Since ancient times, humanity has been interested in the visible movements of celestial bodies: the Sun, Moon and stars. It's hard to imagine Our own solar system seems too big, stretching more than 4 trillion miles from the Sun. Meanwhile, the Sun is only one hundredth of a billion of the other stars that make up the Milky Way galaxy.
Milky Way
The galaxy itself is a huge wheel that rotates, made of gas, dust and more than 200 billion stars. Between them lie trillions of miles of empty space. The sun is anchored on the outskirts of the galaxy, shaped like a spiral: from above, the Milky Way looks like a huge rotating hurricane of stars. Compared to the size of the galaxy, the Solar System is extremely small. If we imagine that the Milky Way is the size of Europa, then the solar system will be no larger in size than a walnut.
solar system
The Sun and its 9 satellite planets are scattered in one direction from the center of the galaxy. Just as planets revolve around their stars, stars also revolve around galaxies.
It will take the Sun about 200 million years at a speed of 588,000 miles per hour to complete a revolution around this galactic carousel. Our Sun is no different from other stars in anything special, except that it has a satellite, a planet called Earth, inhabited by life. Planets and smaller celestial bodies called asteroids revolve around the Sun in their orbits.
First observations of luminaries
Man has been observing the visible movements of celestial bodies and cosmic phenomena for at least 10,000 years. For the first time, records in the chronicles about celestial bodies appeared in ancient Egypt and Sumer. The Egyptians were able to distinguish three types of bodies in the sky: stars, planets, and “stars with tails.” At the same time, celestial bodies were discovered: Saturn, Jupiter, Mars, Venus, Mercury and, of course, the Sun and Moon. The visible movements of celestial bodies are the movement of these objects perceived from the Earth relative to the coordinate system, regardless of daily rotation. Real movement is their movement in outer space, determined by the forces acting on these bodies.
Visible galaxies
Looking into the night sky, you can see our closest neighbor - - in the form of a spiral. The Milky Way, despite its size, is just one of 100 billion galaxies in space. Without using a telescope, you can see three galaxies and part of ours. Two of them are called the Large and Small Magellanic Clouds. They were first seen in southern waters in 1519 by the expedition of the Portuguese explorer Magellan. These small galaxies orbit around milky way, therefore, are our closest cosmic neighbors.
The third galaxy visible from Earth, Andromeda, is approximately 2 million light years away from us. This means that starlight from Andromeda takes millions of years to get closer to our Earth. Thus, we contemplate this galaxy as it was 2 million years ago.
In addition to these three galaxies, you can see part of the Milky Way at night, represented by many stars. According to the ancient Greeks, this group of stars is milk from the breast of the goddess Hera, hence the name.
Visible planets from Earth
Planets are celestial bodies orbiting the Sun. When we observe Venus glowing in the sky, this is because it is illuminated by the Sun and reflects part of sunlight. Venus is Evening Star or Morning Star. People call it differently because it is in different places in the evening and in the morning.
How the planet Venus revolves around the Sun and changes its location. Throughout the day, visible movement of celestial bodies occurs. The celestial coordinate system not only helps to understand the location of luminaries, but also allows you to compile star maps, navigate the night sky by constellations, and study the behavior of celestial objects.
Laws of planetary motion
By combining observations and theories about the movement of celestial bodies, people have deduced the patterns of our galaxy. Scientists' discoveries have helped decipher the visible movements of celestial bodies. discovered were among the first astronomical laws.
The German mathematician and astronomer became the pioneer of this topic. Kepler, having studied the work of Copernicus, calculated the most better shape, which explains the visible movements of celestial bodies - the ellipse, and brought to light the patterns of planetary movement known in scientific world like Kepler's laws. Two of them characterize the movement of the planet in orbit. They read:
Any planet rotates in an ellipse. The Sun is present in one of its focuses.
Each of them moves in a plane passing through the middle of the Sun, while over the same periods the radius vector between the Sun and the planet outlines equal areas.
The third law connects the orbital data of planets within a system.
Lower and upper planets
Studying the visible movements of celestial bodies, physics divides them into two groups: the lower ones, which include Venus, Mercury, and the upper ones - Saturn, Mars, Jupiter, Neptune, Uranus and Pluto. The movement of these celestial bodies in the sphere occurs in different ways. In the process of the observed movement of the lower planets, they experience a change of phases like the Moon. When moving the upper planets, you can notice that they do not change phases; they are constantly facing people with their bright side.
The Earth, along with Mercury, Venus and Mars, belongs to the group of so-called inner planets. They revolve around the Sun in internal orbits, unlike major planets, which rotate in external orbits. For example, Mercury, which is 20 times smaller in its innermost orbit.
Comets and meteorites
In addition to the planets, spinning around the Sun are billions of ice blocks consisting of frozen solid gas, small stones and dust - comets that fill the Solar System. The visible movements of celestial bodies, represented by comets, can only be seen when they approach the Sun. Then their tail begins to burn and glows in the sky.
The most famous of them is Halley's comet. Every 76 years it leaves its orbit and approaches the Sun. At this time it can be observed from Earth. Even in the night sky, you can contemplate meteorites in the form of flying stars - these are clumps of matter that move throughout the Universe at enormous speed. When they fall into the Earth's gravitational field, they almost always burn up. Due to extreme speed and friction with the air shell of the Earth, meteorites become hot and break up into small particles. The process of their combustion can be observed in the night sky in the form of a luminous ribbon.
The astronomy curriculum describes the apparent movements of celestial bodies. 11th grade is already familiar with the patterns according to which the complex movement of planets occurs, the change lunar phases and the laws of eclipses.
II FUNDAMENTALS OF CELESTIAL MECHANICS.
LESSON No. 10. LAWS OF MOTION OF HEAVENLY BODIES.
