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 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 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. Regular solar eclipses by this time already allowed the 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 (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. In 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.
Moon- a satellite of the planet Earth in the solar system: description, history of research, interesting facts, size, orbit, dark side of the moon, scientific missions with photos.
Get away from the city lights on a dark night and admire the beautiful moonlight. Moon is the only terrestrial satellite that rotates around the Earth for more than 3.5 billion years. That is, the Moon accompanies humanity from the moment of its appearance.
Due to its brightness and direct visibility, the satellite has been reflected in many myths and cultures. Some thought it was a deity, while others tried to use it to predict events. Let's take a closer look at interesting facts about the moon.
There is no "dark side"
- There are many stories where the other side of the moon appears. In reality, both sides receive the same amount of sunlight, but only one of them is available for terrestrial viewing. The fact is that the time of the axial lunar rotation coincides with the orbital one, which means that it always turns one side towards us. But we explore the "dark side" with spacecraft.
The moon influences the earth's tides
- Due to gravity, the Moon creates two bulges on our planet. One is on the side turned to the satellite, and the second is on the back. These protrusions cause high and low tides throughout the Earth.
The moon tries to escape
- Every year, the satellite moves away from us by 3.8 cm. If this continues, then in 50 billion years the Moon will simply run away. At that point, it would spend 47 days per orbital flyby.
The weight on the moon is much less
- The moon yields to Earth's gravity, so you'll weigh 1/6 less on a satellite. That is why the astronauts had to jump around like kangaroos.
12 astronauts have landed on the moon
- In 1969, Neil Armstrong stepped on the first satellite during the Apollo 11 mission. The last was Eugene Cernan in 1972. Since then, only robots have been sent to the moon.
No atmospheric layer
- This means that the surface of the Moon, as seen in the photo, is devoid of protection from cosmic radiation, meteorite impacts and solar wind. Significant temperature fluctuations are also noticeable. You won't hear any sounds, and the sky always seems black.
There are earthquakes
- Created by earth's gravity. The astronauts used seismographs and found out that there are cracks and gaps several kilometers below the surface. The satellite is believed to have a molten core.
The first apparatus arrived in 1959
- The Soviet apparatus Luna-1 was the first to land on the moon. He flew past the satellite at a distance of 5995 km, and then went into orbit around the Sun.
Ranks 5th largest in the system
- In diameter, the earth's satellite extends for 3475 km. The Earth is 80 times larger than the Moon, but they are about the same age. The main theory is that at the beginning of formation, a large object crashed into our planet, tearing material into space.
We'll go to the moon again
- NASA plans to create a colony on the lunar surface so that there will always be people there. Work could begin as early as 2019.
In 1950, they planned to detonate a nuclear bomb on a satellite.
- It was a secret Cold War project, Project A119. This would show a significant preponderance of one of the countries.
Size, Mass and Orbit of the Moon
The characteristics and parameters of the Moon should be studied. The radius is 1737 km, and the mass is 7.3477 x 10 22 kg, therefore it is inferior to our planet in everything. However, if compared with the celestial bodies of the solar system, it is clear that it is quite large in size (in second position after Charon). The density indicator is 3.3464 g / cm 3 (in second place among the moons after Io), and gravity is 1.622 m / s 2 (17% of the earth).
The eccentricity is 0.0549, and the orbital path covers 356400 - 370400 km (perihelion) and 40400 - 406700 km (aphelion). It takes 27.321582 days to make a complete circuit around the planet. In addition, the satellite is in the gravitational block, that is, it always looks at us with one side.
Physical characteristics of the moon |
| polar contraction | 0,00125 |
|---|---|
| Equatorial | 1738.14 km 0.273 Earth |
| Polar radius | 1735.97 km 0.273 Earth |
| Medium radius | 1737.10 km 0.273 Earth |
| Large circumference | 10,917 km |
| Surface area | 3.793 10 7 km² 0.074 Earth |
| Volume | 2.1958 10 10 km³ 0.020 Earth |
| Weight | 7.3477 10 22 kg 0.0123 Earth |
| Average density | 3.3464 g/cm³ |
| Acceleration free fall at the equator |
1.62 m/s² |
| First space speed |
1.68 km/s |
| Second space speed |
2.38 km/s |
| Rotation period | synchronized |
| Axis Tilt | 1.5424° |
| Albedo | 0,12 |
| Apparent magnitude | −2,5/−12,9 −12.74 (full moon) |
The composition and surface of the moon
The Moon repeats the Earth and also has an inner and outer core, mantle and crust. The core is a solid iron sphere extending for 240 km. The outer core of liquid iron (300 km) is concentrated around it.
Also in the mantle you can find igneous rocks, where there is more iron than ours. The crust extends for 50 km. The core covers only 20% of the entire object and contains not only metallic iron, but also small impurities of sulfur and nickel. You can see what the structure of the moon looks like in the diagram.
