animals and plants reproduce at a certain phase of the lunar cycle. Lunar rhythms are characteristic of many marine animals and plants of the coastal zone. So, people have noticed a change in well-being depending on the phases of the lunar cycle.

moon- the only celestial body that revolves around the Earth, except for the artificial satellites of the Earth, created by man in recent years.

The moon continuously moves across the starry sky and, in relation to some star, in a day shifts towards the diurnal rotation of the sky by about 13 °, and after 27.1 / 3 days it returns to the same stars, describing a full circle in the celestial sphere. Therefore, the period of time during which the Moon makes a complete revolution around the Earth in relation to the stars is called stellar (or sidereal) month; it is 27.1 / 3 days. The moon moves around the earth in an elliptical orbit, so the distance from the earth to the moon changes by almost 50 thousand km. The average distance from the Earth to the Moon is taken equal to 384 386 km (rounded up - 400 000 km). This is ten times the length of the Earth's equator.

moon itself does not emit light, therefore only its surface illuminated by the sun is visible in the sky - the daytime side. Night, dark, is not visible. Moving across the sky from west to east, the Moon shifts in 1 hour against the background of stars by about half a degree, that is, by an amount close to its apparent size, and in a day - by 13 degrees. FOR a month, the moon in the sky catches up and surpasses the sun, while the lunar phases change: new moon , first quarter , full moon and last quarter .

V new moon The moon cannot be seen even through a telescope. It is located in the same direction as the Sun (only above or below it), and is turned towards the Earth by the night hemisphere. Two days later, when the Moon moves away from the Sun, a narrow crescent can be seen a few minutes before its set in the western side of the sky against the background of the evening dawn. The Greeks called the first appearance of the crescent moon after the new moon "neomenia" ("new moon"). From this moment the lunar month begins.

7 days 10 hours after the new moon, a phase occurs called first quarter... During this time, the Moon moved away from the Sun by 90º. From the Earth, only the right half of the lunar disk is visible, illuminated by the Sun. After sunset moon is located on the southern side of the sky and sets around midnight. Continuing to move from the Sun all the way to the left. moon in the evening it is already on the eastern side of the sky. She comes in after midnight, every day later and later.

When moon turns out to be on the side opposite to the Sun (at an angular distance of 180 from it), comes full moon... 14 days 18 hours have passed since the new moon. After that moon begins to approach the Sun from the right.

There is a decrease in the illumination of the right side of the lunar disk. The angular distance between it and the Sun decreases from 180 to 90º. Again, only half of the lunar disk is visible, but already the left part of it. After the new moon, 22 days have passed 3 hours. last quarter... The moon rises around midnight and shines during the entire second half of the night, by the time the sun rises, it finds itself in the southern side of the sky.

The width of the crescent moon continues to decrease, and itself moon is gradually approaching the Sun from the right (western) side. Appearing in the eastern sky, every day later, the crescent moon becomes very narrow, but the horns are turned to the right and looks like the letter "C".

They say, moon old. An ashy light is visible on the nocturnal part of the disc. The angular distance between the Moon and the Sun decreases to 0º. Finally, moon catches up with the Sun and becomes invisible again. The next new moon is coming. Moon month ended. 29 days passed 12 hours 44 minutes 2.8 seconds, or almost 29.53 days. This period is called synodic month (from the Greek sy "nodos-connection, rapprochement).

The synodic period is associated with the position of a celestial body relative to the Sun, visible in the sky. Lunar synodic month is a period of time between successive phases of the same name The moon.

Your way in the sky relative to the stars moon makes 7 hours 43 minutes 11.5 seconds in 27 days (rounded - 27.32 days). This period is called sidereal (from Latin sideris-star), or stellar month .

№7 Eclipse of the Moon and the Sun, their analysis.

Solar and lunar eclipses are an interesting natural phenomenon, familiar to man since ancient times. They are relatively common, but they are not visible from all areas of the earth's surface and therefore seem rare to many.

A solar eclipse occurs when our natural satellite, the Moon, in its motion passes against the background of the Sun's disk. This always happens at the time of the new moon. The Moon is located closer to the Earth than the Sun, almost 400 times, and at the same time, its diameter is also about 400 times less than the diameter of the Sun. Therefore, the apparent dimensions of the Earth and the Sun are almost the same, and the Moon can cover the Sun with itself. But not every new moon is a solar eclipse. Due to the inclination of the Moon's orbit to Earth's orbit, the Moon usually "misses" a little and passes above or below the Sun at the time of the new moon. However, at least 2 times a year (but not more than five), the moon's shadow falls on the Earth and a solar eclipse occurs.

