Since time immemorial, the moon has been a constant satellite of our planet and the closest celestial body to it. Naturally, a person always wanted to go there. But is it far to fly there and what is the distance to it?

The distance from the Earth to the Moon is theoretically measured from the center of the Moon to the center of the Earth. It is impossible to measure this distance with the usual methods used in ordinary life. Therefore, the distance to the earth's satellite was calculated using trigonometric formulas.

Like the Sun, the Moon experiences constant motion in Earth's sky near the ecliptic. However, this movement is significantly different from the movement of the Sun. So the planes of the orbits of the Sun and the Moon differ by 5 degrees. It would seem that, as a result of this, the trajectory of the Moon in the earth's sky should be similar in general terms to the ecliptic, differing from it only by a shift of 5 degrees:

In this, the movement of the Moon resembles the movement of the Sun - from west to east, in the opposite direction to the daily rotation of the Earth. But besides that, the Moon moves through the earth's sky much faster than the Sun. This is due to the fact that the Earth revolves around the Sun in about 365 days (Earth year), and the Moon around the Earth in just 29 days (lunar month). This difference became the stimulus for breaking down the ecliptic into 12 zodiac constellations (in one month the Sun moves along the ecliptic by 30 degrees). During the lunar month, there is a complete change in the phases of the moon:

In addition to the trajectory of the Moon's motion, the factor of the strong elongation of the orbit is also added. The eccentricity of the Moon's orbit is 0.05 (for comparison, this parameter for the Earth is 0.017). The difference from the circular orbit of the Moon leads to the fact that the apparent diameter of the Moon is constantly changing from 29 to 32 arc minutes.

During the day, the Moon shifts relative to the stars by 13 degrees, and by about 0.5 degrees per hour. Modern astronomers often use lunar occultations to estimate the angular diameters of stars near the ecliptic.

What determines the movement of the moon

An important point in the theory of the motion of the moon is the fact that the orbit of the moon in outer space is not constant and stable. Due to the relatively small mass of the Moon, it is subject to constant perturbations from more massive objects in the Solar System (primarily the Sun and the Moon). In addition, the Moon's orbit is affected by the oblateness of the Sun and the gravitational fields of other planets in the Solar System. As a result, the eccentricity of the Moon's orbit fluctuates between 0.04 and 0.07 with a period of 9 years. The result of these changes was such a phenomenon as a supermoon. A supermoon is an astronomical phenomenon in which the full moon is several times larger in angular size than usual. So during the full moon on November 14, 2016, the Moon was at a record close distance since 1948. In 1948, the Moon was 50 km closer than in 2016.

In addition, fluctuations in the inclination of the lunar orbit to the ecliptic are also observed: by about 18 arc minutes every 19 years.

What is equal to

Spacecraft will have to spend a lot of time flying to the earth's satellite. You cannot fly to the Moon in a straight line - the planet will orbit away from the destination, and the path will have to be corrected. At an escape velocity of 11 km/s (40,000 km/h), the flight will theoretically take about 10 hours, but in reality it will take longer. This is because the ship at the start gradually increases the speed in the atmosphere, bringing it to a value of 11 km / s in order to escape from the Earth's gravitational field. Then the ship will have to slow down when approaching the Moon. By the way, this speed is the maximum that modern spacecraft have been able to achieve.

The notorious American moon flight in 1969, according to official figures, took 76 hours. NASA's New Horizons spacecraft was the fastest to reach the moon in 8 hours and 35 minutes. True, he did not land on the planetoid, but flew past - he had a different mission.

Light from the Earth to our satellite will get very quickly - in 1.255 seconds. But flying at light speeds is still in the realm of fantasy.

You can try to imagine the path to the moon in the usual values. On foot at a speed of 5 km / h, the road to the moon will take about nine years. If you drive a car at a speed of 100 km / h, then it will take 160 days to get to the earth's satellite. If planes flew to the moon, then the flight to it would last about 20 days.