Scientists were able to confirm the presence of water on the satellite, most of which is concentrated at the poles in shaded crater formations and subsurface reservoirs. They think that it appeared due to the contact of the satellite with the solar wind.
Lunar geology is at odds with Earth. The satellite is devoid of a dense atmospheric layer, so there is no weather and wind erosion on it. The small size and low gravity result in rapid cooling and lack of tectonic activity. You can note a huge number of craters and volcanoes. Everywhere there are ridges, wrinkles, highlands and depressions.
The contrast between bright and dark areas is most noticeable. The former are called the lunar hills, but the dark ones are the seas. The uplands were formed by igneous rocks represented by feldspar and traces of magnesium, pyroxene, iron, olivine, magnetite and ilmenite.
Basalt rock formed the basis of the seas. Often these areas coincide with lowlands. Channels can be marked. They are curved and linear. These are lava tubes, cooled and destroyed since volcanic dormancy.
An interesting feature is the lunar domes, created by ejection of lava into the vents. They have gentle slopes, and a diameter of 8-12 km. Wrinkles appeared due to the compression of tectonic plates. Most are found in the seas.
A notable feature of our satellite is the impact craters that form when large space rocks fall. The kinetic impact energy forms a shock wave resulting in depression, causing a lot of material to be ejected.
The craters range from small pits up to 2500 km and a depth of 13 km (Aitken). The largest appeared in early history, after which they began to decrease. You can find about 300,000 depressions with a width of 1 km.
In addition, the lunar soil is of interest. It was formed due to impacts of asteroids and comets billions of years ago. The stones crumbled into fine dust that covered the entire surface.
The chemical composition of regolith differs depending on the position. If the mountains have a lot of aluminum and silicon dioxide, then the seas can boast of iron and magnesium. Geology was investigated not only by telescopic observations, but also by analysis of samples.
Atmosphere of the Moon
The moon has a thin layer of the atmosphere (exosphere), which causes the temperature to fluctuate greatly: from -153°C to 107°C. The analysis shows the presence of helium, neon and argon. The first two are created by solar winds, and the last one is the decay of potassium. There is also evidence of frozen water reserves in craters.
Formation of the Moon
There are several theories of the appearance of the earth's satellite. Some people think that it's all about the gravity of the Earth, which pulled the already finished satellite. They formed together in the solar accretion disk. Age - 4.4-4.5 billion years.
The main theory is the impact. It is believed that a large object (Theia) flew into the proto-Earth 4.5 billion years ago. The ripped material began to rotate along our orbital path and formed the Moon. This is confirmed by computer models. In addition, the tested samples showed almost identical isotopic compositions with us.
Communication with the Earth
The moon revolves around the earth in 27.3 days (stellar period), but both objects move around the sun at the same time, so the satellite spends 29.5 days per phase for the earth (known phases of the moon).
The presence of the moon affects our planet. First of all, we are talking about tidal effects. We notice this when sea levels rise. Earth's rotation is 27 times faster than the moon's. Ocean tides are also enhanced by the frictional adhesion of water to the earth's rotation through ocean floors, water inertia, and basin wobble.
Angular momentum accelerates the lunar orbit and lifts the satellite higher with a longer period. Because of this, the distance between us increases, and the earth's rotation slows down. In a year, the satellite moves away from us by 38 mm.
As a result, we will achieve mutual tidal blocking, repeating the situation of Pluto and Charon. But it will take billions of years. So it's more likely that the Sun will become a red giant and engulf us.
Tides are also observed on the lunar surface with an amplitude of 10 cm for 27 days. Cumulative stress results in moonbeams. And they last an hour longer because there is no water to dampen the vibrations.
Let's not forget about such a magnificent event as an eclipse. This happens if the Sun, the satellite and our planet line up in a straight line. The lunar appears if the full moon is shown behind the earth's shadow, and the solar - the moon is located between the star and the planet. During a total eclipse, the sun's corona can be seen.
The lunar orbit is at an inclination of 5 ° to the earth, so eclipses occur at certain moments. The satellite needs to be near the intersection of the orbital planes. Periodicity covers 18 years.
History of Moon Observations
What does the history of lunar exploration look like? The satellite is located close and visible in the sky, so even prehistoric inhabitants could follow it. Early examples of recording lunar cycles begin in the 5th century BC. e. This was done by scientists in Babylon, who noted the 18-year cycle.
Anaxagoras from Ancient Greece believed that the Sun and the satellite act as large-scale spherical rocks, where the Moon reflected sunlight. Aristotle in 350 BC believed that the satellite is the boundary between the spheres of the elements.
The connection between the tides and the moon was stated by Seleucus in the 2nd century BC. He also thought that the height would depend on the lunar location in relation to the star. The first distance from the Earth and the size was obtained by Aristarchus. His data was improved by Ptolemy.
