How to determine the distance to the moon. For some reason, all the remaining planets of the solar system fit exactly between the earth and the moon. A brief history of the issue
One of the main character traits of any person is curiosity. It is to her that mankind owes most of the scientific discoveries and the benefits of technical progress based on them. Since ancient times, people have gazed with interest at the night sky, in which countless stars were shining, and the moon was slowly floating across the sky. It is not surprising that since then the dream of visiting some heavenly body has not left a person.
The invention of the telescope confirmed the assumption that the Moon is at the minimum distance from the Earth. From that moment on, science fiction writers in their novels sent fearless travelers to this heavenly body. It is interesting that the proposed methods were fully consistent with the spirit of their time: a projectile, a rocket based on a jet engine, an antigravitational substance Keyword (H. Wells), etc. True, no one could say exactly how long to fly to the Moon.
Quite a long time has passed since then. Although the term "a lot" is applicable to the duration of human life, but for history, only a moment has passed. Now the natural is increasingly viewed not just as an abstract goal of flight, but as the basis for the bases of the future. These include settlements under a heavy-duty dome, sealed cities below the surface, automated observatories, and spacecraft filling stations. Truly, the flight of fantasy has no boundaries. It is surprising that while many do not even know how much to the moon.
Now the distance from the Earth to the satellite is calculated with high accuracy. Therefore, knowing the speed, you can calculate how long it takes to fly to the moon. It is known that the distance between the central points of these celestial bodies is 384 400 km. But since to determine the travel time, you need to know the path between the surfaces, you need to subtract the values \u200b\u200bof the radii. It is 6378 km for the Earth, and 1738 km for the satellite. The exact answer to the question: "How long to fly to the moon?" suggests the need to take into account the peculiarities of the orbit of our natural satellite. As you know, the Moon is close to an oval (that is, elliptical), so the path length varies by as much as 12%, which is quite a lot. So, at the closest approach (perigee), the distance is 363 104 km, but at the far point (apogee) it is already 405 696 km. Taking into account the sum of their radii, we subtract the known values \u200b\u200bfrom the smaller number and as a result we get 354 988 km. This is the distance from the Earth to the lunar surface.
Based on the distance voiced above, you can definitely say how long to fly to the moon. It remains only to take into account the speed with which it is planned to carry out such a desired journey. So, the flight time to the surface of a natural satellite depends on the chosen vehicle and takes:
160 days when driving a car traveling at a speed of about 100 km / h;
Accordingly, an airplane flying at least 800 km per hour will take "only" 20 days;
The ships of the American Apollo program reached the surface of our satellite in three days and four hours;
Having developed the second at 11.2 km / s, it will be possible to cover the distance in 9.6 hours;
Having turned into pure energy (remember Arthur Clarke's "Space Odyssey") and moving from (300,000 km / s), the goal can be achieved in a paltry 1.25 s;
Well, for the adherents of the saying: "The quieter you go - the further you will be!" will have to spend at least nine years if you continuously walk at a normal pace at a speed of 5 km / h.
Obviously, the question is: "How long to fly to the moon?" at the present time it can already be considered resolved. It remains only to choose a vehicle, then, depending on the decision made, stock up on the proper patience, the required amount of provisions and hit the road.
Agree, Space, alien planets, star clusters - this is a very, very exciting topic. For example, what is the distance to the moon? Surely many of you once asked this question! Or what is its origin? And what does it consist of? Or maybe even someone lives there? Well, at least microorganisms? The distance to the Moon has always interested humanity.
Development of the concept of the moon
This celestial object has attracted the attention of people since ancient times. And at the dawn of the development of astronomy, the Moon became one of the first objects for observation and study. Information about attempts to trace the pattern of its movement in the firmament and explain them goes back to the Sumerian, Babylonian cultures, ancient Chinese and Egyptian civilizations. And, of course, to ancient Greece. The first known attempt to calculate the distance to the Moon (and also to the Sun) was made by Aristarchus of Samos.
on our companion of the first people, did it in a little over three days. However, the problem here is not only in the speed of the apparatus itself, but in the need to calculate the motion of the moon, fly along a certain arc and land in the required place. Thus, the path follows an arc rather than a straight line. The record time it took for a man-made spacecraft to reach a satellite today is 8 hours and 35 minutes. It was the New Horizons spacecraft launched by NASA.
Is the distance from the Earth to the Moon increasing?
Yes! It really is. Our satellite moves, as it were, in a spiral orbit. And every year the distance to it increases by about 4 centimeters. This is quite a bit for the individual observer. However, our distant ancestors will see the moon much less. Moreover, the weakening gravitational interaction with it will entail a decrease in the activity of the ebb and flow on the Earth and significantly transform the climatic conditions on our planet.