4. Kepler's laws.
6. Conic sections.
7. Revision of Kepler's laws.
1. Development of ideas about the solar system.
The first scientific geocentric system of the world began to take shape in the works of Aristotle and other scientists ancient Greece. It received its completion in the works of the ancient Greek astronomer Ptolemy. According to this system, the Earth is located at the center of the world, hence the name geocentric. The universe is limited by a crystal sphere on which the stars are located. The planets, the Sun and the Moon move between the Earth and the sphere. The ancients believed that uniform Roundabout Circulation- this is ideal movement, and that celestial bodies move exactly this way. But observations showed that the Sun and Moon move unevenly, and to eliminate this obvious contradiction, it was necessary to assume that they move in circles, the centers of which do not coincide either with the center of the Earth or with each other. The even more complex loop-like motion of the planets had to be represented as the sum of two circular uniform movements. Such a system made it possible to calculate with sufficient accuracy for observations mutual arrangement planets for the future. The loop-like motion of the planets is still for a long time remained a mystery and found its explanation only in the teachings of the great Polish astronomer Nicolaus Copernicus
In 1543, his book “On the Rotation of the Celestial Spheres” was published. It outlined a new heliocentric system of the world. According to this system, the Sun is at the center of the world. The planets, including the Earth, revolve around the Sun in circular orbits, and the Moon revolves around the Earth and at the same time around the Sun. The accuracy in determining the positions of the planets did not increase much, but it was the Copernican system that made it possible to simply explain the loop-like motion of the planets. The teachings of Copernicus dealt a crushing blow to the geocentric system of the world. It went far beyond the scope of astronomy and gave a powerful impetus to the development of all natural sciences.
2. Loop-like motion of the planets.
With the naked eye we can observe five planets - Mercury, Venus, Mars, Jupiter and Saturn. Planets are among those luminaries that not only participate in the daily rotation of the celestial sphere, but also shift against the background zodiac constellations, as they revolve around the Sun. If you follow the annual movement of a planet, marking its position on a star chart every week, you may discover main feature visible movement of the planet: the planet describes a loop against the background of the starry sky, which is explained by the fact that we observe the movement of the planets not from a stationary Earth, but from the Earth revolving around the Sun.
3. Johannes Kepler and Isaac Newton.
The two greatest scientists, far ahead of their time, created a science called celestial mechanics, that is, they discovered the laws of motion of celestial bodies under the influence of gravity, and even if their achievements were limited to this, they would still have entered the pantheon of the greats of this world. It so happened that they did not intersect in time. Only thirteen years after Kepler's death Newton was born. Both of them were supporters of the heliocentric Copernican system. After studying the motion of Mars for many years, Kepler experimentally discovered three laws of planetary motion, more than fifty years before Newton discovered the law of universal gravitation. Not yet understanding why the planets move the way they do. It was hard labor and brilliant foresight. But Newton used Kepler’s laws to test his law of gravitation. All three of Kepler's laws are consequences of the law of gravity. And Newton discovered it at the age of 23. At this time, 1664 - 1667, the plague raged in London. Trinity College, where Newton taught, was dissolved indefinitely so as not to worsen the epidemic. Newton returns to his homeland and in two years makes a revolution in science, making three important discoveries: differential and integral calculus, an explanation of the nature of light and the law of universal gravitation. Isaac Newton was solemnly buried in Westminster Abbey. Above his grave stands a monument with a bust and the epitaph “Here lies Sir Isaac Newton, the nobleman who, with the torch of mathematics in his hand, was the first to prove, with the torch of mathematics in his hand, the movements of the planets, the paths of comets and the tides of the oceans... Let mortals rejoice that such an adornment of the human race exists.”
4. Kepler's laws.
The main task of celestial mechanics is the study of the movement of celestial bodies under the influence of universal gravitational forces. Namely, the calculation of the orbits of planets, comets, asteroids, artificial Earth satellites, spacecraft, stars in binary and multiple systems. All problems in the mathematical sense are very difficult and, with rare exceptions, can only be solved by numerical methods using the largest computers. However, model problems in which bodies are considered as material points and the influence of other bodies can be neglected can be solved in general view, i.e., obtain formulas for the orbits of planets and satellites. The simplest problem is considered to be two bodies, when one is much larger than the other and the reference frame is connected to this larger body.
It was for this case that the three laws of planetary motion relative to the Sun were obtained empirically by Johannes Kepler. How did he do it? Kepler knew: the coordinates of Mars on the celestial sphere with an accuracy of 2” according to the observations of his teacher Tycho Brahe; relative distances of planets from the Sun; synodic and sidereal periods of planetary revolution. Then he reasoned something like this.
The position of Mars during opposition is known (see figure). In a triangle ABC
letter A
indicates the position of Mars, IN
- Earth, WITH
- The sun. After a period of time equal to the sidereal period of revolution of Mars (687 days), the planet will return to the point A
, and during this time the Earth will move to the point IN'
. Since the angular speeds of the Earth's movement during the year are known (they are equal to the angular speeds of the apparent movement of the Sun along the ecliptic), we can calculate the angle DIA'
. Having determined the coordinates of Mars and the Sun at the moment the Earth passes through the point IN'
, we can, knowing 2 angles in a triangle, use the sine theorem to calculate the ratio of the side SV'
To AC
. After one more rotation of Mars, the Earth will be in position IN"
and it will be possible to determine the relationship NE"
to the same segment AC
etc. In this way, point by point, one can get an idea of the true shape of the Earth’s orbit, establishing that it is an ellipse with the Sun at its focus. It can be determined that if the time of movement along the arc M3M4 = the time of movement along the arc M1M2, then Pl. SM3M4 = Square SM1M2.
F1 and F2 are the foci of the ellipse, c is the focal length, a is the semimajor axis of the ellipse and the average distance from the planet to the Sun.
5. Newton's law of universal gravitation.
Isaac Newton was able to explain the movement of bodies in outer space using law of universal gravitation . He came to his theory as a result of many years of research on the movement of the Moon and planets. But a simplified conclusion of the law of universal gravitation can be drawn from Kepler’s third law.
Let the planets move in circular orbits, their centripetal accelerations are equal: 
, Where T– the period of revolution of the planet around the Sun, R- radius of the planet's orbit. From Kepler's III law or. Therefore, the acceleration of any planet, regardless of its mass, is inversely proportional to the square of the radius of its orbit: 
.
According to Newton's II law, force F, which imparts this acceleration to the planet, is equal to: https://pandia.ru/text/78/063/images/image010_95.gif" width="125" height="51 src=">, where M– mass of the Sun. Because the F = F', =https://pandia.ru/text/78/063/images/image013_78.gif" width="161" height="54">, where G= 6.67∙10–11 N∙m2/kg2 – gravitational constant ..gif" width="109" height="51">. The gravitational force between the Sun and the planet is proportional to the product of their masses and inversely proportional to the square of the distance between them. This law is valid for any spherical symmetrical bodies, and it is approximately true for any bodies if the distance between them is large compared to their sizes. The acceleration that, according to Newton's second law, a body experiences m, located at a distance r from the body M, equal to: https://pandia.ru/text/78/063/images/image017_68.gif" width="47" height="47">, where is the mass of the Earth, is the distance to its center. Near the surface of the Earth, acceleration free fall is equal to g= 9.8 m/s2. The oblateness of the Earth and its rotation lead to a difference in the force of gravity at the equator and near the poles: the acceleration of gravity at the observation point can be approximately calculated using the formula g = 9,78 ∙ (1 + 0,0053 sin φ ), Where φ – latitude of this point.