The lunar shadow and penumbra fall to the Earth in the form of oval spots, which are at a speed of 1 km. in sec. run across the earth's surface from west to east. In areas caught in the lunar shadow, a total solar eclipse is visible, that is, the Sun is completely covered by the Moon. In areas covered with partial shade, a partial solar eclipse occurs, that is, the Moon covers only part of the solar disk. Outside the penumbra boundary, an eclipse does not occur at all.

The maximum duration of the total eclipse phase does not exceed 7 minutes. 31 sec. But most often it is two to three minutes.

A solar eclipse starts from the right edge of the Sun. When the Moon completely closes the Sun, twilight sets in, as in dark twilight, and the brightest stars and planets appear in the darkened sky, and around the Sun you can see a beautiful radiant radiance of a pearl color - the solar corona, which is the outer layers of the solar atmosphere, not visible outside the eclipse from - for their low brightness in comparison with the brightness of the daytime sky. The appearance of the crown changes from year to year depending on solar activity. A pink glowing ring flashes over the entire horizon - this is the area covered with a lunar shadow penetrates sunlight from neighboring zones, where a total eclipse does not occur, but only the particular is observed.
SOLAR AND LUNAR ECLIPSES

The sun, moon and earth in the new moon and full moon stages rarely lie on the same line, because the lunar orbit does not lie exactly in the plane of the ecliptic, but at an inclination of 5 degrees to it.

Solar eclipses new moons... The moon blocks the sun from us.

Lunar eclipses... Sun, Moon and Earth are in line in stage full moon... The Earth blocks the Moon from the Sun. At the same time, the moon turns brick red.

Every year, on average, there are 4 solar and lunar eclipses. They always accompany each other. For example, if a new moon coincides with a solar eclipse, then a lunar eclipse occurs two weeks later, in the full moon phase.

Astronomically solar eclipses occur when the Moon, while moving around the Sun, completely or partially obscures the Sun. The apparent diameters of the Sun and the Moon are almost the same, so the Moon obscures the Sun completely. But this can be seen from the Earth in the full phase band. A partial solar eclipse is observed on both sides of the full phase strip.

The bandwidth of the total phase of a solar eclipse and its duration depend on the mutual distances of the Sun, Earth and Moon. As a result of changing distances, the apparent angular diameter of the Moon also changes. When it is slightly larger than the solar one, the total eclipse can last up to 7.5 minutes, when it is equal, then one instant, but if it is less, then the Moon does not completely cover the Sun at all. In the latter case, an annular eclipse occurs: a narrow, bright solar ring is visible around the dark lunar disk.

During a total solar eclipse, the Sun appears as a black disk surrounded by aurora (corona). Daylight is so dim that you can sometimes see stars in the sky.

A total lunar eclipse occurs when the moon falls into the cone of the earth's shadow.

A total lunar eclipse can last 1.5-2 hours. It can be observed from all over the night hemisphere of the Earth, where the Moon at the time of the eclipse was above the horizon. Therefore, in a given area, total lunar eclipses can be observed much more often than solar ones.

During a total lunar eclipse of the moon, the lunar disk remains visible, but takes on a dark red hue.

A solar eclipse occurs on a new moon, and a lunar one on a full moon. Most often, there are two lunar and two solar eclipses a year. The maximum possible number of eclipses is seven. After a certain period of time, lunar and solar eclipses are repeated in the same order. This interval was called saros, which translated from Egyptian means - repetition. Saros is approximately 18 years, 11 days. During each Saros, 70 eclipses occur, of which 42 are solar and 28 are lunar. Total solar eclipses from a certain area are observed less frequently than lunar eclipses, once every 200-300 years.

CONDITIONS FOR A SUN ECLIPSE

During a solar eclipse, the Moon passes between us and the Sun and hides it from us. Let us consider in more detail the conditions under which an eclipse of the Sun can occur.

