meaning
The rule of thumb of the average distance between the planet and the sun. 1766, Titius, a German, proposed that by taking a series of 0, 3, 6, 12, 24, 48, 96, 192 ..., then adding 4 to each number and dividing it by 10, we can approximate the distance from each planet to the sun. 1772, the German astronomer Baud further studied this problem and published this law, hence the name Titus-Baud Law, sometimes called Titus Law or Baud Law. This law can be expressed as follows: from near to far from the sun, it corresponds to the nth planet (for mercury, n is not 1, but-∞), and its distance from the sun is a =0.4+0.3×2n-2 (astronomical unit).
After Titius-Bode law was put forward, two discoveries gave it strong support. First, 178 1 year, F.W. Herschel discovered Uranus, which was almost exactly in the orbit predicted by the law. Second, Titius predicted that there should be a celestial body 2.8 astronomical units away from the sun between Mars and Jupiter. 180 1 year, Italian astronomer Piazi discovered ceres at this distance; Since then, astronomers have discovered many asteroids near this distance. However, this rule also has some shortcomings, such as the calculated values of Neptune and Pluto are inconsistent with the observed values, and Mercury N takes-∞ instead of 1, which is hard to understand. In addition, the average distance between some satellites and their planets has a regularity similar to Titius-Bode's law. Although some people have put forward some explanations for the causes of Titius-Bode law, there is still no conclusion.
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Titius-Bode rule
20 1 1-7-22 10: 12:00
1772, the German astronomer Baud summed up and published a rule about planetary spacing in his book "A Guide to Starry Sky Research", which was put forward by German physics professor Titius six years ago. The main content of the rule is: take a series of numbers such as 0, 3, 6, 12, 24, 48, 96, etc ... and add 4 to each number, and then divide it by 10 to get the approximate value of the actual distance between the planet and the sun.
For example, the average distance from Mercury to the Sun is (0+4)/ 10=0.4 (astronomical unit), the average distance from Venus to the Sun is (3+4)/ 10=0.7, and the average distance from the Earth to the Sun is (6+4)/10 =/. 10= 1.6 At this rate, the distance of the next planet should be: (24+4)/ 10=2.8, but there are no planets or other celestial bodies at this distance. Bode believes that the "creator" will not intentionally leave a blank space in this place; Titius thinks that maybe a satellite of Mars is in this position, but in any case, the Titius-Bode law was interrupted at "2.8 (astronomical unit)".
The two farthest planets known at that time were Jupiter and Saturn. It is encouraging to continue to calculate according to the idea of rules. The data given by the rules are compared with the actual situation as follows:
The actual distance between the planet and the sun given by the rules (astronomical units)
Mercury 0.4 0.387
Venus 0.7 0.723
Earth 1.0 1.000
Mars 1.6 1.524
2.8
Jupiter 5.2
Saturn 10.0 9.554
The data calculated by the rules are very similar to the distance between planets, so everyone began to believe that there should be a big planet in "2.8". Bode appealed to other astronomers for this, hoping to organize together to find this "lost" planet.
Some enthusiastic astronomers began to look for the "lost" planet, and several years passed without result. Just when everyone was discouraged and ready to give up this rambling search, in 178 1 year, the British astronomer Herschel accidentally discovered Uranus, the seventh largest planet in the solar system. Surprisingly, the average distance between Uranus and the sun is 19.2 astronomical unit, and the result calculated by Titius-Bode law is (192+4)/6544. All of a sudden, the status of the rules suddenly rose, and almost everyone believed that there must be a big planet in the vacant position of "2.8", but the method was not appropriate, so it was never found.
However, ten years have passed quickly, and the whereabouts of this "lost" planet are still unknown.
Until the beginning of 180 1, an amazing news came from Sicily, Italy. Piazi, the director of a remote observatory, discovered a new celestial body during a routine observation. After calculation, the distance is 2.77 astronomical units, which is very similar to "2.8". Therefore, the new celestial body is considered to be a big planet that many people desperately searched for but never found, and it was named "Ceres".
Then the diameter of Ceres was determined to be more than 700 kilometers, which confused everyone. Why not a big planet but an asteroid? But the shocking thing is yet to come. The following year (1802, March), German doctor Olbers discovered another planet-Pallas Athena-between the orbits of Mars and Jupiter. Except a little smaller, pallas Athena is similar to Ceres, and the distance is basically the same. Then he found the third star-Venus, and the fourth star-Vesta. In the end, the total number of asteroids discovered in the back and forth reached 500,000, all of which were concentrated in a specific area between Mars and Jupiter, the so-called "asteroid belt", and its center position was consistent with the data given by Titius-Bode Law.
