Choose a few commonly used formulas for you, which are commonly used in observation, study and astronomical competitions.
( 1)? Z=90 degrees -h? Z is zenith distance, and H is the horizon height of celestial bodies?
(2)? P=90 degrees-declination? P is the polar distance of celestial bodies, commonly used in equatorial coordinate system?
Formula?
(3)? s=t+a？ STA stands for sidereal time, celestial hour angle and right ascension respectively. Is this an a?
An extremely important formula is a key formula for our astronomical time measurement?
(4)? Height of northern balance line = local latitude? In astronomy and geography, is this a measure? A formula of latitude?
(5) The following are a set of formulas for celestial bodies and transits, which you should remember:
Cost =-tanφtanδ?
cosA=sinδ/cosφ？
This is the relationship between celestial elevation angle T, local latitude φ and celestial declination δ. As for the celestial rising angle t and azimuth angle a ",it is obtained by the following formula:?
T=-t？
A"=360 degrees -A?
The local stellar moments s and s' represent the rising and falling local stellar moments, respectively.
S=t+a？ S=t+a？ S"=T+a？
The related formula of celestial body movement is as follows:
Noon on the celestial body:? A= 180 degrees?
When t=0?
z=φ-δ？ Or? z？ =δ-φ?
Transit time of celestial bodies:? A"=0 degrees?
When T= 12?
Z"= 180 degrees-φ-δ?
There is another expression for the height formula of transit on celestial bodies:?
South of the zenith: h=90-φ+δ？
In the north of zenith, Zhongtian:? h=90+φ-δ？
Newton's law of motion?
Newton's first law (law of inertia): Any object remains in a state of static or uniform linear motion until the force exerted by other objects forces it to change this state. ?
Newton's second law: when an object is acted by an external force, the acceleration obtained by the object is directly proportional to the resultant force; The direction of acceleration is the same as that of external force. ?
Newton's third law: the acting force and reaction force between two objects are on a straight line, equal in size and opposite in direction. They are produced at the same time and disappear at the same time. ?
Kepler's three laws?
The first law: the planet moves around the sun in an elliptical orbit, and the sun is at a focus of the elliptical orbit. ?
The second law: the connecting line (vector diameter) between the planet and the sun sweeps the same area at the same time. That is, vrsinθ= constant (r: the radial length from the sun center to the planet; θ: Angle between planetary speed and vector diameter)?
The third law: The square of the period of revolution of a planet is directly proportional to the cube of the major semi-axis of the orbit. That is, t 2/a 3 = 4 π 2/GM (m: solar mass; G: gravitational constant)?
The law of gravity?
There is mutual attraction between any two particles, and its size is directly proportional to the product of the two particles' mass and inversely proportional to the square of the distance between the two particles. The direction of the force is along the connecting line of two particles, and the expression is f = GMM/R 2 (g: gravitational constant, with the magnitude of 6.67×10-1n? M 2/kg 2)？
Formula for calculating the height of the sun at noon?
H = 90-| φ-δ| (φ: local geographic latitude, always positive; δ: the latitude of the point, which is positive in the second half of the local year and negative in the winter half)?
What is the regression velocity formula of extragalactic galaxies?
V=KD(K: Hubble constant, the current estimated value is 70 kilometers per second per million parsec seconds; D: galaxy distance)
Newton's law of motion
Newton's first law (law of inertia): Any object remains in a state of static or uniform linear motion until the force exerted by other objects forces it to change this state.
Newton's second law: when an object is acted by an external force, the acceleration obtained by the object is directly proportional to the resultant force; The direction of acceleration is the same as that of external force.
Newton's third law: the acting force and reaction force between two objects are on a straight line, equal in size and opposite in direction. They are produced at the same time and disappear at the same time.
Kepler's three laws?
The first law: the planet moves around the sun in an elliptical orbit, and the sun is at a focus of the elliptical orbit.
The second law: the connecting line (vector diameter) between the planet and the sun sweeps the same area at the same time. That is, vrsinθ= constant (r: the radial length from the sun center to the planet; θ: the angle between the planetary speed and the vector diameter)
The third law: The square of the period of revolution of a planet is directly proportional to the cube of the major semi-axis of the orbit. That is, t 2/a 3 = 4 π 2/GM (m: solar mass; G: gravitational constant)
The law of gravity?