The Chinese began predicting lunar eclipses in the 4th century BC. They already knew then that the satellite reflects sunlight and is made in a spherical shape. Alhazen said that the sun's rays are not mirrored, but radiate from each lunar region in all directions.
Until the advent of the telescope, everyone believed that they were seeing a spherical object, as well as a completely smooth one. In 1609, the first sketch appears from Galileo Galilei, who depicted craters and mountains. This and observations of other objects helped advance Copernicus' heliocentric concept.
The development of telescopes has led to the refinement of surface features. All craters, mountains, valleys and seas were named after scientists, artists and prominent figures. Until the 1870s all craters were considered volcanic formations. But it wasn't until later that Richard Proctor suggested that they might be impact marks.
Exploring the Moon
The space age of lunar exploration has allowed a closer look at the neighbor. The Cold War between the USSR and the USA caused all technologies to develop rapidly, and the Moon became the main target of research. It all started with launches of vehicles, and ended with human missions.
In 1958, the Soviet Luna program started, where the first three probes crashed on the surface. But a year later, the country successfully delivers 15 devices and extracts the first information (information about gravity and surface images). Samples were delivered by missions 16, 20 and 24.
Among the models were innovative ones: Luna-17 and Luna-21. But the Soviet program was closed and the probes were limited to only surveying the surface.
In NASA, the launch of probes started in the 60s. In 1961-1965s. the Ranger program was in operation, which created a map of the lunar landscape. Further in 1966-1968-s. landed rovers.
In 1969, a real miracle happened when Apollo 11 astronaut Neil Armstrong took the first step on the satellite and became the first man on the moon. This was the climax for the Apollo mission, which was originally aimed at human flight.
There were 13 astronauts on the Apollo 11-17 missions. They managed to extract 380 kg of rock. Also, all participants were engaged in various studies. After that, there was a long lull. In 1990, Japan became the third country to successfully place its probe above the lunar orbit.
In 1994, the United States sent a ship to Clementine, who was involved in the creation of a large-scale topographic map. In 1998, a scout managed to find ice deposits in craters.
In 2000, many countries became eager to explore the satellite. ESA sent the SMART-1 spacecraft, which first analyzed the chemical composition in detail in 2004. China launched the Chane program. The first probe arrived in 2007 and stayed in orbit for 16 months. The second device also managed to capture the arrival of asteroid 4179 Tutatis (December 2012). Chan'e-3 launched a rover in 2013.
In 2009, the Japanese Kaguya probe entered orbit, studying geophysics and creating two full-fledged video reviews. Since 2008-2009, the first mission from the Indian ISRO Chandrayan has been in orbit. They were able to create high resolution chemical, mineralogical and photogeological maps.
NASA in 2009 used the LRO spacecraft and the LCROSS satellite. The internal structure was considered by two additional NASA rovers launched in 2012.
The treaty between countries says that the satellite remains common property, so all countries can launch missions there. China is actively preparing a colonization project and is already testing its models on people who are closed for a long time in special domes. Not far behind is America, which also intends to populate the moon.
Use the resources of our site to view beautiful and high-quality photos of the Moon in high resolution. Useful links will help you find out the maximum known amount of information about the satellite. To understand which moon is today, just go to the appropriate sections. If you can not buy a telescope or binoculars, then look at the moon in an online telescope in real time. The picture is constantly updated, showing the crater surface. The site also tracks the phases of the moon and its position in orbit. There is a convenient and fascinating 3D model of the satellite, the solar system and all celestial bodies. Below is a map of the lunar surface.
Earth satellites: from artificial to natural
Astronomer Vladimir Surdin about expeditions to the Moon, the landing site of Apollo 11 and the equipment of astronauts:
Click on the image to enlarge it
Story moon mass estimates is hundreds of years old. A retrospective of this process is presented in an article by foreign author David W. Hughes. The translation of this article was made to the extent of my modest knowledge of English and is presented below. newton estimated the mass of the moon at twice the value now accepted as plausible. Everyone has their own truth, but there is only one truth. point in this question we could put the Americans with a pendulum on the surface of the moon. They were there ;) . The same could be done by telemetry operators on the orbital characteristics of the LRO and other ISLs. It is a pity that this information is not yet available.
Observatory
Measuring the Mass of the Moon
Review for the 125th anniversary of the Observatory
David W. Hughes
Department of Physics and Astronomy, University of Sheffield
The first estimate of the lunar mass was made by Isaac Newton. The meaning of this quantity (mass), as well as the density of the Moon, have been the subject of discussion ever since.