Our planet Earth, rotating around its axis during the day, simultaneously moves around the Sun and makes a full revolution in a year. The Earth has a satellite - the Moon. The moon moves around the earth, and makes a complete revolution in 29 1/2 days.

The relative position of these three celestial bodies is changing all the time. When moving around the Earth, the Moon at certain periods of time finds itself between the Earth and the Sun. But the Moon is a dark, opaque solid ball. Caught between the Earth and the Sun, it, like a huge shutter, closes the Sun with itself. At this time, that side of the Moon, which is facing the Earth, turns out to be dark, unlit. Therefore, a solar eclipse can only occur during a new moon. On a full moon, the Moon passes away from the Earth in the opposite direction to the Sun, and may fall into the shadow cast by the globe. Then we will observe a lunar eclipse.

The average distance from the Earth to the Sun is 149.5 million km, and the average distance from the Earth to the Moon is 384 thousand km.

The closer the object is, the larger it seems to us. The Moon, in comparison with the Sun, is almost 400 times closer to us, and at the same time, its diameter is also about 400 times smaller than the Sun's diameter. Therefore, the apparent sizes of the Moon and the Sun are almost the same. The moon, thus, can close the sun from us.

However, the distances of the Sun and Moon from the Earth do not remain constant, but change slightly. This happens because the path of the Earth around the Sun and the path of the Moon around the Earth are not circles, but ellipses. With a change in the distance between these bodies, their apparent sizes also change.

If at the time of a solar eclipse the Moon is at the smallest distance from the Earth, then the lunar disk will be slightly larger than the solar one. The moon will completely cover the sun, and the eclipse will be complete. If, during an eclipse, the Moon is at the greatest distance from the Earth, then it will have a slightly smaller apparent size and will not be able to completely cover the Sun. The light rim of the Sun will remain uncovered, which during an eclipse will be visible as a bright thin ring around the black disk of the Moon. Such an eclipse is called annular.

It would seem that solar eclipses should happen monthly, every new moon. However, this does not happen. If the Earth and the Moon moved in a visible plane, then on each new moon the Moon would indeed appear exactly on a straight line connecting the Earth and the Sun, and an eclipse would occur. In fact, the Earth moves around the Sun in one plane, and the Moon around the Earth in another. These planes do not match. Therefore, often during new moons, the moon comes either higher than the sun or lower.

The apparent path of the moon in the sky does not coincide with the path along which the sun moves. These paths intersect at two opposite points, which are called lunar nodes. Near these points, the paths of the Sun and the Moon come close to each other. And only when the new moon occurs near the node, it is accompanied by an eclipse.

The eclipse will be total or annular if the Sun and Moon are almost in a node during the new moon. If the Sun at the time of the new moon turns out to be at some distance from the node, then the centers of the lunar and solar disks will not coincide and the Moon will only partially cover the Sun. Such an eclipse is called partial.

The moon moves among the stars from west to east. Therefore, the closure of the Sun by the Moon begins from its western, i.e., right, edge. The degree of closure is called by astronomers the phase of the eclipse.

Around the spot of the lunar shadow there is a penumbra region, here the eclipse is frequent. The diameter of the penumbra region is about 6-7 thousand km. For an observer who will be near the edge of this region, only a small fraction of the solar disk will be covered by the Moon. Such an eclipse can go unnoticed at all.

Is it possible to accurately predict the onset of an eclipse? Scientists have established in antiquity that after 6585 days and 8 hours, which is 18 years 11 days 8 hours, eclipses are repeated. This happens because it is after such a period of time that the location of the Moon, Earth and the Sun in space is repeated. This gap was called saros, which means repetition.

During one Saros, on average, there are 43 solar eclipses, of which 15 are partial, 15 are annular and 13 are total. Adding to the dates of eclipses observed during one Saros, 18 years, 11 days and 8 hours, we can predict the onset of eclipses in the future.

In the same place on Earth, a total solar eclipse is observed once every 250 - 300 years.

Astronomers have calculated the conditions for the visibility of solar eclipses for many years to come.

LUNAR ESCAPES

Lunar eclipses are also among the "extraordinary" celestial phenomena. They happen like this. The full light circle of the Moon begins to darken at its left edge, a round brown shadow appears on the lunar disk, it moves further and further and after about an hour covers the entire Moon. The moon fades and turns reddish-brown.