There is mutual attraction between any two particles, and its size is directly proportional to the product of the two particles' mass and inversely proportional to the square of the distance between the two particles. The direction of the force is along the line of two particles, and the expression is f = GMM/R 2 (g: gravitational constant, with the magnitude of 6.67×10-1nm.
Calculation formula of noon sun height
H = 90-| φ-δ| (φ: local geographic latitude, always positive; δ: the latitude of the direct point, which is positive in the second half of the local year and negative in the winter half)
What is the regression velocity formula of extragalactic galaxies?
V=KD(K: Hubble constant, the current estimated value is 70 kilometers per second per million parsec seconds; D: galaxy distance)
The related formula of fate?
Noon on the celestial body:? A= 180 degrees?
When t=0?
z=φ-δ？ Or? z？ =δ-φ?
Transit time of celestial bodies:? A"=0 degrees?
When T= 12?
Z"= 180 degrees-φ-δ?
There is another expression for the height formula of transit on celestial bodies:?
South of the zenith: h=90-φ+δ？
In the north of zenith, Zhongtian:? h=90+φ-δ
Relativity?
What is the special theory of relativity?
Special relativity is based on the theory of four-dimensional space-time view, so to understand the content of relativity, we must first have a general understanding of its space-time view. There are various multidimensional spaces in mathematics, but so far, the physical world we know is only four-dimensional, that is, three-dimensional space plus one-dimensional time. The high-dimensional space mentioned in modern microphysics is another meaning, only mathematical meaning, so I won't discuss it here. ?
Four-dimensional space-time is the lowest dimension that constitutes the real world, and our world happens to be four-dimensional. As for the high-dimensional real space, at least we can't perceive it yet. When a ruler rotates in three-dimensional space (excluding time), its length remains unchanged, but when it rotates, all its coordinate values change and the coordinates are related. The significance of four-dimensional space-time lies in that time is the fourth coordinate, which is related to spatial coordinates, that is to say, space-time is a unified and inseparable whole, and they are a kind of "one change and one change" relationship. ?
Four-dimensional space-time is not limited to this. According to the relationship between mass and energy, mass and energy are actually the same thing. Mass (or energy) is not independent, but related to the state of motion. For example, the greater the speed, the greater the mass. In four-dimensional space-time, mass (or energy) is actually the fourth component of four-dimensional momentum, and momentum is a quantity that describes the motion of matter, so it is natural that mass is related to the state of motion. In four-dimensional space-time, momentum and energy are unified, which are called four vectors of energy momentum. In addition, four-dimensional velocity, four-dimensional acceleration, four-dimensional force and four-dimensional electromagnetic field equations are all defined in four-dimensional space-time. It is worth mentioning that the four-dimensional electromagnetic field equation is more perfect, which completely unifies electricity and magnetism, and the electric field and magnetic field are described by a unified electromagnetic field tensor. The physical laws of four-dimensional space-time are much more perfect than those of three-dimensional, which shows that our world is indeed four-dimensional. It can be said that at least it is much more perfect than Newtonian mechanics. At least because of its perfection, we can't doubt it. ?
In the theory of relativity, time and space constitute an inseparable whole-four-dimensional spacetime, and energy and momentum also constitute an inseparable whole-four-dimensional momentum. This shows that there may be a deep connection between some seemingly unrelated quantities in nature. When we talk about general relativity in the future, we will also see that there is also a profound relationship between the four vectors of space-time and energy momentum. ?
Matter moves forever in interaction, and there is no matter that does not move and there is no matter that does not move. Because matter moves in interaction, it is necessary to describe motion in the relationship of matter, and it is impossible to describe motion in isolation. In other words, motion must have a reference object, and this reference object is the frame of reference. ?