Why did the big planet become 500,000 asteroids? At that time, some people wondered whether the original planet exploded for some reason that people could not know for the time being.
Neptune and Pluto were discovered in 1846 and 1930 respectively, both of which were setbacks of Titius-Bode law. Compare their regular values with the actual distance as follows:
Determine the actual distance between the numerical value and the sun.
Neptune (384+4)/ 10 = 38.830.2
Pluto (768+4)/ 10 = 77.239.6
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Gauss and the discovery of asteroids
Name: Carl? Friedrich? Gauss
Introduction: Carl? Friedrich? Gauss (Johann Carl Friedrich Gauss: 1777- 1855)
German mathematician, born in Brunswick, studied and taught at the University of G? ttingen. His achievements in his life are extremely rich, involving almost all fields of mathematics and enjoying the reputation of "Prince of Mathematics". His head is also printed on German paper money of 10 mark.
Famous saying: Math IST is dead? Mathematics is the queen of science.
In 766, a German middle school teacher found that the distance between the planets in the solar system and the sun conforms to certain laws. Later, Porter, director of the Berlin Observatory, attributed this to the following empirical formula, the so-called Titius? Bode's law:
Where d is the distance from the planet to the sun, expressed in astronomical units. After substituting different values of n into the solution, we can get the following interesting results:
Obviously, all the planets known at that time were in line with Titius? Bode's law, but N=3 has a vacancy and no celestial body corresponds to it. So many astronomers speculated that there should be an unknown planet there, so many astronomers began their own search.
178 1 year, British astronomer William? Herschel accidentally discovered a new planet-Uranus. After observation, people found that Uranus was not the planet they were looking for, but the discovery of Uranus strengthened people's understanding of Titius? Trust in bode's law. Because the actual distance between Uranus and (19.25438+084 astronomical unit) is very close to the calculated value 19.6 when N=6. This has greatly increased people's confidence.
At180111,there is good news in the New Year bell. Italian astronomer Piazi discovered a new celestial body at Palermo Observatory in Sicily. Of course, Piazi wasn't sure it was a new planet at first. He once thought it was a comet. However, due to illness, Piazi had to suspend observation, Ceres was submerged in the light of the sun, and it was difficult to observe, so Piazi failed to follow up observation. This celestial body just disappeared.
Piazi made his observations public and asked scholars from all over the world to help him find the missing celestial bodies again. After hearing the news, Gauss, a great German mathematician, immediately set out to calculate. Based on the data of three observations, Gauss invented a new method to solve the approximate orbit of planets, and solved the problem quickly according to this new method, and completed the calculation in a few days. Later, astronomers really re-observed the planet near the location predicted by Gauss. Since then, Gaussian method has been widely used in astronomy.
This newly discovered celestial body was later proved to be a planet between Jupiter and Mars and was named Ceres. But it was soon discovered that there were many similar celestial bodies between Mars and Jupiter, which were collectively called asteroids because they were not very big. However, what about Titius, who once played an important role in the search for asteroids? Bode's law, but few people believed it later. Is it because Neptune discovered by 1846 no longer conforms to Titius? Bode's Law (calculated value is 38.8, actual distance is 30. 1 104 astronomical unit). Some people think that Titius? Bode's rule may reflect some characteristics of solar system dynamics, but how to explain and treat abnormal phenomena is difficult to solve. Therefore, after making great contributions to the discovery of asteroids, Titius? Bode's rule gradually faded out of the historical stage.
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On the law of planetary distance. Also known as Bode's Law. 1766, J.D. Titius of Germany first put forward the empirical relationship, 1772, J.E. Bode of Germany published a summary formula: an = 0.4+0.3× 2n-2, where an is the average distance from the nth planet to the sun expressed in astronomical units. N is the order from near to far (but the position of Mercury and Uranus discovered in 178 1 year coincides with that of n =, and the asteroid was discovered in 180 1 year (consistent with A5 = 2.8). However, the physical meaning of Bode's formula is unclear. Neptune discovered in 1846 and Pluto discovered in 1930 deviate greatly from this formula, so many people still hold a negative attitude and think that it is an empirical formula to help memory at best. With the development of research, many formulas of planetary distance are put forward, and the commonly used form is an+ 1 ∶ an = β (β is a constant related to planetary mass). Moreover, in some satellite systems, conventional satellites have a similar relationship. The physical meaning of this rule needs further discussion.