The diameter of the Earth is almost 4 times the diameter of the Moon, and the shadow from the Earth, even at the distance of the Moon from the Earth, is more than 2 1/2 times the size of the Moon. Therefore, the Moon can completely plunge into the earth's shadow. A total lunar eclipse is much longer than a solar eclipse: it can last 1 hour and 40 minutes.

For the same reason that solar eclipses do not occur every new moon, lunar eclipses do not occur every full moon. The largest number of lunar eclipses in a year is 3, but there are years without eclipses at all; this was, for example, 1951.

Lunar eclipses are repeated at the same time interval as solar ones. During this interval, in 18 years 11 days 8 hours (saros), there are 28 lunar eclipses, of which 15 are partial and 13 are total. As you can see, the number of lunar eclipses in Saros is much less than solar eclipses, and yet lunar eclipses can be observed more often than solar ones. This is due to the fact that the Moon, plunging into the shadow of the Earth, ceases to be visible on the entire half of the Earth not illuminated by the Sun. This means that each lunar eclipse is visible over a much larger territory than any solar one.

An eclipsed moon does not disappear completely, like the sun during a solar eclipse, but is faintly visible. This happens because part of the sun's rays comes through the earth's atmosphere, refracts in it, enters the earth's shadow and hits the moon. Since the red rays of the spectrum are least scattered and attenuated in the atmosphere. The moon during an eclipse takes on a copper-red or brown hue.

CONCLUSION

It is difficult to imagine that solar eclipses occur so often: after all, each of us has to observe eclipses extremely rarely. This is explained by the fact that during a solar eclipse, the shadow from the Moon does not fall on the entire Earth. The fallen shadow has the shape of an almost round spot, the diameter of which can reach at most 270 km. This spot will cover only a negligible fraction of the earth's surface. At the moment, only on this part of the Earth will a total solar eclipse be visible.

The moon moves in its orbit at a speed of about 1 km / sec, that is, faster than a rifle bullet. Consequently, its shadow moves at high speed along the earth's surface and cannot cover any one place on the globe for a long time. Therefore, a total solar eclipse can never last more than 8 minutes.

Thus, the lunar shadow, moving along the Earth, describes a narrow but long strip, on which a total solar eclipse is consistently observed. The total solar eclipse strip is several thousand kilometers long. And yet the area covered by the shadow turns out to be insignificant in comparison with the entire surface of the Earth. In addition, oceans, deserts and sparsely populated areas of the Earth often find themselves in a total eclipse strip.

The sequence of eclipses repeats almost exactly in the same order over a period of time called saros (saros is an Egyptian word meaning "repetition"). Saros, known in antiquity, is 18 years and 11.3 days. Indeed, eclipses will repeat in the same order (after some initial eclipse) after as long as necessary for the same phase of the Moon to occur at the same distance of the Moon from the node of its orbit, as in the initial eclipse.

During each Saros, 70 eclipses occur, of which 41 are solar and 29 are lunar. Thus, solar eclipses occur more often than lunar ones, but at a given point on the surface of the Earth, lunar eclipses can be observed more often, since they are visible on the whole hemisphere of the Earth, while solar eclipses are visible only in a relatively narrow strip. It is especially rare to see total solar eclipses, although there are about 10 of them during each Saros.

№8 The Earth is like a ball, an ellipsoid of revolution, a 3-axis ellipsoid, a geoid.