Introduction
Weight is one of the most inconvenient quantities to measure in an astronomical context. We usually measure the force of an unknown mass on a known mass, or vice versa. In the history of astronomy, there was no concept of "masses", say, the Moon, the Earth, and the Sun (MM M , M E , M C) until time Isaac Newton(1642 - 1727). After Newton, fairly accurate mass ratios were established. So, for example, in the first edition of the Beginnings (1687), the ratio M C / M E \u003d 28700 is given, which then increases to M C / M E \u003d 227512 and M C / M E \u003d 169282 in the second (1713) and third (1726) publications, respectively, in connection with the refinement of the astronomical unit. These relationships highlighted the fact that the Sun was more important than the Earth and provided significant support for the heliocentric hypothesis. Copernicus.
Data on the density (mass/volume) of a body helps to estimate its chemical composition. The Greeks more than 2200 years ago obtained fairly accurate values for the sizes and volumes of the Earth and the Moon, but the masses were unknown, and the densities could not be calculated. Thus, even though the Moon looked like a sphere of stone, it could not be scientifically confirmed. In addition, the first scientific steps towards elucidating the origin of the moon could not be taken.
By far the best method for determining the mass of a planet today, in the space age, relies on the third (harmonic) Kepler's law. If the satellite has a mass m, revolves around the Moon with mass M M , then
where a is the time-averaged average distance between M M and m, G is Newton's constant of gravity, and P is the period of the orbit. Since M M >> m, this equation gives the value of M M directly.
If an astronaut can measure the acceleration of gravity, G M, on the lunar surface, then
where R M is the lunar radius, a parameter that has been measured with reasonable accuracy since Aristarchus of Samos, about 2290 years ago.
Isaac Newton 1 did not measure the mass of the Moon directly, but attempted to estimate the relationship between the solar and lunar masses using sea tide measurements. Even though many people before Newton assumed that tides were related to the position and influence of the moon, Newton was the first to look at the subject in terms of gravity. He realized that the tidal force created by a body of mass M at a distance d proportional M/d 3 . If this body has diameter D and density ρ , this force is proportional to ρ D 3 / d 3 . And if the angular size of the body, α , small, tidal force is proportional to ρα 3. So the tide-forming power of the Sun is slightly less than half of the lunar one.
Complications arose because the highest tide was recorded when the Sun was actually 18.5° from the syzygy, and also because the lunar orbit does not lie in the plane of the ecliptic and has an eccentricity. Taking all this into account, Newton, on the basis of his observations, that “Up to the mouth of the River Avon, three miles below Bristol, the height of the rise of water in the spring and autumn syzygies of the luminaries (according to the observations of Samuel Sturmy) is about 45 feet, but in quadratures only 25 ”, concluded, “that the density of the substance of the Moon to the density of the substance of the Earth is related as 4891 to 4000, or as 11 to 9. Therefore, the substance of the Moon is denser and more earthy than the Earth itself”, and “the mass of the substance of the Moon will be in the mass of the substance of the Earth as 1 in 39.788” (Beginnings, Book 3, Proposition 37, Problem 18).
Since the current value for the ratio between the mass of the Earth and the mass of the Moon is given as M E / M M = 81.300588, it is clear that something went wrong with Newton. In addition, a value of 3.0 is somewhat more realistic than 9/5 for the syzygy height ratio? and quadrature tide. Also Newton's inaccurate value for the mass of the Sun was a major problem. Note that Newton had very little statistical precision, and his quoting of five significant figures in M E /MM M is completely unsound.
Pierre-Simon Laplace(1749 - 1827) devoted considerable time to the analysis of tidal heights (especially in Brest), concentrating on the tides in the four main phases of the moon at both solstices and equinoxes. Laplace 2, using a short series of observations from the 18th century, obtained an M E /MM M value of 59. By 1797, he corrected this value to 58.7. Using an extended set of tidal data in 1825, Laplace 3 obtained M E /M M = 75.
Laplace realized that the tidal approach was one of many ways to figure out the lunar mass. The fact that the Earth's rotation complicates the tidal models, and that the end product of the calculation was the Moon/Sun mass ratio, obviously bothered him. Therefore, he compared his tidal force with the results of measurements obtained by other methods. Laplace 4 further writes the M E /MM M coefficients as 69.2 (using d'Alembert coefficients), 71.0 (using Bradley's Maskeline analysis of nutation and parallax observations), and 74.2 (using Burg's work on the lunar parallax inequality). Laplace apparently considered each result equally credible and simply averaged the four values to arrive at an average. “La valeur le plus vraisembable de la masse de la lune, qui me parait resulted des divers phenomenes 1/68.5” (ref 4, p. 160). The average ratio M E /M M equal to 68.5 is repeatedly found in Laplace 5 .
It is quite understandable that by the beginning of the nineteenth century, doubts about the Newtonian value of 39.788 should have arisen, especially in the minds of some British astronomers who were aware of the work of their French colleagues.