Gravity behaves unusually inside the Earth. If the Earth is taken to be a homogeneous sphere, the force of gravity increases in proportion to the distance r from the center of the sphere.
6. Conic sections.
Conic sections are formed when a right circular cone intersects a plane. Conic sections include second-order curves: ellipse , parabola And hyperbola . All of them are the locus of points, the distances from which to given points (tricks) or up to a given straight line (directrix) there is a constant value. For example, an ellipse is defined as the locus of points for which the sum of the distances from two given points (foci F1 and F2) is a constant value and equal to the length of the major axis: F1M+F2M=2a=const. The degree of elongation of an ellipse is characterized by its eccentricity e. Eccentricity e = c/a. When the foci coincide with the center e = 0, and the ellipse turns into circle . Major axle shaft A is the average distance from the focus to the ellipse. The point of the ellipse closest to the focus is called the periapsis, the most distant is called the apocenter. The distance from the focus to the periapsis is PF1 = a (1 – e), to the apocenter – F1A = a (1 + e).
7. Revision of Kepler's laws.
So Kepler discovered his laws empirically. Newton derived Kepler's laws from the law of universal gravitation. As a result of this, the first and third laws underwent changes. Kepler's first law was generalized and its modern formulation is as follows: The trajectories of motion of celestial bodies in the central gravitational field are conical sections: an ellipse, a circle, a parabola or a hyperbola, at one of the foci of which is the center of mass of the system. The shape of the trajectory is determined by the total energy of the moving body, which consists of kinetic energy TO body mass m, moving at speed v, and potential energy U body located in a gravitational field at a distance r from a body with mass M. In this case, the law of conservation of the total energy of the body applies. E=K +U = const; K =mv2 /2, U=- GMm/ r.
The law of conservation of energy can be rewritten as: (2).
Constant h called constant energy
. It is directly proportional to the total mechanical energy of the body E and depends only on the initial radius vector r0 and initial speed v 0. At h < 0 кинетической энергии тела недостаточно для преодоления гравитационной связи. Величина радиус-вектора тела ограничена сверху и имеет место обращение по замкнутой, эллиптической орбите. Такое движение можно уподобить движению маятника – тот же самый переход кинетической энергии в потенциальную во время подъема и обратный – при опускании. Подобное движение называется finite
, i.e. closed. For h= 0, with an unlimited increase in the radius vector of the body, its speed decreases to zero - this is a parabolic motion. This kind of movement infinitely
, unlimited in space. At h> 0 the kinetic energy of the body is sufficiently large, and at an infinite distance from the attracting center the body will have a non-zero speed of removal from it - this is motion along a hyperbola. Thus, we can say that the body moves relative to the attracting center only along orbits that are conical sections. As follows from formula (2), the approach of a body to the attracting center should always be accompanied by an increase in the orbital speed of the body, and its removal by a decrease in accordance with Kepler’s second law. Kepler's second law has not been revised, but the third has been refined, and it reads like this: ratio of the cube of the semimajor axis. planetary orbit to the square of the period of revolution of the planet around the Sun is equal to the sum of the masses of the Sun and the planet, g
de (3)
M
Q
And m
masses of the Sun and planet, respectively; A
And T
– semimajor axis and period of revolution of the planet. Unlike the first two, Kepler's third law applies only to elliptical orbits.
In a generalized form, this law is usually formulated ( 4)
like this: The product of the sums of the masses of celestial bodies and their satellites with the squares of their sidereal periods of revolution are related as the cubes of the semimajor axes of their orbits, where M 1 and M 2 - masses of celestial bodies, m 1 and m 2 - respectively, the masses of their satellites, A 1 and A 2 - semimajor axes of their orbits, T 1 and T 2 - sidereal periods of circulation. It is necessary to understand that Kepler's law relates the characteristics of the motion of components of any arbitrary and independent space systems.
This formula can simultaneously include Mars with a satellite, and the Earth with the Moon, or the Sun with Jupiter.
If we apply this law to the planets of the solar system and neglect the masses of the planets M1 and M 2 compared to the mass of the Sun M☼ (i.e. M 1 << M☼, M 2 << M☼), then we get the formulation of the third law given by Kepler himself.
8. Determination of the masses of celestial bodies.
https://pandia.ru/text/78/063/images/image026_47.gif" width="157" height="53 src=">. Substituting here the values of the semi-major axes of the Earth and the Moon and their periods of revolution, we obtain that M U=3.3·10-6 M☼. Well, the absolute mass of the Sun is quite easy to calculate. Using directly formula (3), for the Sun-Earth pair, discarding the mass of the Earth due to its smallness in comparison with the mass of the Sun, we obtain for M☼=2·1030 kg.
Kepler's third law allows us to calculate not only the mass of the Sun, but also the masses of other stars. True, this can only be done for binary systems; the mass of single stars cannot be determined in this way. By measuring the relative positions of double stars over a long period of time, it is often possible to determine their orbital period T and find out the shape of their orbits. If the distance R to the binary star and the maximum αmax and minimum αmin angular dimensions of the orbit are known, then the semimajor axis of the orbit can be determined a= R (α max+ α min)/2 , then using equation (3) we can calculate the total mass of the binary star. If, based on observations, we determine the distance from the stars to the center of mass x1 And x2, or rather the attitude x1/x2, which remains constant, then the second equation appears x 1 / x 2 = m 2 / m 1 , making it possible to determine the mass of each star separately.
D.Z. § 8,9, 10. Problems 7,8 p.47.
Quick survey questions
1. What is the name of the point of the planet’s orbit closest to the Sun?:
2. What is the name of the most distant point of the Moon’s orbit?
3. How does the speed of motion of a comet change as it moves from perihelion to aphelion?
5. How does the synodic period of the outer planets depend on the distance to the Sun?
6. Why are they trying to build cosmodromes closer to the equator?
7. How does the gravitational field change inside the Earth?
8. Formulate Kepler's laws.
9. What is the average radius of the planet’s orbit?
Topic 3. Solar system and the movement of celestial bodies.