Assumptions about the sphericity of the earth appeared in the 6th century BC, and from the 4th century BC, some of the evidence known to us was expressed that the Earth has the shape of a ball (Pythagoras, Eratosthenes). The proofs of the sphericity of the Earth by ancient scientists were based on the following phenomena:
- a circular view of the horizon in open spaces, plains, seas, etc.;
- the circular shadow of the Earth on the surface of the Moon at lunar eclipses;
- change in the height of stars when moving from north (N) to south (S) and back, due to the bulge of the midday line, etc. In the work "On the sky" Aristotle (384 - 322 BC) indicated that The earth is not only spherical in shape, but also has finite dimensions; Archimedes (287 - 212 BC) argued that the surface of water in a calm state is a spherical surface. They also introduced the concept of a spheroid of the Earth, as a geometric figure close in shape to a ball.
The modern theory of studying the figure of the Earth originates from Newton (1643 - 1727), who discovered the law of universal gravitation and applied it to study the figure of the Earth.
By the end of the 80s of the 17th century, the laws of motion of planets around the Sun were known, the very exact dimensions of the globe, determined by Picard from degree measurements (1670), the fact of a decrease in the acceleration of gravity on the Earth's surface from north (N) to south (S ), the laws of mechanics of Galileo and Huygens' research on the motion of bodies along a curvilinear trajectory. Generalization of these phenomena and facts led scientists to a well-founded view of the spheroidism of the Earth, i.e. its deformation in the direction of the poles (flatness).
The famous work of Newton - "Mathematical principles natural philosophy"(1867) expounds a new teaching about the figure of the Earth. Newton came to the conclusion that the figure of the Earth should be in the form of an ellipsoid of revolution with a slight polar compression (this fact was justified by him by a decrease in the length of the second pendulum with decreasing latitude and decreasing gravity from pole to equator due to the fact that “Earth slightly higher at the equator ").
Based on the hypothesis that the Earth consists of a homogeneous mass of density, Newton theoretically determined the polar compression of the Earth (α) in the first approximation equal to approximately 1: 230. In fact, the Earth is inhomogeneous: the crust has a density of 2.6 g / cm3, while the average density of the Earth is 5.52 g / cm3. The uneven distribution of the Earth's masses produces extensive gentle bulges and concavities, which combine to form hills, depressions, depressions and other forms. Note that individual elevations above the Earth reach heights of more than 8000 meters above the ocean surface. It is known that the surface of the World Ocean (MO) occupies 71%, land - 29%; average depth of MO (World Ocean) 3800m, and average height sushi - 875 m. total area the earth's surface is 510 x 106 km2. From the given data, it follows that most of the Earth is covered with water, which gives grounds to take it for a level surface (UE) and, ultimately, for the general figure of the Earth. The figure of the Earth can be imagined by imagining a surface, at each point of which the force of gravity is directed along the normal to it (along the plumb line).
A complex figure of the Earth, limited by a level surface, which is the beginning of the report of heights, is usually called a geoid. Otherwise, the surface of the geoid, as an equipotential surface, is fixed by the surface of the oceans and seas in a calm state. Below continents, the surface of the geoid is defined as the surface perpendicular to the lines of force (Figure 3-1).
P.S. The name of the Earth's figure - geoid - was proposed by the German physicist I.B. Listig (1808 - 1882). When mapping the earth's surface, on the basis of many years of research by scientists, a complex geoid figure, without sacrificing accuracy, is replaced by a mathematically simpler one - ellipsoid of revolution. Ellipsoid of rotation- a geometric body formed as a result of the rotation of an ellipse around a minor axis.
The ellipsoid of revolution comes close to the body of the geoid (the deviation does not exceed 150 meters in some places). The dimensions of the earth's ellipsoid were determined by many scientists in the world.
Fundamental studies of the figure of the Earth, carried out by Russian scientists F.N. Krasovsky and A.A. Izotov, allowed to develop the idea of ​​a triaxial earth ellipsoid, taking into account large geoid waves, as a result, its main parameters were obtained.
In recent years (late XX and early XXI centuries), the parameters of the Earth's figure and external gravitational potential have been determined using space objects and the use of astronomical-geodetic and gravimetric research methods so reliably that now it comes on the assessment of their measurements in time.
The triaxial terrestrial ellipsoid, which characterizes the figure of the Earth, is subdivided into a common terrestrial ellipsoid (planetary), suitable for solving global problems of cartography and geodesy, and a reference ellipsoid, which is used in certain regions, countries of the world and their parts. An ellipsoid of revolution (spheroid) is a surface of revolution in three-dimensional space formed by rotating the ellipse around one of its principal axes. An ellipsoid of revolution is a geometric body formed as a result of the rotation of an ellipse around a minor axis.

Geoid- the figure of the Earth, limited by the level surface of the gravity potential, coinciding in the oceans with the mean ocean level and extended under the continents (continents and islands) so that this surface is everywhere perpendicular to the direction of gravity. The surface of the geoid is smoother than the physical surface of the Earth.

