Scientists have said that the Earth will be devastated by the mysterious planet X Nibiru. Orbital velocities of the planets of the Solar System: characteristics and trajectories

Even in ancient times, pundits began to understand that it is not the Sun that revolves around our planet, but everything happens exactly the opposite. Nicolaus Copernicus put an end to this controversial fact for humanity. The Polish astronomer created his heliocentric system, in which he convincingly proved that the Earth is not the center of the Universe, and all planets, in his firm belief, revolve in orbits around the Sun. The work of the Polish scientist “On the Rotation of the Celestial Spheres” was published in Nuremberg, Germany in 1543.

The ancient Greek astronomer Ptolemy was the first to express ideas about how the planets are located in the sky in his treatise “The Great Mathematical Construction of Astronomy”. He was the first to suggest that they make their movements in a circle. But Ptolemy mistakenly believed that all the planets, as well as the Moon and the Sun, move around the Earth. Before Copernicus's work, his treatise was considered generally accepted in both the Arab and Western worlds.

From Brahe to Kepler

After the death of Copernicus, his work was continued by the Dane Tycho Brahe. The astronomer, a very wealthy man, equipped the island he owned with impressive bronze circles, on which he applied the results of observations of celestial bodies. The results obtained by Brahe helped the mathematician Johannes Kepler in his research. It was the German who systematized the movement of the planets of the solar system and derived his three famous laws.

From Kepler to Newton

Kepler was the first to prove that all 6 planets known at that time moved around the Sun not in a circle, but in ellipses. The Englishman Isaac Newton, having discovered the law of universal gravitation, significantly advanced humanity’s understanding of the elliptical orbits of celestial bodies. His explanations that the ebb and flow of tides on Earth are influenced by the Moon turned out to be convincing to the scientific world.

Around the Sun

Comparative sizes of the largest satellites of the Solar System and the Earth group planets.

The time it takes the planets to complete a revolution around the Sun is naturally different. For Mercury, the closest star to the star, it is 88 Earth days. Our Earth goes through a cycle in 365 days and 6 hours. The largest planet in the solar system, Jupiter, completes its revolution in 11.9 Earth years. Well, Pluto, the most distant planet from the Sun, has a revolution of 247.7 years.

It should also be taken into account that all the planets in our solar system move, not around the star, but around the so-called center of mass. At the same time, each, rotating around its axis, sways slightly (like a spinning top). In addition, the axis itself may shift slightly.

solar system– these are 8 planets and more than 63 of their satellites, which are being discovered more and more often, several dozen comets and a large number of asteroids. All cosmic bodies move along their own clearly directed trajectories around the Sun, which is 1000 times heavier than all the bodies in the solar system combined. The center of the solar system is the Sun, a star around which the planets orbit. They do not emit heat and do not glow, but only reflect the light of the Sun. There are now 8 officially recognized planets in the solar system. Let us briefly list them all in order of distance from the sun. And now a few definitions.

Planet is a celestial body that must satisfy four conditions:
1. the body must revolve around a star (for example, around the Sun);
2. the body must have sufficient gravity to have a spherical or close to it shape;
3. the body should not have other large bodies near its orbit;
4. the body should not be a star

Satellites of the planets. The solar system also includes the Moon and the natural satellites of other planets, which they all have except Mercury and Venus. Over 60 satellites are known. Most of the satellites of the outer planets were discovered when they received photographs taken by robotic spacecraft. Jupiter's smallest satellite, Leda, is only 10 km across.

More similar to Earth in size and brightness. Observing it is difficult due to the clouds enveloping it. The surface is a hot rocky desert. Period of revolution around the Sun: 224.7 days.
Diameter at the equator: 12104 km.
Rotation period (rotation around an axis): 243 days.
Surface temperature: 480 degrees (average).
Atmosphere: dense, mostly carbon dioxide.
How many satellites: 0.
The main satellites of the planet: 0.

Because of its resemblance to Earth, it was believed that life existed here. But the spacecraft that descended to the surface of Mars found no signs of life. This is the fourth planet in order. Period of revolution around the Sun: 687 days.
Diameter of the planet at the equator: 6794 km.
Rotation period (rotation around an axis): 24 hours 37 minutes.
Surface temperature: -23 degrees (average).
The planet's atmosphere: thin, mostly carbon dioxide.
How many satellites: 2.
The main satellites in order: Phobos, Deimos.

It is number 2, the largest of the planets in the solar system. Saturn attracts attention thanks to its ring system formed of ice, rocks and dust that orbit the planet. There are three main rings with an outer diameter of 270,000 km, but their thickness is about 30 meters. Period of revolution around the Sun: 29 years 168 days.
Diameter of the planet at the equator: 120536 km.
Rotation period (rotation around an axis): 10 hours 14 minutes.
Surface temperature: –180 degrees (average).
Atmosphere: Mainly hydrogen and helium.
Number of satellites: 18 (+ rings).
Main satellites: Titan.

At the moment, Neptune is considered the last planet in the solar system. Its discovery took place through mathematical calculations, and then it was seen through a telescope. In 1989, Voyager 2 flew past. He took stunning photographs of the blue surface of Neptune and its largest moon, Triton. Period of revolution around the Sun: 164 years 292 days.
Diameter at the equator: 50538 km.
Rotation period (rotation around an axis): 16 hours 7 minutes.
Surface temperature: –220 degrees (average).
Atmosphere: Mainly hydrogen and helium.
Number of satellites: 8.
Main satellites: Triton.