How ancient Greek astronomers calculated the distance to the moon

The Moon was the first celestial body to which it was possible to calculate the distance from the Earth. It is believed that astronomers in ancient Greece were the first to do this.

They tried to measure the distance to the Moon from time immemorial - the first to try to do this was Aristarchus of Samos. He estimated the angle between the Moon and the Sun at 87 degrees, so it turned out that the Moon is 20 times closer than the Sun (the cosine of an angle equal to 87 degrees is 1/20). The angle measurement error resulted in a 20-fold error, today it is known that this ratio is actually 1 to 400 (the angle is approximately 89.8 degrees). The big error was caused by the difficulty of estimating the exact angular distance between the Sun and the Moon using the primitive astronomical instruments of the Ancient World. By this time, regular solar eclipses had already allowed ancient Greek astronomers to conclude that the angular diameters of the Moon and the Sun were approximately the same. In this regard, Aristarchus concluded that the Moon is 20 times smaller than the Sun (actually, about 400 times).

To calculate the size of the Sun and Moon relative to the Earth, Aristarchus used a different method. We are talking about observations of lunar eclipses. By this time, ancient astronomers had already guessed the reasons for these phenomena: the Moon is eclipsed by the shadow of the Earth.

The diagram above clearly shows that the difference in distances from the Earth to the Sun and to the Moon is proportional to the difference between the radii of the Earth and the Sun and the radii of the Earth and its shadow to the distance of the Moon. At the time of Aristarchus, it was already possible to estimate that the radius of the Moon is approximately 15 arc minutes, and the radius of the earth's shadow is 40 arc minutes. That is, the size of the Moon turned out to be about 3 times smaller than the size of the Earth. From here, knowing the angular radius of the Moon, it was easy to estimate that the Moon is about 40 Earth diameters from the Earth. The ancient Greeks could only roughly estimate the size of the Earth. So Eratosthenes of Cyrene (276 - 195 BC), based on differences in the maximum height of the Sun above the horizon in Aswan and Alexandria during the summer solstice, determined that the radius of the Earth is close to 6287 km (the modern value is 6371 km). If we substitute this value into Aristarchus' estimate of the distance to the Moon, then it will correspond to approximately 502 thousand km (the modern value of the average distance from the Earth to the Moon is 384 thousand km).

A little later, the mathematician and astronomer of the 2nd century BC. e. Hipparchus of Nicaea calculated that the distance to the earth's satellite is 60 times greater than the radius of our planet. His calculations were based on observations of the movement of the Moon and its periodic eclipses.

Since at the time of the eclipse the Sun and the Moon will have the same angular dimensions, then according to the rules of similarity of triangles, you can find the ratio of the distances to the Sun and to the Moon. This difference is 400 times. Applying these rules again, only in relation to the diameters of the Moon and the Earth, Hipparchus calculated that the diameter of the Earth is 2.5 times greater than the diameter of the Moon. That is, R l \u003d R s / 2.5.

At an angle of 1′, one can observe an object whose dimensions are 3,483 times smaller than the distance to it - this information was known to everyone at the time of Hipparchus. That is, with an observed radius of the Moon of 15′, it will be 15 times closer to the observer. Those. the ratio of the distance to the Moon to its radius will be 3483/15= 232 or S l = 232R l.

Accordingly, the distance to the Moon is 232 * R s / 2.5 = 60 radii of the Earth. It turns out 6 371 * 60 = 382 260 km. The most interesting thing is that the measurements made with the help of modern instruments confirmed the correctness of the ancient scientist.

Now the measurement of the distance to the Moon is carried out with the help of laser instruments, which make it possible to measure it with an accuracy of several centimeters. In this case, the measurements take place in a very short time - no more than 2 seconds, during which the Moon moves away in orbit by about 50 meters from the point where the laser pulse was sent.