Geoid shape is not precise mathematical expression, and for the construction of cartographic projections, the correct geometric figure is selected, which differs little from the geoid. The best approximation of a geoid is the shape obtained by rotating an ellipse about a short axis (ellipsoid)

The term "geoid" was proposed in 1873 by the German mathematician Johann Benedict Listing to denote geometric shape more accurately than an ellipsoid of revolution, reflecting the unique shape of planet Earth.

An extremely complex figure - a geoid. It exists only in theory, but in practice it can neither be touched nor seen. You can imagine a geoid in the form of a surface, the force of gravity at each point of which is directed strictly vertically. If our planet were a regular ball, uniformly filled with some substance, then the plumb line at any of its points would look at the center of the ball. But the situation is complicated by the fact that the density of our planet is inhomogeneous. In some places there are heavy rocks, in others voids, mountains and depressions are scattered over the entire surface, plains and seas are also unevenly distributed. All this changes the gravitational potential at each specific point. The fact that the shape of the globe is a geoid is also to blame for the ethereal wind that blows on our planet from the north.

Seems like a stupid question and maybe even a school student can answer it. Nevertheless, the rotation mode of our satellite is not described accurately enough and, moreover, in the calculations there is gross mistake- the presence of water ice at its poles has not been taken into account. This fact should be clarified, as well as remember that the first to point out the fact of the strange rotation of our natural satellite was the great Italian astronomer: Gian Domenico Cassini.

How does the moon rotate?

It is well known that the equator of the Earth is inclined 23 ° and 28 'to the plane of the ecliptic, that is, the plane closest to the Sun. It is this fact that leads to the change of seasons, which is extremely important for life on our planet. We also know that the plane of the Moon's orbit is tilted at an angle of 5 ° 9 'in relation to the plane of the ecliptic. We also know that the Moon is always directed towards the Earth with one side. The action of tidal forces on Earth depends on this. In other words, the Moon rotates around the Earth in the same time it takes to complete a revolution around its own axis. Thus, we automatically receive part of the answer to the question indicated in the title: "The moon rotates around its axis and its period is exactly equal to the full revolution around the Earth."

However, who knows the direction of rotation of the moon's axis? This fact is not known to everyone, and moreover, astronomers admit their mistake in the formula for calculating the direction of rotation, and this is due to the fact that the calculations did not take into account the presence of water ice at the poles of our satellite.

There are craters on the lunar surface in close proximity to the poles that never receive sunlight... In those places, it is constantly cold and it is quite possible that in these places reserves of water ice could be stored, delivered to the Moon by comets falling on its surface.

NASA scientists have also proven the truth of this hypothesis. This is easy to understand, but another question arises: “Why are there areas that are never illuminated by the Sun? The craters are not deep enough to hide their reserves, provided there is a general favorable geometry. "

Take a look at the photo of the moon's south pole:

This image was captured by NASA with the Lunar Reconnaissance Orbiter, a spacecraft in orbit around the Moon that continually takes photographs of the Moon's surface for optimal planning of future missions. Each photo taken at the South Pole, over six months, was binarized so that each pixel illuminated by the Sun was assigned a value of 1, while in the shade a value of 0. These photographs were then processed by defining for each pixel percent of the time during which it was lit. As a result of "lighting the map", scientists saw that some areas remain always in the shadow, and several (volcanic ridges or peaks) remain always visible to the Sun. Grayscale rather than reflecting areas that have gone through a period of illumination, which is dimming. Really impressive and instructive.

Let's return, however, to our question. To achieve this result, namely, to be constantly in complete darkness of large areas, it is necessary that the axis of rotation of the Moon was directed to the right with respect to the Sun, in particular, which is practically perpendicular to the ecliptic.

However, the lunar equator is tilted with respect to the ecliptic by only 1 ° 32 '. It would seem an insignificant indicator, but it suggests that there is water at the poles of our satellite, which is in a physical state - ice.

This geometric configuration had already been studied and translated into law by the astronomer Gian Domenico Cassini in 1693 in Liguria, during his study of tides and their effect on the satellite. With respect to the Moon, they sound like this:

1) The period of rotation of the Moon is synchronized with the period of revolution around the Earth.
2) The axis of rotation of the Moon is maintained at a fixed angle relative to the plane of the ecliptic.
3) The axes of rotation, the normal to the orbit and the normal ecliptic lie in the same plane.

After three centuries, these laws have recently been tested using more modern methods of celestial mechanics, which have confirmed their accuracy.