Finlayson 6 returned to the tidal technique and when using the syzygy measurement? and quadrature tides at Dover for the years 1861, 1864, 1865, and 1866, he obtained the following M E /M M values: 89.870, 88.243, 87.943, and 86.000, respectively. Ferrell 7 extracted the principal harmonics from nineteen years of tidal data at Brest (1812 - 1830) and obtained a much smaller ratio M E / M M = 78. Harkness 8 gives a tidal value M E /M M = 78.65.
So-called pendulum method based on the measurement of acceleration due to gravity. Returning to Kepler's third law, taking into account Newton's second law, we obtain
where aM is the time-averaged distance between the Earth and the Moon, P M- lunar sidereal period of revolution (i.e. the length of the sidereal month), gE acceleration due to gravity on the Earth's surface, and R E is the radius of the earth. So
According to Barlow and Brian 9 , this formula was used by Airy 10 to measure M E /M M, but was inaccurate due to the smallness of this quantity and accumulated - the accumulated uncertainty in the values of the quantities aM , gE, R E, and P M.
As telescopes became more advanced and the accuracy of astronomical observations improved, it became possible to solve the lunar equation more accurately. The common center of mass of the Earth/Moon system moves around the Sun in an elliptical orbit. Both the Earth and the Moon revolve around this center of mass every month.
Observers on Earth thus see, during each month, a slight eastward and then a slight westward shift of an object's celestial position, compared to the object's coordinates that it would have had the Earth not had a massive satellite. Even with modern instruments, this movement is not detectable in the case of stars. It can, however, be easily measured for the Sun, Mars, Venus, and asteroids that pass nearby (Eros, for example, at its nearest point is only 60 times further away than the Moon). The amplitude of the monthly shift of the position of the Sun is about 6.3 arcseconds. Thus
where a C- the average distance between the Earth and the center of mass of the Earth-Moon system (this is about 4634 km), and a S is the average distance between the Earth and the Sun. If the average Earth-Moon distance a M it is also known that
Unfortunately, the constant of this “lunar equation”, i.e. 6.3", this is a very small angle, which is extremely difficult to measure accurately. In addition, M E / M M depends on an accurate knowledge of the Earth-Sun distance.
The value of the lunar equation can be several times greater for an asteroid that passes close to the Earth. Gill 11 used 1888 and 1889 positional observations of asteroid 12 Victoria and a solar parallax of 8.802" ± 0.005" and concluded that M E /M M = 81.702 ± 0.094. Hinks 12 used a long sequence of observations of asteroid 433 Eros and concluded that M E /M M = 81.53±0.047. He then used the updated solar parallax and the corrected values for asteroid 12 Victoria by David Gill and obtained a corrected value of M E /M M = 81.76±0.12.
Using this approach, Newcomb 13 derived M E /M M =81.48±0.20 from observations of the Sun and planets.
Spencer John s 14 analyzed observations of the asteroid 433 Eros as it passed 26 x 10 6 km from Earth in 1931. The main task was to measure solar parallax, and a commission of the International Astronomical Union was set up in 1928 for this purpose. Spencer Jones found that the lunar equation constant is 6.4390 ± 0.0015 arcseconds. This, combined with a new value for the solar parallax, resulted in a ratio of M E /M M =81.271±0.021.
Precession and nutation can also be used. The pole of the Earth's axis of rotation precesses around the pole of the ecliptic every 26,000 years or so, which also manifests itself in the movement of the first point of Aries along the ecliptic at about 50.2619" per year. The precession was discovered by Hipparchus more than 2000 years ago. small periodic motion known as nutation, found James Bradley(1693~1762) in 1748. Nutation mainly occurs because the plane of the lunar orbit does not coincide with the plane of the ecliptic. The maximum nutation is about 9.23" and a complete cycle takes about 18.6 years. There is also additional nutation produced by the Sun. All of these effects are due to moments of forces acting on the Earth's equatorial bulges.
The magnitude of the steady-state lunisolar precession in longitude, and the amplitudes of the various periodic nutations in longitude, are functions of, among other things, the mass of the Moon. Stone 15 noted that the lunisolar precession, L, and the nutation constant, N, are given as:
where ε=(M M /M S) (a S /a M) 3 , a S and a M are the average Earth-Sun and Earth-Moon distances;
e E and e M are the eccentricities of the earth's and lunar orbits, respectively. The Delaunay constant is represented as γ. In the first approximation, γ is the sine of half the angle of inclination of the lunar orbit to the ecliptic. The value of ν is the displacement of the node of the lunar orbit,
during the Julian year, in relation to the line of equinoxes; χ is a constant that depends on the average perturbing force of the Sun, the moment of inertia of the Earth, and the angular velocity of the Earth in its orbit. Note that χ cancels out if L is divisible by H. Stone substituting L = 50.378" and N = 9.223" got M E / M M = 81.36. Newcomb used his own measurements of L and N and found M E / M M = 81.62 ± 0.20. Proctor 16 found that M E /M M = 80.75.