§1. solar system
The Solar System includes the Sun, 9 large planets with their 34 satellites, more than 100,000 small planets (asteroids), about 1011 comets, as well as countless small, so-called meteoric bodies (from 100 m in diameter to negligible dust particles).
The Sun occupies a central position in the Solar System. Its mass is 750 times greater than the mass of all other bodies included in this system. The gravitational extension of the Sun is the main force that determines the movement of all bodies of the Solar System orbiting around it. The average distance from the Sun to the planet Pluto, the farthest from it, is 6 billion km, which is very small compared to the distances to the nearest stars.
All the major planets - Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto - revolve around the Sun in the same direction (in the direction of the axial rotation of the Sun itself), in almost circular orbits. The plane of the earth's orbit, the ecliptic, is taken as the main plane when calculating the inclinations of the orbits of planets and other bodies revolving around the Sun.
Thanks to the almost circular shape of planetary orbits and the large gaps between them, the possibility of close encounters between planets is excluded. This ensures the long-term existence of the planetary system.
The planets also rotate around their axis, and for all planets except Venus and Uranus, rotation occurs in the forward direction, that is, in the same direction as their revolution around the Sun. The extremely slow rotation of Venus occurs in the opposite direction, and Uranus rotates as if lying on its side.
Most satellites orbit their planets in the same direction as the planet's axial rotation. The orbits of such satellites are usually circular and lie near the plane of the planet’s equator, forming a reduced semblance of a planetary system. Such, for example, is the system of satellites of Uranus and Jupiter. Satellites located far from the planet have reverse movements.
Saturn, Jupiter and Uranus, in addition to individual satellites of noticeable size, have many small satellites, as if merging into continuous rings. These satellites move in orbits so close to the planet that its tidal force prevents them from combining into a single body.
The vast majority of the orbits of currently known minor planets lie between the orbits of Mars and Jupiter. All minor planets orbit the Sun in the same direction as the major planets, but their orbits are usually elongated and inclined to the ecliptic plane
Comets move mainly in orbits close to parabolic. Some comets have elongated orbits of relatively small sizes. For these comets, called periodic, direct movements predominate, that is, movements in the direction of the planets' rotation.
Planets are divided into two groups, differing in mass, chemical composition, rotation speed and number of satellites. The four planets closest to the Sun are terrestrial planets , consist of dense rocky substance and metals. Giant planets - Jupiter, Saturn, Uranus and Neptune are much more massive, they consist mainly of light substances and therefore, despite the enormous pressure in their depths, they have low density. For Jupiter and Saturn, the main part of their mass is hydrogen and helium. For Uranus and Neptune, ice and rocky substances make up the bulk of their mass.
The interiors of the planets and some large satellites (for example, the Moon) are in a hot state.
Venus, Earth, and Mars have atmospheres consisting of gases released from their depths. The atmospheres of giant planets are a direct continuation of their interiors: these planets do not have a solid or liquid surface. When immersed inside, atmospheric gases gradually transform into a condensed state.
The nuclei of comets are similar in chemical composition to the giant planets: they consist of water ice and ice of various gases with an admixture of rocky substances. Almost all small planets in their composition belong to the rocky planets of the terrestrial group.
Debris from small planets formed when they collide with each other sometimes falls to Earth in the form of meteorites. Measurements of the age of meteorites have shown that they, and therefore the entire solar system, have existed for about 5 billion years.
The dynamic and physical features of the structure of the Solar System indicate that the planets were formed from gas and dust matter that once formed a planetary cloud around the Sun. The Terrestrial planets were formed as a result of the accumulation of rocky solid particles, and for the giant planets, the formation began with the accumulation of rocky-ice particles, and then was supplemented by the addition of gases (mainly hydrogen and helium).
§2. Kepler's laws
Studying the results of many years of observations of the planet Mars by the Danish astronomer T. Brahe, the German scientist Johannes Kepler discovered that the orbit of Mars is not a circle, but has an elongated ellipse shape. The ellipse has two such points F1 and F2 (Fig. 1), the sum of the distances ( r1 And r2 ) from any point B of the ellipse is a constant value.
https://pandia.ru/text/78/111/images/image002_190.gif" width="77 height=57" height="57">
The line connecting any point of the ellipse with one of its foci is called radius vector this point.
Kepler studied the movements of all the planets known at that time and deduced 3 laws of planetary motion:
Firstly, the orbits of all planets (not just Mars) are ellipses with a common focus at which the Sun is located. The degree of elongation of the orbits of different planets is different. The Earth's eccentricity is very small and the Earth's orbit differs little from a circle. The most elongated orbits are those of Mercury and Pluto.
Secondly, each planet moves in its orbit in such a way that its radius vector describes in equal time intervals equal areas(the areas of sectors A1A2F and B1B2F are equal). This means that the closer a planet is to the Sun, the faster its orbital speed.
Astronomy" href="/text/category/astronomiya/" rel="bookmark">astronomical unit), then, by determining from observations the period of revolution of a planet in years ( T), it is easy to obtain the value of the semi-major axis of this planet (α) using the formula:
For example, T Mars = 1.88 years, then according to the formula α orbit of Mars = 1.52 a. e.
Thus, Mars is almost one and a half times farther from the Sun than Earth.
The laws of planetary motion established by Kepler once again clearly show that the world of planets is a harmonious system governed by a single force, the source of which is the Sun.
§3. Configurations
Configurations are the characteristic positions of the planets of the Solar System in their orbits in relation to the sun and Earth.
They are different for the lower (inner) planets, which are closer to the Sun than the Earth (Mercury, Venus) and for the upper (outer) planets, whose orbits are located beyond the orbit of the Earth (the rest of the planets).
The moment at which the lower planet crosses the straight line connecting the centers of the Sun and the Earth is called its bottom connection . Near the inferior conjunction, the planet is visible as a narrow crescent. Directly at the moment of inferior conjunction, the planet is not visible, since it faces the Earth with its hemisphere not illuminated by the Sun. However, at this time, the phenomenon of a planet passing across the solar disk may occur, when the planets - Venus or Mercury - can be observed in the form of a black circle moving along the solar disk.
Continuing to move in orbit, the lower planet for an earthly observer reaches a certain greatest angular distance from the Sun, after which it begins to approach it again. The position of the greatest angular offset is called elongation . Mercury at elongation is about 28°, Venus is about 48° from the Sun. There are elongations eastern, when the planet is observed in the evening after sunset, and Western when it is visible in the morning, before sunrise.