If you were even a little interested in the topic of space and our place in it, you definitely wondered: what is the distance from the Earth to the Moon.
The increased attention to the moon can be explained very simply. This is because it is a natural satellite of our planet. Moreover, it is located closest of all satellites to the Sun. That is, it is inextricably linked with us. It is also worth noting that it is in second place in terms of brightness and in fifth largest. But this is only relative to the solar system.
How the distance from the Earth to the Moon was calculated earlier
As you know, the satellite of our planet was discovered in. Interestingly, even then people had a question, at what distance from it is.
Many scientists have resorted to different methods to calculate the distance between the Earth and the Moon.
It is now, thanks to modern and space technology, we have visited it, studied and measured everything that is possible. But how did the ancient astronomers calculate this interval?
In fact, the Moon is the first cosmic body, the distance to which could be determined. As it turned out, scientists from Ancient Greece did this first.
For example, Aristarchus of Samos. He determined the angle between the Sun and the Moon at 87 degrees. Hence it follows that the satellite of the planet is 20 times closer than our main star. Now we know that this is a wrong view. Of course, at that time, the astronomer used the tools at hand for calculations, and did not have the knowledge that is available to us. But in any case, he contributed to this issue.
A few hundred years before our era, Eratosthenes of Cyrene determined the radius of the Earth. Interestingly, it is not much different from modern indicators. But the very fact of using the radius of the planet and calculating the distance to the satellite already at that time was simply shocking. Let the ancient calculations are not entirely correct, but they laid the foundation for the consideration of this issue.
For example, another scientist Hipparchus of Nicaea, based on observations of the movement of our satellite, expressed his opinion. He believed that the Earth-Moon gap is 60 times greater than the radius of the planet.
Modern calculations
Now astronomers not only calculate the distance between the Earth and the Moon, but also calculate the movement of our satellite. After all, as it became known, he is constantly moving. Therefore, the space that separates us also changes.
In fact, based on the collected knowledge, methods have emerged that allow you to measure the space between space objects with high accuracy.
Modern calculations are based on Brown's theory, which was developed in the 19th and 20th centuries. Already at that time, it was used trigonometric formula with over 1400 items. Moreover, she described the movement of the moon.
At the moment, different methods are used to measure the gap between astronomical bodies. For example, the radar method. Indeed, it allows you to determine the distance with an accuracy of several kilometers.
One of the specific measurement techniques was the laser ranging method. On it, the distance is determined with a slight inaccuracy (only a few centimeters). It uses corner reflectors that are installed on the moon. It is interesting that for this, in the 1970s, the whole Apollo program was launched. As a result of successful operations, several reflectors were delivered to the surface of the planet's satellite and installed. Thus, scientists were able to conduct laser ranging sessions. As a result, the most accurate distance from the Earth to the Moon was determined.
In addition, theoretical calculations have the same validity.
What is the distance from the Earth to the Moon
Since the Moon is in constant motion, the path to it also changes accordingly. The planet's satellite is periodically approaching or moving away from the Earth. For this reason, scientists calculate the average distance. It is important that it is measured between the axes of the centers of the bodies. Moreover, the measurement takes place in kilometers, which are determined by the periods of motion of objects, their phases, cycles and periods of interaction.
At the moment the distance from the Earth to the Moon is 384399
km. However, the average number of this interval is often considered 384400
km.
In addition, you need to know that every year the distance between us and our satellite increases by about 4 cm. This is mainly due to the spiral motion of the planet in its orbit, which reduces the force of gravity. Which, as you know, holds the body.
In conclusion, we can say that the constant movement of cosmic bodies requires attention. Because with this movement, the characteristics and the gap between objects change. Of course, modern astronomy continues to observe and study space. And that definitely matters a lot.
Movement is life
Aristotle
Some interesting facts
The moon is the only astronomical object that has been visited by humans (not counting the Earth).
There is a so-called moon illusion. The moment it lies below the horizon, an optical illusion occurs. More precisely, its size appears to us to be larger than when it is high in the sky.
As you know, light is the fastest in the world. It needs a little more than a second to cover the distance from the Earth to the Moon.
In theory, all the planets of our solar system would fit in the gap between the Earth and the Moon.
384 467 kilometers - this is the distance that separates us from the nearest large cosmic body, from our only natural satellite - the Moon. This begs the question: how did scientists find out about this? After all, you cannot, in fact, walk from the Earth to the Moon with a meter in your hands!