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Brief introduction of astronomical units:
Astronomical unit (AU) is a unit of length, which is approximately equal to the average distance from the earth to the sun. One of astronomical constants. The basic unit for measuring distance in astronomy, especially the distance between celestial bodies in the solar system. The average distance from the earth to the sun is an astronomical unit. An astronomical unit is about 65438+496 million kilometers. 1976, the international astronomical union defined an astronomical unit as the distance between a particle with negligible mass and undisturbed orbit, and an object with a period of revolution of 365.983 days (that is, one gauss year) and a mass of about one sun. At present, the recognized astronomical unit is149,597,870,69130m (about/kloc-0.5 billion kilometers or 93 million miles).
When the astronomical unit was first used, its actual size was not very clear, but the distance between planets could be calculated by heliocentric geometry and the laws of planetary motion. Later, through parallax and modern radar, the actual size of astronomical units was finally found accurately. However, due to the uncertainty of the gravitational constant (only five or six significant bits), the mass of the sun cannot be very accurate. If the position of the planet is calculated in international units, its accuracy will inevitably decrease in the process of unit conversion. Therefore, these calculations are usually based on solar mass and astronomical units, not kilograms and kilometers.
The distance of one astronomical unit. It is equivalent to the average distance from the earth to the sun, which is about 1.496× 10 8 km.
In life, astronomical units (astronomical numbers) are often used to describe a very large number. ...
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Historical deduction
One of astronomical constants. In astronomy, the basic unit of measuring distance, especially the distance between celestial bodies in the solar system, is represented by a.
Before 1938, astronomical unit refers to the average distance from the center of mass of the Earth-Moon system to the sun without the perturbation of big planets (see perturbation theory), or the half-length diameter of the unperturbed elliptical orbit of the center of mass of the Earth-Moon system around the sun. According to Kepler's law, there are the following relationships among Gaussian gravitational constant k, solar mass s, mass m of the earth-moon system, average distance a from the earth-moon system to the sun and period of revolution t of the earth around the sun: [1].
When the mass of the sun is taken as the astronomical mass unit (that is, S= 1) and the average distance from earth-moon system to the sun is taken as the astronomical distance unit (that is, A= 1), Gauss can calculate k=0.0 1720209895 according to the inaccurate T and m/S values at that time. 1938 the 6th international astronomical union decided to fix the value of k, which will never change. According to this k value, when S= 1, A= 1, and m=0, the t value can be calculated as 365.63 calendar days.
Therefore, the definition of astronomical unit can be changed to: when the period of revolution is 365 ~ 363 calendar days, the half-length diameter of the imaginary undisturbed planetary elliptical orbit with zero mass is equal to one astronomical unit. According to the accurate t value and m/S value, the semi-long diameter of the daily orbit of the earth-moon system can be calculated as 1.00000003 astronomical unit. Because the earth's motion is influenced by the perturbation of other celestial bodies, the average distance between the sun and the earth is actually 1.336 astronomical unit.
Before the 1960s, astronomical units were derived from the measurement of solar parallax π ⊙. In newcomb's astronomical constant system, the solar parallax π⊙=8 and 80, and the length of the corresponding astronomical unit is equal to149,500,000 kilometers. Since the 1960s, radar astronomy has achieved accurate results. So astronomical units are derived from the speed of light c and the travel time τA per unit distance. 1964, the astronomical constant system of the international astronomical union took a as1600× 10/0 meter, and took it as the basic constant.
This value starts from 1968 and is used until 1983. 1976, the astronomical constant system of the international astronomical union took a as 1.49597870× 10 meter, and changed it into a derived constant, which will be adopted uniformly from 1984.
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calculate
In the astronomical constant system of 1976, it is defined as the distance that light travels in vacuum for 499.82 seconds. Its value is1.49597870×1011m (representing power). 1 astronomical unit is equal to1.58129×10 (-5) light years, that is, 4.848 13× 10 (-6) parsec.
Light years are units of length, not time. A light year is the distance that light travels in a vacuum in one year.
The speed of light in vacuum is constant (the speed is about 300,000 km/s).
1ly=9.46x 10^ 12km
Parsec (pc) 1pc refers to the angle when the solar system is viewed from the celestial body 1 ".
1pc = 2.06× 105 au = 3.26 ly
1PC is approximately equal to 30835997962819660.8m.