The moment the lower planet passes directly behind the Sun is called top connection . Near the superior conjunction, the planet is observed as a complete disk.
For the upper planets, moments are distinguished confrontation , Western and Eastern quadratures and connections . In opposition, the upper planet is visible on the side of the sky opposite to the Sun, while the distance between it and the Earth is the smallest. This period is most favorable for astronomical observations of its surface. in quadratures, the angle between the directions to the planet and the sun is 90°. In conjunction, the upper planet, just like the lower one, goes behind the disk of the Sun and is lost in its rays. During this period, the distance from the Earth to the planet is greatest.
The Moon, in its revolution around the Earth, appears either between the Sun and the Earth, like the lower planet, or further from the Sun, like the upper planet. Therefore, in relation to the Moon, astronomers more often use special terminology, although in essence the moment of the new moon is similar to the inferior conjunction, the moment of the full moon is analogous to opposition.
§4. Elements of planetary orbits
The orientation of the orbit in space, its size and shape, as well as the position of the celestial body in orbit are determined by 6 quantities called orbital elements .
Some characteristic points of the orbits of celestial bodies have their own names: perihelion – the point of the orbit of a celestial body moving around the Sun closest to the Sun; aphelion – the point of the elliptical orbit farthest from the Sun.
If the motion of a body relative to the Earth is considered, then the point of the orbit closest to the Earth is called perigee , and the farthest one is climax .
In more common tasks, when the attracting center can mean different celestial bodies, the names are used: periapsis – the point closest to the center of the orbit; apocenter – the point farthest from the center of the orbit.
Orbital elements– 6 quantities that determine the shape and dimensions of the orbit of a celestial body ( a, e), its position in space ( i, Ω , ω ), as well as the position of the celestial body itself in orbit:
1) The shape and dimensions of the orbit are determined semimajor axis of the orbit (a = OP) and orbital eccentricity e .
https://pandia.ru/text/78/111/images/image007_87.gif" align="left" width="257" height="113 src=">For an elliptical orbit, the value e lies within 0 ≤ e< 1.
At e= 0 orbit has the shape of a circle; the closer e to unity, the more elongated the orbit. When e = 1, the orbit is no longer closed and has the form of a parabola; for e > 1 the orbit is hyperbolic.
2) The orientation of the orbit in space is determined relative to a certain plane, taken as the main one. For planets, comets and other bodies of the Solar System, such a plane serves ecliptic plane. The position of the orbital plane is specified by two orbital elements: longitude of the ascending nodeΩ And orbital inclinationi.
Longitude of the ascending node Ω - this is the angle at the Sun between the line of intersection of the orbital and ecliptic planes and the direction to the Aries point. The angle is measured along the ecliptic from the point of the vernal equinox clockwise to the ascending node of the orbit Ω, i.e., the point at which the body crosses the ecliptic, moving from the southern hemisphere to the northern. The opposite point is called descending node , and the line connecting the nodes is line of nodes .
0° ≤ Ω ≤ 360°
Q
– plane of the planet’s orbit
P – ecliptic plane
3) Position of the orbit in the plane Q determined by the perihelion argument ω , which is the angular distance of the orbital perihelion from the ascending node ω = Ω P.
4) As the sixth element that determines the position of a celestial body in orbit at any particular moment in time, use moment of passage through perihelion To .
The angle at the Sun, measured from the direction of perihelion to the direction of the body, is called true anomaly ν . The true anomaly when a body moves along its orbit changes unevenly: in accordance with Kepler’s second law, the body moves faster near perihelion P and slower at aphelion A. The true anomaly is calculated using formulas through the average anomaly.
§5. The concept of perturbed motion
The planets in their motion are attracted not only to the Sun, but also to each other. In star clusters, each star is attracted to all the others. The movement of artificial Earth satellites is influenced by forces caused by the non-spherical shape of the earth and the resistance of the earth's atmosphere, as well as the attraction of the Moon and the Sun. These additional forces are called disturbing , and the effects they cause in the movement of celestial bodies are disturbances . Due to disturbances, the orbits of celestial bodies continuously change slowly.
The study of the movement of celestial bodies taking into account disturbing forces is carried out by a special science - celestial mechanics.
Methods developed in celestial mechanics make it possible to very accurately determine the position of any bodies in the Solar System many years in advance. More complex computational methods are used to study the motion of artificial celestial bodies.
§6. Apparent daily movement of luminaries
During the day, each star makes a full revolution along its daily parallel. In Fig. the daily parallel of the star is depicted σ .
https://pandia.ru/text/78/111/images/image011_62.gif" align="left" width="252" height="132 src=">a) At the equator, the poles of the world lie on the horizon and coincide with points of north and south. The daily parallels of the stars in this case are in vertical planes.
b) At the north pole, the axis of the world is directed vertically upward, i.e. the north celestial pole P coincides with zenith z. The daily paths of all stars are in planes parallel to the horizon.
The position of the meridian becomes uncertain. Any direction from this point on the earth's surface will be south.
§7. Elongation of stars
Azimuth" href="/text/category/azimut/" rel="bookmark">azimuth during movement along the daily parallel fluctuates within ±A from the north point, with |A| ≤ 90°.
Elongation they call the position of stars when their azimuth takes extreme values. Depending on which side of the celestial sphere they occur, eastern and western elongations are distinguished. In Fig. star 1 has east elongation E E and western elongation E W. The star does not have 2 elongations.
§8. Ephemerides
Ephemerides are tables containing information about the position of celestial bodies in the sky, the speed of their movement, stellar magnitudes and other data necessary for astronomical observations. Ephemeris are compiled for future times based on the results of previously performed observations.
When calculating ephemeris, theories of the movement of celestial bodies and the laws of changes in their brightness are used.
Depending on the accuracy of the materials used, the ephemeris is calculated forward for different periods time. Thus, ephemerides of minor planets, containing their celestial coordinates, are compiled a year or more in advance. Ephemerides of artificial Earth satellites, whose movements are influenced by certain forces that cannot be accurately accounted for (for example, the resistance of the atmosphere, the density of which is constantly changing), can be compiled with the necessary accuracy only 1-2 months in advance.
Ephemeris may also contain telescope mounting angles, moon phases, and other information that helps make observations rationally. For example, observations of the Polar Star can be carried out not only at night, but also during daylight hours; To do this, it is necessary to compile in advance a special table of approximate horizontal coordinates (working ephemeris) - azimuth A and heights h Polar. By orienting the device according to their values, you can find the image of the North Star in the field of view of the pipe.