Galileo once pointed out that the motion of a moving ship is inseparable from the motion of a stationary ship. That is to say, when you are completely isolated from the outside world in a closed cabin, even if you have the most developed mind and the most advanced instruments, you can't perceive whether your ship is moving at a constant speed or at a standstill. There is no way to perceive speed because there is no reference. For example, we don't know the whole motion state of our whole universe, because the universe is closed. Einstein cited it as the first basic principle of special relativity: the principle of special relativity. Its content is: the inertial system is completely equivalent and indistinguishable. ?
The famous Michelson-Morey experiment completely negates the ether theory of light and draws the conclusion that light has nothing to do with the frame of reference. In other words, whether you stand on the ground or on a speeding train, the measured speed of light is the same. This is the second basic principle of special relativity, the principle of constant speed of light. ?
From these two basic principles, we can directly deduce all the contents of special relativity, such as coordinate transformation formula and velocity transformation formula. For example, the speed change is contrary to the traditional law, but it has been proved to be correct in practice. For example, the speed of the train is 10m/s, and the speed of a person on the train is also10m/s. People on the ground see that the speed of people in the car is not 20m/s, but (20- 10 (-65438). In general, this relativistic effect can be completely ignored, but it increases obviously when it is close to the speed of light, such as when the train speed is zero. 99 times the speed of light, people's speed is zero. 99 times the speed of light, then the conclusion of the ground observer is not 1. 98 times the speed of light, but 0. 999949 times the speed of light. The people in the car didn't slow down when they saw the light coming from behind, which was also the speed of light for him. So in this sense, the speed of light cannot be surpassed, because no matter in which reference system, the speed of light is constant. Velocity transformation in particle physics has been proved by countless experiments and is impeccable. It is precisely because of this unique property of light that it is chosen as the only scale of four-dimensional space-time. ?
General relativity?
Einstein's Second Theory of Relativity (19 16). This theory holds that gravity is caused by the distortion of space-time geometry (that is, the geometry that not only considers the distance between points in space, but also considers the distance between points in space-time), so the gravitational field affects the measurement of time and distance.
General relativity: Einstein's theory that all observers (no matter how they move) must have the same idea based on scientific laws. It explains gravity according to the curvature of four-dimensional space-time
General relativity (generalized? Relativity? ) is Einstein's theory of gravity established in geometric language in 19 15. It combines special relativity with Newton's law of universal gravitation, and changes gravity to describe space-time bent by matter and energy to replace the traditional view that gravity is a force. Therefore, special relativity and the law of universal gravitation are only special cases of general relativity under special circumstances. Special relativity is the case that there is no gravity; The law of universal gravitation is the situation that the distance is close, the gravity is small and the speed is slow. ?
Background?
1907, Einstein published a paper on the influence of gravity and acceleration on light in special relativity, and the prototype of general relativity began to take shape. 19 12 years, Einstein published another paper to discuss how to describe gravity field in geometric language. At this point, the kinematics of general relativity appeared. 19 15 years, Einstein's field equation was published, and the dynamics of the whole general theory of relativity was finally completed. ?
After 19 15, the development of general relativity mostly focused on solving the field equation, and the physical explanation of the solution and the search for possible experiments and observations also accounted for a large part. However, because the field equation is a nonlinear partial differential equation, it is difficult to solve, so only a few solutions were solved before the computer was applied to science. Among them, there are three most famous solutions: Schwarzschild solution (the? Schwarzschild? Solution? ( 19 16)),? That? Reisner Nord stron? m？ Solution? And then what? That? Chloe? Solution.?
The observation of general relativity has also made a lot of progress. The precession of mercury is the first evidence to prove the correctness of general relativity. It was measured before the appearance of relativity, and it was not explained theoretically until Einstein discovered it. In the second experiment, 19 19 Eddington measured the starlight deflection caused by the solar gravitational field during the solar eclipse in Africa, which was completely consistent with the prediction of general relativity. At this time, the general theory of relativity has been widely accepted by the public and most physicists. After that, there were many experiments to test the theory of general relativity and confirm its correctness. ?