Evolution of Methods for Measuring the Distance to the Moon

Only with the invention of the telescope, astronomers were able to obtain more or less accurate values ​​for the parameters of the Moon's orbit and the correspondence of its size to the size of the Earth.

A more accurate method of measuring the distance to the moon appeared in connection with the development of radar. The first radiolocation of the Moon was carried out in 1946 in the USA and Great Britain. Radar made it possible to measure the distance to the Moon with an accuracy of several kilometers.

An even more accurate method of measuring the distance to the moon has become laser location. To implement it, several corner reflectors were installed on the Moon in the 1960s. It is interesting to note that the first experiments on laser ranging were carried out even before the installation of corner reflectors on the surface of the Moon. In 1962-1963, several experiments were carried out at the Crimean Observatory of the USSR on laser ranging of individual lunar craters using telescopes with a diameter of 0.3 to 2.6 meters. These experiments were able to determine the distance to the lunar surface with an accuracy of several hundred meters. In 1969-1972, astronauts of the Apollo program delivered three corner reflectors to the surface of our satellite. Among them, the reflector of the Apollo 15 mission was the most perfect, since it consisted of 300 prisms, while the other two (the Apollo 11 and Apollo 14 missions) only had a hundred prisms each.

In addition, in 1970 and 1973, the USSR delivered two more French corner reflectors to the lunar surface aboard the Lunokhod-1 and Lunokhod-2 self-propelled vehicles, each of which consisted of 14 prisms. The use of the first of these reflectors has a remarkable history. During the first 6 months of operation of the lunar rover with a reflector, it was possible to conduct about 20 sessions of laser location. However, then, due to the unfortunate position of the lunar rover, it was not possible to use the reflector until 2010. Only pictures of the new LRO apparatus helped to clarify the position of the lunar rover with the reflector, and thereby resume work sessions with it.

In the USSR, the largest number of laser ranging sessions were carried out on the 2.6-meter telescope of the Crimean Observatory. Between 1976 and 1983, 1400 measurements were made with this telescope with an error of 25 centimeters, then the observations were discontinued due to the curtailment of the Soviet lunar program.

In total, from 1970 to 2010, approximately 17,000 high-precision laser location sessions were conducted in the world. Most of them were associated with the Apollo 15 corner reflector (as mentioned above, it is the most advanced - with a record number of prisms):

Of the 40 observatories capable of performing laser ranging of the Moon, only a few can perform high-precision measurements:

Most of the ultra-precise measurements were made with the 2-meter telescope at the Texas MacDonald Observatory:

At the same time, the most accurate measurements are made by the APOLLO instrument, which was installed on the 3.5-meter telescope at the Apache Point Observatory in 2006. The accuracy of its measurements reaches one millimeter:

Evolution of the Moon and Earth system

The main goal of increasingly accurate measurements of the distance to the Moon is to try to better understand the evolution of the Moon's orbit in the distant past and in the distant future. By now, astronomers have come to the conclusion that in the past the Moon was several times closer to the Earth, and also had a much shorter rotation period (that is, it was not tidally trapped). This fact confirms the impact version of the formation of the Moon from the ejected matter of the Earth, which prevails in our time. In addition, the tidal effect of the Moon leads to the fact that the speed of the Earth's rotation around its axis gradually slows down. The speed of this process is an increase in the Earth's day every year by 23 microseconds. In one year, the Moon moves away from the Earth by an average of 38 millimeters. It is estimated that if the Earth-Moon system survives the transformation of the Sun into a red giant, then in 50 billion years the Earth day will be equal to the lunar month. As a result, the Moon and Earth will always face each other with only one side, as is currently observed in the Pluto-Charon system. By this time, the Moon will move away to approximately 600 thousand kilometers, and the lunar month will increase to 47 days. In addition, it is assumed that the evaporation of the Earth's oceans in 2.3 billion years will accelerate the process of the Moon's removal (the Earth's tides significantly slow down the process).