Compilation of the Polyarnaya ephemerides (i.e., the procedure for calculating approximate horizontal coordinates - height h and azimuth a at the expected moments of observation):
from AE choose φ ; local sidereal time s found by maternity time D .
The height of the celestial pole is equal to the latitude h p = φ
From a triangle zσk sides zk And zσ can, with some assumption, be considered equal to each other: 90°-φ-χ = 90°- h ,
where φ+χ = h .
In astronomical tables the value χ usually denoted by ƒ , Then h = φ+ƒ
Therefore, to determine h Polar, the required value is ƒ local sidereal time s and add it to φ .
Polar azimuth a is taken from the same tables by arguments s And φ . Next, the working ephemeris of Polyarnaya is calculated at a certain moment of observation with a given interval (for example, 30m).
Topic 4. Rotation of the Earth and Moon. Factors causing changes in the coordinates of stars.
§1. Features of the orbital and rotational motion of the Earth
Earth is one of the planets in the solar system. Like other planets, it moves around the Sun in an elliptical orbit, the semimajor axis of which (i.e., the average distance between the centers of the Earth and the Sun) is adopted in astronomy as a unit of length (au) to measure the distances between celestial bodies within solar system. The distance from the Earth to the Sun at different points of the orbit is not the same; at perihelion (January 3) it is approximately 2.5 million km less, and at aphelion (July 3) it is the same amount greater than the average distance, which is 149.6 million km.
As our planet moves in its orbit around the Sun, the plane of the Earth’s equator (inclined to the plane of the orbit at an angle of 23°27’) moves parallel to itself in such a way that in some parts of the orbit the globe is inclined towards the Sun with its northern hemisphere, and in others – with its southern hemisphere.
The daily rotation of the globe occurs with an almost constant angular velocity with a period of 23h56m04.1s, i.e. for one sidereal day. The axis of the Earth's daily rotation is directed with its northern end approximately towards the star alpha Ursa Minor , which is therefore called the North Star.
§2. Movement of the earth's poles
The axis of rotation of the Earth does not occupy a constant position in the body of the Earth, which seems to sway on its axis, as a result of which the earth’s poles describe a complex curve on the earth’s surface, not moving away from a certain average position by more than 0.3-0.4”. Due to the wandering of the pole on the surface of the Earth, the geographical coordinates of points located on the surface of the Earth - latitude and longitude - must change.
One of the features of the Earth is its magnetic field, thanks to which we can use a compass. The magnetic pole of the earth, to which the north end of the compass needle is attracted, does not coincide with the North Geographic Pole, but is located at a point with coordinates ≈ 76° N. w. and 101° W. d. The magnetic pole, located in the southern hemisphere of the Earth, has coordinates 66° south. w. and 140° E. d. (in Antarctica).
§3. Movement of the Moon
The Moon is the celestial body closest to Earth, natural satellite of our planet. It orbits the Earth at a distance of about 400 thousand km. The diameter of the Moon is only 4 times smaller than that of the Earth, it is equal to 3476 km. Unlike the Earth, which is compressed at the poles, the Moon is much closer in shape to a regular sphere.
When viewed from the North Pole, the Moon, like all the planets and satellites of the Solar System, orbits the earth in a counterclockwise direction. It takes 27.3 days to complete one revolution around the Earth. The time of one revolution of the Moon around the Earth is exactly equal to the time of one revolution around its axis. Therefore, the Moon is constantly turned to the Earth with the same side. It is assumed that in early periods During its history, the Moon rotated around its axis somewhat faster and, therefore, turned towards the Earth in different parts its surface. But due to the proximity of the massive Earth, significant tidal waves arose in the solid body of the Moon. They acted on the rapidly rotating Moon. The process of deceleration of the Moon continued until it was constantly turned to the Earth with only one side. This is where the concepts of visible and reverse side Moons. In total, 59% of the lunar surface can be seen from Earth.
§4. Precession and nutation
When the top rotates, its axis is practically never stationary. Under the influence of gravity, in accordance with the laws rotational movement, the axis of the top moves, describing a conical surface. The earth is a big top. And its axis of rotation, under the influence of the gravitational force of the Moon and the Sun on the equatorial excess (the equator seems to have more matter than the poles due to the oblateness of the Earth), also slowly rotates.
The Earth's rotation axis describes a cone with an angle of 23.5° near the ecliptic axis, as a result of which the celestial pole moves around the ecliptic pole in a small circle, making one revolution in approximately 26,000 years. this movement is called precession .
The consequence of precession is a gradual shift of the vernal equinox point towards the apparent movement of the Sun by 50.3” per year. for this reason, the Sun annually enters the vernal equinox 20 minutes earlier than it makes a full revolution in the sky.
Changing the position of the celestial equator and celestial pole, as well as moving the Aries point causes a change in the equatorial and ecliptic celestial coordinates. Therefore, when giving the coordinates of celestial bodies in catalogs or depicting them on maps, they must indicate the “epoch,” i.e., the moment in time for which the positions of the equator and the Aries point were taken when determining the coordinate system.
To a large extent, precession occurs under the influence of the gravitational forces of the Moon. The forces that cause precession, due to changes in the position of the Sun and Moon relative to the Earth, are constantly changing. Therefore, along with the movement of the Earth’s axis of rotation along the cone, its small vibrations are observed, called nutation . Under the influence of precession and nutation, the celestial pole describes a complex wave-like curve among the stars.
The rate of change in the coordinates of stars due to precession depends on the position of the stars on the celestial sphere. The declinations of different stars vary over the year from +20” to -20” depending on right ascension. Right ascensions change in a more complex way due to precession, and their corrections depend on both the right ascensions and the declinations of the stars. Precession tables are published in astronomical yearbooks.
Precession and nutation only change the orientation of the Earth's rotation axis in space and do not affect the position of this axis in the Earth's body. Therefore, neither the latitude nor the longitude of places on the earth’s surface change due to precession and nutation, and these phenomena do not affect the climate.
§5. Aberration of light
Light aberration is the apparent deviation of celestial bodies from their true position on the firmament, caused by the relative movement of the celestial body and the observer.
The phenomenon of aberration can be compared to what a person experiences in the pouring rain. A man standing in the rain holds his umbrella above his head. But when he walks, he is forced, if he wants to stay dry, to tilt the umbrella forward, and the faster he walks, the more he has to tilt the umbrella. And although the raindrops still fall straight down, it seems to the person that they are coming from the point towards which he tilted the umbrella.