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Calculation method
Astronomers use triangle parallax method, spectral parallax method, cluster parallax method, statistical parallax method, cepheid parallax method and mechanical parallax method to determine the distance between stars and us. The measurement of the distance between stars is of great significance for studying the spatial position of stars and calculating the luminosity and velocity of stars.
There are more than 50 stars within 0/6 light-years from the sun/kloc-. The nearest is proxima centauri Centauri, about 4.2 light years away from the sun, about 40 trillion kilometers. It is not easy to measure the distance between celestial bodies by trigonometric parallax method. Astronomers divide the celestial bodies that need to be measured into several grades according to the distance.
The celestial bodies that are very close to us, and the farthest ones are not more than 100 light years (1 light years =9.46? 10 12km), astronomers measured their distance by triangular parallax method. Triangular parallax method is to put the measured celestial body on the vertex of an extra-large triangle, and the two ends of the diameter of the earth's orbit around the sun are the other two vertices of the triangle. By measuring the angle of view from the earth to the celestial body, and then using the known orbit diameter of the earth around the sun, we can use the triangle formula to calculate the distance from the celestial body to us.
We can't use the triangle parallax method to measure the distance between the celestial bodies a little farther away and the earth, because we can't accurately measure their parallax on the earth.
Mobile clustering method
At this time, it is necessary to measure the distance by kinematics, which is also called the moving cluster method in astronomy, and the distance is determined according to their moving speed. However, when using the kinematics method, it must be assumed that all the stars in the moving cluster are moving at equal and parallel speeds in the Milky Way. For celestial bodies outside the Milky Way, kinematics methods cannot determine their distance from the Earth. Cepheid parallax method is also called standard candlelight method.
There is a formula in physics about the relationship between luminosity, brightness and distance. S∝L0/r2
Measure the luminosity L0 and brightness S of the celestial body, and then use this formula to know the distance R of the celestial body. The meanings of luminosity and brightness are different. Brightness means that the luminous body we see has how bright, which we can measure directly on the earth. Brightness refers to the luminous ability of the luminous object itself. The key is to try to know it and get a distance. Astronomer Leuther discovered Cepheid Variable Stars, and there is a definite relationship between their photoperiod and luminosity.
Therefore, the luminosity can be determined by measuring the light variation period, and then the distance can be calculated. If there is a Cepheid variable in a galaxy outside the Milky Way, then we can know the distance between this galaxy and us. Those more distant galaxies, even if there are Cepheid variables, can't be observed. Of course, we must find another way.
Triangular parallax method and Cepheid parallax method are the two most commonly used ranging methods. The scale of the former is several hundred light years, and the latter is several million light years. Statistical methods and indirect methods are used in the middle area. The largest scale is Hubble's Law, with a scale of 65.438+00 billion light years.
Hubble's law method
1929, Edwin Hubble studied the relationship between the apparent velocity and distance of extragalactic galaxies. At that time, only 46 extragalactic galaxies could use their apparent velocities, and only 24 of them had calculated their distances. Hubble obtained a roughly linear proportional relationship between apparent velocity and distance.
Modern accurate observation has confirmed this linear proportional relationship.
V = H0×d
Where v is the regression velocity, d is the galaxy distance, and H0 = 100 kKM. S-1MPC (the value of h0 is 0). Using Hubble's law, we can first measure the red shift δ ν/ν, and then get V through the Doppler effect δ ν/ν = V/C, and then get D.
Hubble's law reveals that the universe is expanding. This expansion is a uniform expansion of the whole space. Therefore, the observer will see exactly the same expansion at any point. From the point of view of any galaxy, all the galaxies revolve around it, and the farther away the galaxies are, the faster they expand each other.
example
Pluto is 39.5 astronomical units from the sun.
Jupiter is 5.2 astronomical units from the sun.
The average diameter of Betelgeuse is 2.57 astronomical units.
The distance from the earth to the moon is 0.0026 astronomical unit.
Approximate conversion value with other units
1 astronomical distance unit (au) =1.49597870×1kloc-0/m =149,600,000 km = 92,960.
1 light year (ly) = 9.4605536×1015m = 63239.8 astronomical distance unit.
1 parsec (PC) = 3.085678×1016m = 206264.8 astronomical distance unit =3.26 163 1 light-year.
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Chapter 1: Famous Reading Words: Famous Reading Words.
1, wind, rain, reading, sound in the ear; Family affairs, state affairs, what's going on in the world, e