In addition, calculations show that in the future the Moon will again begin to approach the Earth due to tidal interaction with each other. When approaching the Earth at 12 thousand km, the Moon will be torn apart by tidal forces, the debris of the Moon will form a ring like the known rings around the giant planets of the Solar System. Other known satellites of the Solar System will repeat this fate much earlier. So Phobos is given 20-40 million years, and Triton is about 2 billion years.

Every year, the distance to the earth's satellite increases by an average of 4 cm. The reasons are the movement of the planetoid in a spiral orbit and the gradually decreasing power of the gravitational interaction between the Earth and the Moon.

Between the Earth and the Moon, theoretically, you can place all the planets of the solar system. If you add up the diameters of all the planets, including Pluto, you get a value of 382,100 km.

At any given time, the Moon is no closer than 361,000 and no further than 403,000 kilometers from the Earth. The distance from the Moon to the Earth changes because the Moon revolves around the Earth not in a circle, but in an ellipse. In addition, the Moon is little by little moving away from the Earth by an average of 5 centimeters per year. People have been observing the gradually decreasing moon for many centuries. A day may come when the Moon will break away from the Earth and fly away into space, becoming an independent celestial body. But this may not happen. The balance of gravitational forces keeps the Moon firmly in Earth orbit.

Why is the moon moving away from the earth?

Any moving body wants by inertia to continue its path in a straight line. A body moving in a circle tends to break away from the circle and fly tangentially to it. This tendency to break away from the axis of rotation is called centrifugal force. You feel the centrifugal force at the playground, on the high-speed swings, or when the car swerves sharply and pushes you against the door.

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Interesting facts about the moon

The word "centrifugal" means "running away from the center". The moon also strives to follow this force, but it is kept in orbit by the force of the earth's gravity. The moon stays in orbit because the centrifugal force is balanced by the earth's gravity. The closer to the planet its satellite is, the faster it revolves around it.

What is the reason? Any moving object has a moment of momentum. The moment of a rotating body depends on the mass, speed and distance from the axis of rotation. The moment can be calculated by multiplying these three quantities together. Scientists have found that the moment of rotation of a given body does not change. Therefore, when an object approaches the axis of rotation, due to the law of conservation of moment, it will rotate faster, since the mass in this equation cannot be changed arbitrarily.

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The moon used to be much closer to the earth

This law is called the law of conservation of torque. The moon makes one revolution around the earth in about 27 days. But 2.8 billion years ago, the Moon, closer to us, revolved around the Earth in 17 days. According to Clark Chapman, an astronomer at the Planetary Science Institute in Tucson, Arizona, the Moon was once even closer. At the time of the formation of the Lunar Earth 4.6 billion years ago, the period of the Moon's revolution was only 7 days. If then anyone could see the moon, he would be amazed by the huge size of the rising blood-red moon.

The tide of the oceans repels the moon

Surprisingly, the tides of the oceans are the very force that pushes the Moon away from the Earth. It happens like this. The gravitational force of the moon acts on the waters of the earth's oceans, attracting them. But the Earth does not stand still - it rotates around its axis. When the waters of the ocean swell, rushing towards the Moon, the Earth, by its rotation, sort of tears this mass of water from it.

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At the same time, the gravitational force of oceanic water pulls the Moon, but not directly towards itself, but slightly forward, in the course of the rotation of the globe. Therefore, the Moon receives an impulse directed not strictly along the radius of its orbit, but along a tangent to it. This phenomenon lengthens the moon's orbit. As the imperceptible (month after month) lengthening of the lunar orbit, the Moon is little - little by little moving away from the Earth. The process is very slow and imperceptible to the eye, but it lasts for millions of years and the total result is very noticeable.