Similarly, to a moving observer, the light of a celestial body seems to come not from the point at which the body is located, but from another point, shifted relative to the first in the direction of movement of the observer. Let some star be at the pole of the ecliptic. Its light falls on the Earth perpendicular to the direction of the speed of the Earth moving in its orbit. However, an astronomer pointing his telescope at the pole of the ecliptic will not see the star in the center of the field of view: a ray of light entering the lens of such a telescope needs time to pass through its entire tube, and during this time the tube will move along with the Earth and the image of the star will not will fall into the center of the field of view.
Thus, in order to observe the celestial body in the center of the field of view, the telescope has to be tilted at a certain angle forward according to the movement of the observer.
§5. Parallax
When riding on a train, pillars standing along the rails flash outside the window. Buildings located a few tens of meters away run back more slowly. railway. And very slowly, reluctantly, houses and groves, located somewhere near the horizon, lag behind the train. The speed at which the direction of an object changes when the observer moves is less, the further away the object is from the observer. And from this it follows that the magnitude of the angular displacement of the object, which is called parallactic displacement or simply parallax , you can characterize the distance to an object.
It is impossible to detect the parallactic displacement of a star by moving along the earth's surface: the stars are too far away, and the parallaxes during such movements are far beyond the possibility of their measurement.
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In this case, parallax is calculated for an imaginary observer moving from the center of the Earth to the equator point at which the star is on the horizon.
The daily movement of the Sun (as well as other celestial bodies) across the sky is a consequence of the rotation of the Earth around its axis, which is directed from west to east, and, accordingly, the apparent movement of the Sun occurs from east to west. However, due to the presence of a slope earth's axis to the orbital plane around the Sun, the sunrise/sunset points as the Earth revolves around the Sun are constantly shifting, and as a result, sunrise/sunset in the east/west occurs only near the equinoxes, which fall on the beginning of the 20th of March and September. In summer, the northern hemisphere of the Earth faces the Sun, respectively, in mid-latitudes the sunrise point shifts to the northeast, and the sunset point to the northwest, and in winter, the Earth exposes the southern hemisphere to the Sun and the sunrise occurs in the southeast, and sunset in the southwest .
The annual path of the Sun relative to the stars is associated with the revolution of the Earth around the Sun. Of course, due to the fact that the stars are invisible during the day, it is difficult to track this movement of the Sun, although during the day, due to this movement, the Sun moves against the background of the stars by a whole degree (i.e., by two of its visible sizes). However, the presence of this movement is indicated by the appearance of the starry sky changing with the seasons, and specifically by the observed constellations. For example, the constellation Orion can be observed in the dark sky from autumn to mid-spring, but during the rest of the year the Sun is too close to this constellation (although it does not directly pass through it), and in the daytime sky the stars that make up this constellation can be seen with the naked eye does not seem possible. The Sun, when observed from Earth throughout the year, moves across the sky along a line called the ecliptic, which indicates the plane of the Earth's orbit (more precise definition− plane of the orbit of the center of mass of the Earth-Moon system) and passes through 13 constellations (Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Ophiuchus, Sagittarius, Capricorn, Aquarius and Pisces). Since the Earth revolves around the Sun in an elliptical orbit, the orbital speed is a variable value, which naturally affects the apparent movement of the Sun along the ecliptic. The apparent movement is also uneven - the Sun passes one half of the ecliptic more slowly (when the Earth is more distant from the luminary), and the second - faster, due to this, in the northern hemisphere, spring and summer are somewhat longer than autumn and winter. When it’s summer in the northern hemisphere, the Earth is farthest from the Sun and moves slowest in its orbit, and when it’s winter, it’s closest and moves faster (in the southern hemisphere it’s still the other way around).
Apparent motion of the moon
The plane of the lunar orbit has an inclination of 5 degrees to the plane of the earth's orbit around the Sun, thus the apparent movement of the Moon relative to the stars passes close to the ecliptic line. But the speed of this movement is much greater than that of the Sun. If the Sun moves relative to the stars across the sky by an amount equal to its apparent diameter in half an Earth day, then the Moon covers the same distance in about 1 hour, and since the Moon can be observed in the dark sky, it is not difficult to track this displacement against the background of the stars. The Moon moves in its orbit in the same direction as the Earth rotates around its axis (counterclockwise when viewed from the north pole), so the apparent movement of the Moon against the background of stars will occur from west to east. Due to the even greater ellipticity of the lunar orbit than the earth's, the apparent motion of the Moon will be more uneven. The Moon travels relative to the stars (and around the Earth) in 27 days, 7 hours, 43 minutes, 11.5 seconds. During the new moon, the Moon is in the same direction in the sky as the Sun (i.e., between the Earth and the Sun) and therefore faces the unlit side. However, gradually moving further and further from the star to the east, the edge of the lunar disk illuminated by the Sun begins to grow, and so on until the full moon. The full Moon rises in the eastern sky and roughly follows the daily path of the Sun six months ago. Thus, in the northern hemisphere in the summer months, when the Sun rises in the northeast, rises high and sets in the northwest - the Moon, in turn, rises in the southeast, does not rise high above the horizon, and sets in the south in the morning. west (like the Sun during the day in the northern hemisphere in winter). The presence of intersections of the planes of the lunar and earth's orbits gives us the opportunity to observe phenomena such as solar and lunar eclipses. However, they occur only if the following conditions, independent of each other, are simultaneously met - the Moon on its path relative to the stars must be close to the point of intersection of this path with the ecliptic, and there must also be a new moon (for a solar eclipse) or a full moon (for a lunar eclipse).
Apparent motion of planets
The orbital planes of the planets have an inclination of no more than a few degrees to the plane of the Earth's orbit, therefore, their apparent path relative to the stars passes close to the ecliptic, but the trajectory of this movement is much more complex than that of the Sun and Moon. Initially moving in the same direction as the Moon and the Sun (from west to east (forward motion)), the planets at some point begin to slow down, stop, and then move for some time from east to west (retrograde motion), after after which they slow down again and again switch to direct movement. The trajectory of movement when changing directions has the shape of a loop.