The motion of the Moon around the Earth would be exactly an ellipse if the Moon and Earth were the only bodies in the solar system. The fact that they are not leads to the lunar parallax inequality. Due to the attraction of other bodies in the solar system, and the Sun in particular, the moon's orbit is extremely complex. The three largest inequalities to be applied are due to evection, variation, and the annual equation. In the context of this paper, variation is the most important inequality. (Historically, Sedilloth says that the lunar variation was discovered by Abul-Wafa in the 9th century; others attribute this discovery to Tycho Brahe.)
The lunar variation is caused by the change that comes from the difference in solar attraction in the Earth-Moon system during the synodic month. This effect is zero when the distances from the Earth to the Sun and the Moon to the Sun are equal, in a situation occurring very close to the first and last quarter. Between the first quarter (through the full moon) and the last quarter, when the Earth is closer to the Sun than the Moon, and the Earth is predominantly pulled away from the Moon. Between the last quarter (through the new moon) and the first quarter, the Moon is closer to the Sun than the Earth, and therefore the Moon is predominantly pulled away from the Earth. The resulting residual force can be decomposed into two components, one tangent to the lunar orbit and the other perpendicular to the orbit (ie, in the Moon-Earth direction).
The position of the Moon changes by as much as ±124.97 arcseconds (according to Brouwer and Clements 17) from the position it would have if the Sun were infinitely far away. It is these 124.9" that are known as the parallax inequality.
Since these 124.97 arcseconds correspond to four minutes of time, it should be expected that this value can be measured with sufficient accuracy. The most obvious consequence of the parallax inequality is that the interval between the new moon and the first quarter is about eight minutes, i.e. longer than from the same phase to the full moon. Unfortunately, the accuracy with which this quantity can be measured is somewhat diminished by the fact that the lunar surface is uneven and that different lunar edges must be used to measure the lunar position in different parts of the orbit. (In addition to this, there is also a slight periodic variation in the apparent half-diameter of the Moon due to the changing contrast between the brightness of the Moon's edge and the sky. This introduces an error that varies between ±0.2" and 2", see Campbell and Neison 18).
Roy 19 notes that the lunar parallax disparity, P, is defined as
According to Campbell and Neyson 18, the parallax inequality was established as 123.5" in 1812, 122.37" in 1854, 126.46" in 1854, 124.70" in 1859, 125.36" in 1867, and 125.46" in 1868. Therefore, the Earth/Moon mass ratio can be calculated from observations of parallax inequalities if other quantities, and especially solar parallax (i.e. a S) are known. This has led to a dichotomy among astronomers. Some suggest using the Earth/Moon mass ratio from the parallax inequality to estimate the average Earth-Sun distance. Others propose to evaluate the former through the latter (see Moulton 20).
Finally, consider the perturbation of planetary orbits. The orbits of our nearest neighbors, Mars and Venus, which are under the gravitational influence of the Earth-Moon system. Due to this action, orbital parameters such as eccentricity, node longitude, inclination, and perihelion argument change as a function of time. An accurate measurement of these changes can be used to estimate the total mass of the Earth/Moon system, and by subtraction, the mass of the Moon.
This suggestion was first made by Le Verrier (see Young 21). He emphasized the fact that the motions of the nodules and perihelions, although slow, were continuous and thus would be known with increasing accuracy as time went on. Le Verrier was so fired up with this idea that he abandoned observations of the then transit of Venus, being convinced that the solar parallax and the Sun/Earth mass ratio would eventually be found much more accurately by the perturbation method.
.JPG)
The earliest point comes from Newton's Principia.
The accuracy of the known lunar mass.
Measurement methods can be divided into two categories. Tidal technology requires special equipment. A vertical pole with graduations is lost in the coastal mud. Unfortunately, the complexity of the tidal environment around the coasts and bays of Europa meant that the resulting lunar mass values were far from accurate. The tidal force with which bodies interact is proportional to their mass divided by the cube of the distance. So be aware that the end product of the calculation is actually the ratio between the lunar and solar masses. And the relation between the distances to the Moon and the Sun must be precisely known. Typical tidal values of M E / M M are 40 (in 1687), 59 (in 1790), 75 (in 1825), 88 (in 1865), and 78 (in 1874), highlighting the difficulty inherent in interpretation. data.