Probably, someday the Moon will be so far from the Earth that the force of the earth's gravity will weaken, and the Moon will be able to go on an independent flight around the Sun. However, scientists believe that such loneliness is unlikely to threaten the Moon. After all, the tides act on the Earth too. The movement of masses of ocean water slows down the rotation of the Earth, so in 100 years the day increases by about half a minute. (Billions of years ago, a day lasted no more than six hours.)

Perhaps billions of years ago, the Moon revolved around the Earth in just 7 days.

In the future, after millions of years, the length of the day and the time of one revolution of the Moon around the Earth will still be equal, but will already far exceed twenty-four hours. When the Moon is far enough away from the Earth, their rotations will be more synchronous and the tides of the oceans will be exactly under the Moon. That's when the gravity of water will have an attractive effect on the Moon, and it will cease to move away from the Earth. The process will reverse when the tidal regions are behind the Moon. The Moon's orbit will begin to shorten, and it will gradually approach the Earth. Maybe there will come a time when the huge moon will again appear in the sky.

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• Could the Earth slow down...

MOSCOW, June 22 - RIA Novosti. Assumptions that the Moon in the future may leave the orbit of the Earth's satellite contradicts the postulates of celestial mechanics, Russian astronomers interviewed by RIA Novosti say.

Earlier, many Internet media, citing the words of Gennady Raikunov, director general of the "space" Central Research Institute of Mechanical Engineering, reported that in the future the Moon could leave the Earth and become an independent planet moving in its own orbit around the Sun. According to Raikunov, in this way the Moon can repeat the fate of Mercury, which, according to one hypothesis, was a satellite of Venus in the past. As a result, according to the general director of TsNIIMash, the conditions on Earth may become similar to those of Venus and will be unsuitable for life.

"It sounds like some kind of nonsense," Sergey Popov, a researcher at the Sternberg State Astronomical Institute of Moscow State University (GAISh), told RIA Novosti.

According to him, the Moon is really moving away from the Earth, but very slowly - at a speed of about 38 millimeters per year. "In a few billion years, the period of the Moon's revolution will simply increase by one and a half times, and that's it," Popov said.

"The moon cannot completely leave. She has nowhere to get energy in order to escape," he said.

Five week day

Another employee of the SAI Vladimir Surdin said that the process of moving the Moon away from the Earth would not be endless, eventually it would be replaced by an approach. "The statement "The moon can leave the Earth's orbit and turn into a planet" is wrong," he told RIA Novosti.

According to him, the removal of the Moon from the Earth under the influence of the tides causes a gradual decrease in the speed of rotation of our planet, and the speed of the departure of the satellite will gradually decrease.

In about 5 billion years, the radius of the lunar orbit will reach its maximum value - 463 thousand kilometers, and the duration of the earth's day will be 870 hours, that is, five modern weeks. At this moment, the speeds of rotation of the Earth around its axis and the Moon in orbit will become equal: the Earth will look at the Moon on one side, just as the Moon is now looking at the Earth.

“It would seem that tidal friction (the deceleration of its own rotation under the influence of lunar gravity) should disappear in this case. However, solar tides will continue to slow down the Earth. But now the Moon will be ahead of the Earth’s rotation and tidal friction will begin to slow down its movement. The Earth, however, is very slow, since the strength of solar tides is small," the astronomer said.

“Such a picture is drawn to us by celestial-mechanical calculations, which no one, I think, will dispute today,” Surdin noted.

The loss of the moon will not turn the Earth into Venus

Even if the Moon disappears, this will not turn the Earth into a copy of Venus, Alexander Bazilevsky, head of the laboratory for comparative planetology at the Vernadsky Institute of Geochemistry and Analytical Chemistry of the Russian Academy of Sciences, told RIA Novosti.

"On the conditions on the surface of the Earth, the departure of the moon will have little effect. There will be no ebb and flow (they are mostly lunar) and the nights will be moonless. We will survive," the agency's source said.