In addition, the expansion of the universe has also created another climax of general relativity. From 1922, researchers found that the solution of the field equation would be an expanding universe. Einstein naturally did not believe that the universe would rise or fall at that time, so he added a cosmological constant to the field equation, which made it possible to solve a solution that implicitly defined the universe. But there are two problems with this solution. Theoretically, the solution of a hidden universe is unstable in litigation. In addition, in 1929, Hubble discovered that the universe is actually expanding. This experimental result made Einstein give up the cosmological constant and declared that it was the biggest mistake in my life. Maximum? Mistake? Are you online? Mine? But according to the recent observation of a supernova, the expansion of the universe is accelerating. So the cosmological constant seems to have the possibility of resurrection, and the dark energy in the universe may be explained by the cosmological constant.
Basic assumptions?
Equivalence principle: Gravity and inertia force are completely equivalent. ?
Principle of general relativity: the form of physical laws is constant in all reference systems. ?
Main content?
Einstein put forward the "equivalence principle", that is, gravity and inertia force are equivalent. This principle is based on the equivalence of gravitational mass and inertial mass. According to the principle of equivalence, Einstein extended the principle of relativity in a narrow sense to the principle of relativity in a broad sense, that is, the form of physical laws is unchanged in all reference systems. The motion equation of an object is the geodesic equation in the reference system. Geodesic equation has nothing to do with the inherent properties of the object itself, but only depends on the local geometric properties of time and space. And gravity is the expression of local geometric properties of time and space. The existence of material mass will cause the bending of time and space. In curved space-time, objects still move along the shortest distance (that is, along the geodesic-in Euclidean space). For example, the geodesic movement of the earth in curved space-time caused by the sun actually revolves around the sun, resulting in a gravitational effect. Just like on the surface of the earth, if you move in a straight line, you actually walk around the great circle on the surface of the earth.
Drake formula?
Drake formula (Drake? Equation, also known as Sagan formula (Sagan? Equation) or Green Bank Formula (Green? The bank? Equation)), by astronomer Frank derek (Frank? Drake) put forward a formula in the1960s to infer "the number of highly intelligent civilizations of planets that may come into contact with us inside and outside the Milky Way". Drake's formula is as follows:
This formula seems a bit complicated. It calculates how many civilized societies (n) may exist in our galaxy through the product of a series of possibilities.
R* represents the number of new stars in our galaxy in a year. Space consists of debris scattered by supernova explosion (once every 30 years on average) and hydrogen, a by-product of the big bang that formed the universe. Gradually, under the influence of gravity and the impact of the new supernova explosion, these substances are concentrated in one place, slowly accumulated and finally become stars. Repeat this process.
Fp refers to the average number of planets owned by the new star thus formed. In a star, there are two or three suns of the same size, called binary stars and Samsung, which alternate around each other. Some people think that it is impossible to form a planet in this case. But aren't there giant planets like Jupiter and Saturn in our solar system? This can be regarded as Samsung, and both binary stars and Samsung may have planets. But a star usually has several planets, which is uncertain.
Ne refers to the conditions in which life may occur and evolve in these planets. Life must have a lot of liquid water. However, if the planet is too far away from the star, water will freeze into ice; Too close will turn into steam. In order for life to evolve, it is necessary to have land made of ancient rocks. If the planet is too big, it is impossible to meet these conditions. In addition, there must be an atmosphere, and asteroids may drift and lose the atmosphere due to lack of gravity. Moreover, if the rotation period is too long, not only the temperature difference between day and night is too large, but also the strong wind keeps blowing, making it difficult to produce life.
Fl stands for the proportion of planets that meet these conditions that actually have life and evolution. Evolution must have DNA, which is an extremely complex and huge genetic way of producing compounds, and the possibility of this formation is very slim.
Fi stands for the probability that life will evolve into wisdom. Bacteria, trees and grass can't evolve into intelligent creatures. They don't have a nervous system, and they don't have the necessary spine to grow to a certain size. The most primitive animal with nervous system and spine is fish. And if fish stay in the water all the time, they will not evolve into intelligent creatures. ? First of all, fish should become four legs, can walk on land, then climb trees, learn to grasp things with fingers, and evolve to walk upright. In this way, the division of labor between feet and hands will be full of wisdom after a long time. However, the process may not be so smooth. There are many living planets, but if there are only bacteria, plants and shellfish, it is difficult to produce intelligent creatures.