All other methods relied on accurate telescopic observations of astronomical positions. Detailed observations of stars over long periods of time have led to the derivation of constants for precession and nutation of the Earth's axis of rotation. They can be interpreted in terms of the ratio between lunar and solar masses. Accurate positional observations of the Sun, planets and some asteroids over several months have led to an estimate of the distance of the Earth from the center of mass of the Earth-Moon system. Careful observations of the position of the Moon as a function of time during the month have led to the amplitude of the parallactic inequality. The last two methods, together, relying on measurements of the Earth's radius, the length of the sidereal month, and the acceleration of gravity on the Earth's surface, led to an estimate of the magnitude of , rather than the mass of the Moon directly. Obviously, if known only to within ± 1%, the mass of the Moon is indeterminate. To obtain the M M / M E ratio with an accuracy of, say, 1, 0.1, 0.01%, it is required to measure the value with an accuracy of ± 0.012, 0.0012, and 0.00012%, respectively.
Looking back over the historical period from 1680 to 2000, it can be seen that the lunar mass was known ± 50% between 1687 and 1755, ± 10% between 1755 and 1830, ± 3% between 1830 and 1900, ± 0.15% between 1900 and 1968, and ± 0.0001% between 1968 and present. Between 1900 and 1968 the two meanings were common in serious literature. The lunar theory indicated that M E /MM M = 81.53, and the lunar equation and the lunar parallax inequality gave a somewhat smaller value of M E /MM M = 81.45 (see Garnett and Woolley 22). Other values have been cited by researchers who have used different solar parallax values in their respective equations. This minor confusion was removed when the light orbiter and command module flew well-known and well-measured orbits around the moon during the Apollo era. The current value of M E /M M = 81.300588 (see Seidelman 23) is one of the most accurately known astronomical quantities. Our exact knowledge of the actual lunar mass is clouded by uncertainties in Newton's constant of gravity, G.
Importance of the lunar mass in astronomical theory
Isaac Newton did very little with his newfound lunar knowledge. Even though he was the first scientist to measure the lunar mass, his M E / M M = 39.788 would seem to merit little contemporary commentary. The fact that the answer was too small, almost twice, was not realized for more than sixty years. Physically significant is only the conclusion that Newton drew from ρ M /ρ E =11/9, which is that "the body of the Moon is denser and more earthly than that of our earth" (Beginnings, Book 3, Proposition 17, Corollary 3).
Fortunately, this fascinating, albeit erroneous, conclusion will not lead conscientious cosmogonists into a dead end in an attempt to explain its meaning. Around 1830, it became clear that ρ M /ρ E was 0.6 and M E / M M was between 80 and 90. Grant 24 noted that "this is the point at which greater precision did not appeal to the existing foundations of science", alluding, that accuracy is unimportant here simply because neither astronomical theory nor the theory of the origin of the moon relied heavily on these data. Agnes Clerk 25 was more cautious, noting that "the lunar-terrestrial system... was a particular exception among bodies influenced by the Sun."
The Moon (mass 7.35-1025 g) is the fifth of ten satellites in the solar system (starting from number one, these are Ganymede, Titan, Callisto, Io, Luna, Europa, Saturn's Rings, Triton, Titania, and Rhea). Relevant in the 16th and 17th centuries, the Copernican Paradox (the fact that the Moon revolves around the Earth, while Mercury, Venus, Earth, Mars, Jupiter and Saturn revolves around the Sun) has long been forgotten. Of great cosmogonic and selenological interest was the ratio of masses “main / most massive-secondary”. Here is a list of Pluto/Charon, Earth/Moon, Saturn/Titan, Neptune/Triton, Jupiter/Callisto and Uranus/Titania, coefficients such as 8.3, 81.3, 4240, 4760, 12800 and 24600, respectively. This is the first indication of their possible joint origin by bifurcation through the condensation of body fluid (see, for example, Darwin 26, Jeans 27, and Binder 28). In fact, the unusual Earth/Moon mass ratio led Wood 29 to conclude that it "indicates quite clearly that the event or process that created the Earth's Moon was unusual, and suggests that some weakening of the normal aversion to the involvement of special circumstances may be acceptable." in this issue."
Selenology, the study of the origin of the moon, became "scientific" with the discovery in 1610 by Galileo of the moons of Jupiter. The moon has lost its unique status. Then Edmond Halley 30 discovered that the lunar orbital period changes with time. This was not the case, however, until the work of G.Kh. Darwin in the late 1870s, when it became clear that the original Earth and Moon were much closer together. Darwin suggested that the early resonance-induced bifurcation, rapid rotation and condensation of the molten Earth led to the formation of the Moon (see Darwin 26). Osmond Fisher 31 and W.H. Pickering 32 even went so far as to suggest that the Pacific Basin is a scar that was left when the Moon broke away from the Earth.
The second major selenological fact was the Earth/Moon mass ratio. The fact that there was a violation of the meanings for the Darwin theses was noted by A.M. Lyapunov and F.R. Moulton (see, for example, Moulton 33). . Together with the low combined angular momentum of the Earth-Moon system, this led to the slow death of Darwin's theory of tides. It was then proposed that the Moon was simply formed elsewhere in the solar system and then captured in some complex three-body process (see eg C 34).