“On the path of Venus, with a terrible warming up, the Earth can go because of our stupidity - if we bring it with greenhouse gas emissions to a very strong warming up. And even then I’m not sure that we will be able to ruin our climate so irreversibly,” the scientist said.

According to him, the hypothesis that Mercury was a satellite of Venus, and then left the orbit of the satellite and became an independent planet, was really put forward. In particular, American astronomers Thomas van Flandern and Robert Harrington wrote about this in 1976, in an article published in the journal Icarus.

"Calculations have shown that this is possible, which, however, does not prove that it was so," Bazilevsky said.

In turn, Surdin notes that "later works have practically rejected it (this hypothesis)."

We know the structure of the solar system, where in the center is our Sun, the source of energy and life on Earth. The sun is huge, in terms of mass it is approximately equal to 333,000 Earth masses, in a radius of 109 Earth radii. All planets revolve around the Sun and almost every planet has its own satellites. Our Earth is the third planet from the Sun and has one natural satellite - the Moon. This Earth-Moon pair formed about 4.5 billion years ago.

There are three hypotheses of the origin and origin of the Moon:

1 Hypothesis:

It was put forward by J. Darwin at the end of the century. According to this hypothesis, the Moon and the Earth initially made up one common molten mass, the rotation speed increased as it cooled and compressed, as a result, this mass was divided into two parts. Small - the Moon, large - the Earth. This hypothesis explains the low density of the Moon, formed from the outer layers of the original mass. But there is a serious objection from the point of view of the existing geochemical differences between the rocks of the Earth's shell and the lunar rocks.

2 Hypothesis:

The capture hypothesis, developed by the German scientist K. Weizsacker, the Swedish scientist H. Alfven and the American scientist G. Urey, suggests that the Moon was originally a small planet, which, when passing near the Earth, became a satellite of the Earth as a result of the influence of the Earth's gravity.

The probability of such an event is very small, and, moreover, in this case one would expect a greater difference between terrestrial and lunar rocks.

3 Hypothesis:

According to the third hypothesis, developed by Soviet scientists - O. Yu. Schmidt and his followers in the middle of the 20th century, the Moon and the Earth were formed simultaneously by combining and compacting a large swarm of small particles. But the Moon as a whole has a lower density than the Earth, so the substance of the protoplanetary cloud should have separated with the concentration of heavy elements in the Earth. In connection with this, an assumption arose that the Earth was the first to form, surrounded by a powerful atmosphere enriched in relatively volatile silicates; with subsequent cooling, the substance of this atmosphere condensed into a ring of planetesimals, from which the Moon was formed.

The last hypothesis at the current level of knowledge (70s of the 20th century) seems to be the most preferable.

At present, the Moon is at a distance of 3.844 * 108 m from us. The measurement results show that the Moon is moving away by an average of 4 cm annually, and this leads to a slowdown of the Moon around the Earth. Therefore, it can already be assumed that over time the Moon will become closer to the Sun and the first to fall into its hot embrace.

An astronomer from the United States, Lee Anna Wilson from the University of Iowa, studying the fate of the Moon, calculated that over time, she would make one revolution around the Earth not 27.32 days, as it is now, but for a long time. The orbit of the Moon will be disturbed, it will be attracted faster by the Sun, weaker by the Earth until it hits a point where the forces of gravity and the forces of attraction of the Sun will tear it apart. The moon will crack and fall into pieces, i.e. our satellite will end its existence in the form of a ring of debris revolving around the Earth. This ring will be similar to the ring of Saturn.

According to preliminary calculations of scientists, this ring will not live long and at the end it will “rain”, that is, it will fall on our Earth - first small particles, and then those that are larger.

If it really comes to this, then our Earth will follow the Sun, but other alternatives are possible. The Earth, having lost its satellite - the Moon, will revolve around the Sun for years alone. And much depends on the luminary itself - the Sun, because it will also change all the time. All these options are hypothetical, and we suppose to look at this fact from the other side.