Fc represents the proportion of intelligent creatures who can communicate with the outside world. At present, the earth mainly uses radio waves as a means of interstellar communication, but in the depths of the Amazon basin in South America and the mountains of New Guinea, uncivilized primitive people live. They don't understand agriculture and animal husbandry, and they also lack the technology to make metal objects such as iron. They can only hunt with simple bows and sticks. They didn't evolve from apes to humans recently. Like us, they evolved hundreds of thousands of years ago. To have advanced science and technology, we must also have certain conditions that can accommodate countless changes and accumulated experience. Therefore, planets with intelligent life may not all reach a high level of civilization, and they may not all be in contact with the outside world, so that we can perceive their existence.
L stands for the average life span of civilization. The earth civilization is not highly developed, but it has been threatened by nuclear war and public hazards. The higher the level of civilization, the greater the possibility of being destroyed, because there is great power to promote its progress and great power to destroy it, and an accident may make civilization perish. If the life span of all developed civilizations is short, then if there are developed civilizations on other planets, they may have died out long ago.
We can't calculate L and Fc, so scientists have different views on the value of n. carl sagan calculated that there is a highly developed alien civilization in every 6.5438+million stars in the Milky Way, and he calculated that there is a civilized planet in every 6.5438+million stars at most. Therefore, Sagan thinks that there may be life in such close stars as Tewatseki and Jettret, Guli I and i I I..
According to this formula, Drake predicted that 4000 civilized societies would have the ability to communicate. Asimov calculated 530,000 in the book Foreign Civilization.
Some people also question this equation of alien civilization, thus denying that there are developed civilizations besides the earth in the Milky Way. For example, Hugh Croskey of the former Soviet Union thinks that other planets with nuclear weapons will be destroyed by nuclear war, so the life span of developed civilizations is very short, and there may be no other civilizations in the galaxy except the earth.
Another view is that the predicted value of the equation is too much and unreliable. For example, Macher Hart, an American astronomer, thinks that if there was a developed civilization in the Milky Way, it would have colonized the Milky Way long ago, so it's impossible that we haven't discovered it yet. This shows that there is no other civilization except the earth in the Milky Way, but there may be outside the Milky Way. ?
Formula of transit time of stars?
In the past, people had to look at the stars at night through satellite images to determine the best time. Now, after more than 40 years of painstaking exploration, an old man in Changyanbao village has finally worked out a formula, and anyone with a little knowledge of astronomy can easily calculate the best time for a star to appear. ?
Sun Ming, 64, is an out-and-out farmer with only primary education. In the 1960s, the village production team sent people to patrol at night, all of which were based on the stars to set the shift change time, which was extremely inaccurate. So he became interested in when the stars were brightest. Although he only attended primary school, he studied hard in middle school and university and devoted himself to astronomy. After more than 40 years of research, he finally came up with a formula that can accurately calculate the brightest time of a star (that is, the transit time of a star). The formula is: the brightest time of the star (Beijing time) = (the right ascension time of the star+the time difference between an observation point and Beijing+12 hours)-the right ascension time of the sun on that day. This formula can calculate which stars pass through the local area at all times, which provides great convenience for stargazers. ?
/kloc-which star is the brightest in the night of March in 0/9? Sun Lao used his formula to show the reporter the brightest time of arcturus in The Patriarch. The steps are as follows: First, at 14, find out that the right ascension of arcturus is 12, and then find out that the right ascension of the sun on that day is 23: 48. Then use formula 1 to calculate: the brightest time in arcturus = (14: 00, 12: 00 +44: 00)-23: 48 = 3: 08 in the morning. In other words, at 3: 08 a.m. on 19, arcturus was the nearest and brightest. ?
Yesterday, the reporter asked the National Time Service Center of Chinese Academy of Sciences (formerly Shaanxi Observatory) for the formula of Lao Sun Manming. Verified by relevant experts, the formula is basically correct. Experts also told reporters: "It is really commendable that a farmer with only a primary school education can work out this formula. This formula is completely worth telling students in the classroom of the university. "