The third basic fact was the lunar density. The Newtonian value of ρ M /ρ E 1.223 became 0.61 by 1800, 0.57 by 1850, and 0.56 by 1880 (see Brush 35). At the dawn of the nineteenth century, it became clear that the Moon had a density that was about 3.4 g cm -3. At the end of the 20th century, this value remained almost unchanged and amounted to 3.3437±0.0016 g cm -3 (see Hubbard 36). Obviously, the lunar composition was different from the composition of the Earth. This density is similar to the density of rocks at shallow depths in the Earth's mantle and suggests that the Darwinian bifurcation occurred in a heterogeneous rather than homogeneous Earth at a time that occurred after differentiation and basic morphogenesis. Recently, this similarity has been one of the main facts contributing to the popularity of the ram hypothesis of lunar formation.
It was noted that the average density of the moon was the same like meteorites(and possibly asteroids). Gullemine 37 pointed density of the moon in 3.55 times more than water. He noted that "it was so curious to know the density values of 3.57 and 3.54 for some meteorites collected after they hit the surface of the Earth". Nasmyth and Carpenter 38 noted that "the specific gravity of the lunar about the same as silicon glass or diamond: and oddly enough it almost coincides with the meteorites that we find lying on the ground from time to time; therefore, the theory is confirmed that these bodies were originally fragments of lunar matter, and probably were once ejected from lunar volcanoes with such force that they fell into the sphere of earth's gravity, and ultimately fell to the earth's surface.
Urey 39, 40 used this fact to support his theory of capture of lunar origin, although he was concerned about the difference between the lunar density and the density of certain chondrite meteorites, and other terrestrial planets. Epic 41 considered these differences to be insignificant.
findings
The mass of the moon is extremely uncharacteristic. It is too large to place our satellite comfortably among planetary captured asteroid clusters, like Phobos and Deimos around Mars, the Himalia and Ananke clusters around Jupiter, and the Iapetus and Phoebe clusters around Saturn. The fact that this mass is 1.23% of the Earth is unfortunately only a minor clue among many in support of the proposed impact-origin mechanism. Unfortunately, today's popular "Mars-sized body hits the newly differentiated Earth and knocks out a lot of material" theory has some petty problems. Even though this process has been recognized as possible, it does not guarantee that it is likely. like “why did only one moon form at that time?”, “why don't other moons form at other times?”, “why did this mechanism work on planet Earth, and not touch our neighbors Venus, Mars, and Mercury?” come to mind.
The mass of the Moon is too small to place it in the same category as Pluto's Charon. 8.3/1 The ratio between the masses of Pluto and Charon, a coefficient that indicates that the pair of these bodies is formed by a bifurcation of condensation, the rotation of an almost liquid body, and is very far from the value of 81.3/1 of the mass ratio of the Earth and the Moon.
We know the lunar mass to within one part of 10 9 . But we cannot help feeling that the general answer to this precision is “so what”. As a guide, or a hint about the origin of our heavenly partner, this knowledge is not enough. In fact, in one of the last 555-page volumes on the subject 42 , the index does not even include "lunar mass" as an entry!
References
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(2) P.-S. laplace, Mem. Acad.des Sciences, 45, 1790.
(3) P.-S. laplace, Volume 5, Livre 13 (Bachelier, Paris), 1825.
(4) P.-S. laplace, Traite de Mechanique Celeste, Tome 3 (rimprimerie de Crapelet, Paris), 1802, p, 156.
(5) P.-S. laplace, Traite de Mechanique Celeste, Volume 4 (Courcicr, Paris), 1805, p. 346.
(6) H. P. Finlayson, MNRAS, 27, 271, 1867.
(7)W.E, Fcrrel, Tidal Researches. Appendix to Coast Survey Report for 1873 (Washington, D. C) 1874.
(8) W. Harkness, Washington Observatory Observations, 1885? Appendix 5, 1891
(9) C. W. C. Barlow ScG. H, Bryan, Elementary Mathematical Astronomy(University Tutorial Press, London) 1914, p. 357.
(10) G. B. Airy, Mem. ras., 17, 21, 1849.
(11) D. Gill, Annals of the Cape Observatory, 6, 12, 1897.
(12) A. R. Hinks, MNRAS, 70, 63, 1909.
(13) S. Ncwcomb, Supplement to the American Ephemeris for tSy?(Washington, D.C.), 1895, p. 189.
(14) H. Spencer Jones, MNRAS, 10], 356, 1941.
(15) E. J. Stone, MNRAS, 27, 241, 1867.
(16) R. A. Proctor, Old and Nets Astronomy(Longmans, Green, and Co., London), )