The motion of planets closer to the Sun than the Earth (inferior planets) is somewhat different from the motion of planets that are further away from the Earth (upper planets). Venus moves across the sky faster than the Sun in the forward direction, overtakes it, then stops no more than 47 degrees from the Sun (this is the point of maximum angular distance from the luminary (eastern elongation)), after which it switches to a retrograde motion and passes the Sun again and again stops no further than 47 degrees from the luminary (western elongation) then again switches to direct motion. Mercury is also moving, only the size of the loop will be smaller, since Mercury is closer to the Sun and its angular distance from the sun is very small, a maximum of 28 degrees. In the case of Mars and other upper planets, the movement in the forward direction will be slower than that of the Sun, therefore, the planets will gradually lag behind it, while being increasingly west of the sun. When the planet is in the opposite direction from the Sun, its movement against the background of the stars will slow down, and it will switch to a backward movement, which will soon slow down and again move to a forward movement, after which the planet will begin to approach the Sun in the sky. The further away the upper planet is, the smaller the size of the loop will be when changing directions of movement.
Changes in directions of motion are caused by the unequal orbital speed of the planets. The retrograde motion of Venus and Mercury occurs when they overtake the Earth, moving in their orbit and at the same time being on the same side of the Sun with the Earth. And in the case of the upper planets, on the contrary, the Earth overtakes them and because of this they receive a retrograde motion. Loops are obtained due to the fact that the planetary orbits do not lie in the same plane, but have, albeit small, inclinations relative to the plane of the earth’s orbit.
Apparent motion of stars
When the apparent motion of the bodies of the Solar System was considered, the phrase “motion relative to the stars” was very often mentioned, which can give the impression that the stars are completely motionless. In reality, this is not the case, it’s just that the speeds of stars are so small compared to the distances to them that it is almost impossible to notice their movement with the naked eye, even over decades. The movement is best seen in those stars that have high real speeds across the observer’s line of sight and at the same time are still in relative proximity to the Sun, so that this speed is at least somehow noticeable, because when removed from hundreds of light years, even at transverse speeds of hundreds of km/s, the position of the star will change extremely slowly . Among the stars (except the Sun), Barnard's Star has the highest proper motion in the sky - a very dim red dwarf, which, despite a distance of 6 light years from the Sun, is not visible to the naked eye. But, nevertheless, this star moves across the sky by 10 arcseconds per year, which is more than 180 times less than its apparent diameter full moon. It is not difficult to guess that it takes approximately the same number of years for a star to move against the background of more distant stars in the sky to a distance equal to the size of the Moon. But this is only one star with such a large proper motion; for other stars these motions are much slower.
Space exploration has long gone beyond imagination:
– every year astronauts go beyond the Earth;
– people launch satellites, some of which have already crossed the solar system;
– huge telescopes observe the stars from the orbit of our planet.
Who was the first pioneer in the sky? What incredible theories are behind our space achievements? What does the future hold for us? This book will briefly and clearly tell you about the most important discoveries in the field of astronomy, about the people who made them.
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Tycho Brahe's observations and measurements allowed his student, the German scientist Johannes Kepler, to make next step in the development of astronomy.
Geocentric Ptolemaic world system and Copernican heliocentric system
Calculating the orbit of Mars, Kepler discovered that it is not a circle, as Copernicus and other scientists believed, but an ellipse. At first, he did not extend this conclusion to other planets, but later he realized that not only Mars, but all planets have an ellipsoidal orbit. Thus, Kepler's first law of planetary motion was discovered. In modern formulation it sounds like this: each planet of the solar system revolves in an ellipse, at one of the foci of which the Sun is located.
The second law of planetary motion was a logical consequence of the first. Even before the formulation of the first law, while observing the movement of Mars, Kepler noticed that the planet moves slower the further it is from the Sun. The elliptical shape of the orbit fully explains this feature of motion. Over equal periods of time, a straight line connecting a planet to the Sun describes equal areas - this is Kepler’s second law.
The second law explains the change in the speed of the planet, but does not provide any calculations. The formula for calculating how fast the planets rotate and how long it takes to travel around the Sun is Kepler's third law.
Kepler's research put an end to the dispute between the world systems of Ptolemy and Copernicus. He convincingly proved that the Sun, not the Earth, is at the center of our system. After Kepler, no further attempts were made in the scientific world to revive the geocentric system.
The accuracy of the three laws of planetary motion discovered by Kepler was confirmed by numerous astronomical observations. Nevertheless, the basis and reasons for these laws remained unclear until at the end of the 17th century. Newton's genius did not manifest itself.
Everyone knows the story of how Newton discovered the law of universal gravitation: an apple fell on his head, and Newton realized that the apple was attracted to the Earth. In the extended version of this legend, there is also the Moon, which the scientist looked at while sitting under an apple tree.
After the apple fell, Newton realized that the force that caused the apple to fall and the force that kept the Moon in Earth's orbit were of the same nature.
In reality, of course, everything was far from so simple. Before the discovery of the famous law, Newton devoted many years to the study of mechanics, the laws of motion and interaction between bodies. He was not the first to suggest the existence of gravitational forces. Galileo Galilei spoke about this, but he believed that attraction to the Earth acts only on our planet and extends only to the Moon. Kepler, who discovered the laws of planetary motion, was sure that they work exclusively in space and have no relation to terrestrial physics. Newton was able to combine these two approaches - he was the first to realize that physical laws, primarily the law of universal gravitation, are universal and applicable to all material bodies.
The essence of the law of universal gravitation comes down to the fact that there is attraction between absolutely all bodies in the Universe. The force of attraction depends on two main quantities - the mass of bodies and the distance between them. The heavier the body, the more strongly it attracts lighter bodies. The Earth attracts the Moon and holds it in its orbit. The Moon also has a certain effect on our planet (it causes tides), but the gravitational force of the Earth, due to its larger mass, is greater.
In addition to the law of universal gravitation, Newton formulated three laws of motion. The first of them is called the law of inertia. It states: if no force is applied to a body, it will remain in a state of rest or uniform rectilinear movement. The second law introduces the concept of force and acceleration, and these two quantities, as Newton proved, depend on the mass of the body. The greater the mass, the less acceleration will be for a certain applied force. Newton's third law describes the interaction of two material objects. Its simplest formulation says: action is equal to reaction.
The discoveries made by Isaac Newton and the formulas he derived gave astronomy a powerful tool that made it possible to advance this science far forward. Many phenomena that had no explanation before have revealed their nature. It became clear why planets revolve around the Sun, and satellites revolve around planets, without flying into outer space: they are held by the force of gravity. The speed of the planets remains uniform due to the law of inertia. The round shape of celestial bodies also received its explanation: it is acquired due to gravity, attraction to a more massive center.
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