Nevertheless, attempts to measure the distance to the Moon were made in antiquity. The ancient Greek scientist Aristarchus of Samos tried to do this, the same one who was the first to express the idea of \u200b\u200ba heliocentric system! He also knew that the Moon, like the Earth, has the shape of a ball and does not emit its own light, but shines with reflected sunlight. He suggested that at the time when the Moon looks like a half-disk for an observer from Earth. Between it, the Earth and the Sun, a right-angled triangle is formed, in which the distance between the Moon and the Sun and between the Moon and the Earth are legs, and the distance between the Sun and the Earth is the hypotenuse.
Therefore, you need to find the angle between the directions to the Moon and to the Sun, and then using the appropriate geometric calculations, you can calculate how many times the Earth-Moon leg is shorter than the Earth-Sun hypotenuse. Alas, the technology of that time did not allow us to accurately determine the time when the Moon occupies a position at the top of the mentioned right triangle, and in such calculations, a small error in measurements leads to large errors in calculations. Aristarchus was mistaken almost 20 times: it turned out that the distance to the Moon is 18 times less than the distance to the Sun, in reality it is less than 394 times.
A more accurate result was obtained by another ancient Greek scientist - Hipparchus. True, he adhered to the geocentric system, but the reason lunar eclipses understood correctly: the moon falls into the shadow of the earth, and this shadow has the shape of a cone, the top of which is located away from the moon. The contour of this shadow can be observed during an eclipse on the disk of the Moon, and by the bend of the edge it is possible to determine the ratio of its cross section and the size of the Moon itself. Given that the Sun is much farther away than the Moon, it was possible to calculate how far away the Moon had to be for the shadow to shrink to that size. Such calculations led Hipparchus to the conclusion that the distance from the Earth to the Moon is 60 Earth radii, or 30 diameters. The diameter of the Earth was calculated by Eratosthenes - in translation into modern measures of length 12,800 kilometers - thus, according to Hipparchus, the distance from the Earth to the Moon is 384,000 kilometers. As you can see, it is very close to the truth, especially when you consider that he had nothing but simple goniometric devices!
In the 20th century, the distance from the Earth to the Moon was measured with an accuracy of three meters. For this purpose, several reflectors were delivered to the surface of our space "neighbor" about 30 years ago. A focused laser beam is sent to these reflectors from the Earth, the speed of light is known, and the distance to the Moon is calculated from the time it takes the laser beam to travel "back and forth". This method is called laser ranging.
Speaking about the distance from the Earth to the Moon, it should be remembered that we are talking about the average distance, because the Moon's orbit is not circular, but elliptical. At the point farthest from the Earth (apogee), the distance between the Earth and the Moon is 406 670 km, and at the closest (perigee) - 356 400 km.
From 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 how far is to fly there and how far is 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 by the usual methods used in everyday life. Therefore, the distance to the earth satellite was calculated using trigonometric formulas.
Like the Sun, the Moon experiences constant motion in the 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 in 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 in addition, the moon moves across 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 only 29 days (lunar month). This difference became an incentive to break down the ecliptic into 12 zodiacal constellations (in one month the Sun shifts 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, the factor of strong elongation of the orbit is also added. The eccentricity of the Moon's orbit is 0.05 (for comparison, for the Earth, this parameter 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.
In a day, the Moon is shifted relative to the stars by 13 degrees, in an hour by about 0.5 degrees. Modern astronomers often use the lunar coverings 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 unchanging and stable. Due to the relatively small mass of the Moon, it is subject to constant disturbances from more massive objects of the Solar System (primarily the Sun and the Moon). In addition, the Moon's orbit is influenced by the flattening of the Sun and the gravitational fields of other planets in the Solar System. As a result, the value of the eccentricity of the Moon's orbit fluctuates between 0.04 and 0.07 with a period of 9 years. The consequence of these changes was such a phenomenon as a supermoon. Supermoon is an astronomical phenomenon during 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 observed: by about 18 arc minutes every 19 years.
What is equal
Spacecraft will have to spend a lot of time on the flight to the earth's satellite. You cannot fly to the Moon in a straight line - the planet will orbit away from the destination point, and the path will have to be corrected. At a second cosmic speed 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 its 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 managed to achieve.
America's notorious 1969 flight to the moon took 76 hours, according to official figures. NASA's New Horizons spacecraft managed to reach the Moon the fastest - in 8 hours 35 minutes. True, he did not land on the planetoid, but flew past - he had another mission.
Light from the Earth to our satellite will reach very quickly - in 1.255 seconds. But flying at light speeds is still out of 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 go by 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, the flight to it would last about 20 days.
How astronomers in ancient Greece calculated the distance to the moon
The moon became the first celestial body to which it was possible to calculate the distance from the Earth. It is believed that the first to do this were astronomers in ancient Greece.
They have tried to measure the distance to the moon since 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 to 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 in 400 (the angle is approximately 89.8 degrees). The large error was caused by the difficulty of estimating the exact angular distance between the Sun and the Moon using primitive astronomical instruments of the ancient world. Regular solar eclipses by this time had already allowed ancient Greek astronomers to conclude that the angular diameters of the Moon and the Sun are approximately the same. In this regard, Aristarchus concluded that the Moon is 20 times smaller than the Sun (in fact, about 400 times).
Aristarchus used a different method to calculate the size of the Sun and Moon relative to the Earth. We are talking about observing 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 the 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 at 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 located 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 the 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 (modern value 6371 km). If we substitute this value into Aristarchus's 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, a 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 moment of the eclipse the Sun and the Moon will have the same angular dimensions, then according to the rules of similarity of triangles, the ratio of the distances to the Sun and the Moon can be found. 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 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 equal to 3483/15 \u003d 232 or S l \u003d 232R l.
Accordingly, the distance to the Moon is 232 * R s / 2.5 \u003d 60 Earth radii. This turns out to be 6 371 * 60 \u003d 382 260 km. The most interesting thing is that the measurements made with modern instruments confirmed the correctness of the ancient scientist.
Now the measurement of the distance to the moon is carried out using laser devices, which can be measured with an accuracy of several centimeters. In this case, measurements take place in a very short time - no more than 2 seconds, during which the Moon moves away in orbit about 50 meters from the point of sending the laser pulse.
The 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 \u200b\u200bof the parameters of the Moon's orbit and the correspondence between its size and the size of the Earth.
A more accurate method for measuring the distance to the moon appeared in connection with the development of radar. The first radar 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 ranging. For its implementation in the 1960s, several corner reflectors were installed on the Moon. It is interesting to note that the first laser ranging experiments were carried out even before the installation of corner reflectors on the lunar surface. 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, the Apollo astronauts delivered three corner reflectors to the surface of our satellite. Among them, the most perfect was the reflector of the Apollo 15 mission, since it consisted of 300 prisms, while the other two (the Apollo 11 and Apollo 14 missions) had only one hundred prisms each.
In addition, in 1970 and 1973, the USSR delivered to the lunar surface two more French corner reflectors on board the self-propelled vehicles Lunokhod-1 and Lunokhod-2, each of which consisted of 14 prisms. The first of these reflectors has an extraordinary history. During the first 6 months of operation of the Lunokhod with a reflector, it was possible to carry out about 20 sessions of laser ranging. However, then, due to the unfortunate position of the lunar rover, it was not possible to use the reflector until 2010. Only the images of the new LRO spacecraft helped to clarify the position of the lunar rover with the reflector, and thus resume the sessions of work with it.
In the USSR, the largest number of laser ranging sessions was carried out with the 2.6-meter telescope of the Crimean Observatory. Between 1976 and 1983, 1400 measurements were carried out with this telescope with an error of 25 centimeters, then observations were stopped due to the curtailment of the Soviet lunar program.
In total, from 1970 to 2010, approximately 17 thousand high-precision laser ranging sessions were conducted in the world. Most of them were associated with the Apolonna 15 corner reflector (as mentioned above, it is the most perfect - with a record number of prisms):
Of the 40 observatories that are capable of 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 McDonald Observatory in Texas:
At the same time, the most accurate measurements are performed by the APOLLO instrument, which was installed on the 3.5-meter telescope of 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. To date, 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 captured). 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 rotation of the earth around its axis gradually slows down. The rate 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's day will be equal to the lunar month. As a result, the Moon and Earth will always be turned to each other by only one side, as is now observed in the Pluto-Charon system. By this time, the Moon will move away to about 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 lead to an acceleration of the Moon's removal process (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 the tidal interaction with each other. When approaching the Earth by 12 thousand km, the Moon will be torn apart by tidal forces, the fragments of the Moon form a ring like the well-known rings around the giant planets of the Solar System. Other well-known satellites of the Solar System will repeat this fate much earlier. So Phobos is assigned 20-40 million years, and Triton is about 2 billion years old.
Each 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 of the Earth and the Moon.
It is theoretically possible to place all the planets of the solar system between the Earth and the Moon. If you add up the diameters of all the planets, including Pluto, you get a value of 382,100 km.