How did the planets appear? Approximately 5–6 billion years ago, one of the disk-shaped gas and dust clouds of our large Galaxy (Milky Way) began to shrink toward the center, gradually forming the present Sun. Further, according to one theory, under the influence of powerful forces of attraction, a large number of dust and gas particles revolving around the Sun began to stick together into balls - forming future planets. As another theory says, the gas and dust cloud immediately broke up into separate clusters of particles, which compressed and became denser, forming the current planets. Now 8 planets revolve around the Sun constantly.

On March 13, 1781, English astronomer William Herschel discovered the seventh planet of the solar system - Uranus. And on March 13, 1930, American astronomer Clyde Tombaugh discovered the ninth planet of the solar system - Pluto. By the beginning of the 21st century, it was believed that the solar system included nine planets. However, in 2006, the International Astronomical Union decided to strip Pluto of this status.

There are already 60 known natural satellites of Saturn, most of which were discovered using spacecraft. Most of the satellites consist of rocks and ice. The largest satellite, Titan, discovered in 1655 by Christiaan Huygens, is larger than the planet Mercury. The diameter of Titan is about 5200 km. Titan orbits Saturn every 16 days. Titan is the only moon to have a very dense atmosphere, 1.5 times larger than Earth's, consisting primarily of 90% nitrogen, with moderate methane content.

The International Astronomical Union officially recognized Pluto as a planet in May 1930. At that moment, it was assumed that its mass was comparable to the mass of the Earth, but later it was found that Pluto’s mass is almost 500 times less than the Earth’s, even less than the mass of the Moon. Pluto's mass is 1.2 x 10.22 kg (0.22 Earth's mass). Pluto's average distance from the Sun is 39.44 AU. (5.9 to 10 to 12 degrees km), radius is about 1.65 thousand km. The period of revolution around the Sun is 248.6 years, the period of rotation around its axis is 6.4 days. Pluto's composition is believed to include rock and ice; the planet has a thin atmosphere consisting of nitrogen, methane and carbon monoxide. Pluto has three moons: Charon, Hydra and Nix.

At the end of the 20th and beginning of the 21st centuries, many objects were discovered in the outer solar system. It has become obvious that Pluto is only one of the largest Kuiper Belt objects known to date. Moreover, at least one of the belt objects - Eris - is a larger body than Pluto and is 27% heavier. In this regard, the idea arose to no longer consider Pluto as a planet. On August 24, 2006, at the XXVI General Assembly of the International Astronomical Union (IAU), it was decided to henceforth call Pluto not a “planet”, but a “dwarf planet”.

At the conference, a new definition of a planet was developed, according to which planets are considered bodies that revolve around a star (and are not themselves a star), have a hydrostatically equilibrium shape and have “cleared” the area in the area of ​​their orbit from other, smaller objects. Dwarf planets will be considered objects that orbit a star, have a hydrostatically equilibrium shape, but have not “cleared” the nearby space and are not satellites. Planets and dwarf planets are two different classes of objects in the Solar System. All other objects orbiting the Sun that are not satellites will be called small bodies of the Solar System.

Thus, since 2006, there have been eight planets in the solar system: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune. The International Astronomical Union officially recognizes five dwarf planets: Ceres, Pluto, Haumea, Makemake, and Eris.

On June 11, 2008, the IAU announced the introduction of the concept of "plutoid". It was decided to call celestial bodies revolving around the Sun in an orbit whose radius is greater than the radius of Neptune’s orbit, whose mass is sufficient for gravitational forces to give them an almost spherical shape, and which do not clear the space around their orbit (that is, many small objects revolve around them) ).

Since it is still difficult to determine the shape and thus the relationship to the class of dwarf planets for such distant objects as plutoids, scientists recommended temporarily classifying all objects whose absolute asteroid magnitude (brilliance from a distance of one astronomical unit) is brighter than +1 as plutoids. If it later turns out that an object classified as a plutoid is not a dwarf planet, it will be deprived of this status, although the assigned name will be retained. The dwarf planets Pluto and Eris were classified as plutoids. In July 2008, Makemake was included in this category. On September 17, 2008, Haumea was added to the list.

The material was prepared based on information from open sources

Dr. Alexander Vilshansky

An approach to understanding the reason for the pushing of some bodies towards others (pushing [Amer.] - pushing) was substantiated based on the idea of ​​gravitons (graviton hypothesis). This approach makes it possible to understand the reasons for the rotational motion of planets in the solar system. The reason for the rotation of the Sun itself is not discussed in this article.

Movement of planets in orbits

The eternal and constant motion of the planets in their circumsolar orbits seems to be somewhat mysterious. It is difficult to imagine that there is absolutely nothing preventing the Earth from moving in orbit at a speed of 30 km/sec. Even assuming the absence of ether, there is a sufficient amount of more or less coarse cosmic dust and small meteorites through which the planet passes. And if for large planets this factor is quite small, then with a decrease in the size of the body (up to an asteroid), its mass decreases much faster than the cross section, which determines the dynamic resistance to motion. Nevertheless, most asteroids rotate in orbits at a constant speed, without signs of braking. It seems that Newtonian “attraction” alone is not enough to keep the system in eternal rotation. Such an explanation can be proposed within the framework of the graviton hypothesis set out in.

"Space Broom"

Fig.1 (image on the left) shows the trajectories of gravitons that take part in creating “pushing” (pushing force) if they pass through a large mass that does not rotate. In this case, the pattern of forces creating pressure on the smaller mass is completely symmetrical. Figure 2 (image on the right) shows the trajectories of gravitons and the total force exerted on a small body by a rotating large mass. It can be seen that the sector from which gravitons come, forming the right (relative to half) part of the absorbed flow, compensating the left part of the free flow, turns out to be slightly larger than the number of gravitons coming from the left hemisphere. Therefore, the total vector X is slightly larger than the vector Y, which creates a deviation of the resulting vector Z. This vector, in turn, can be decomposed into two vectors. One of them is directed exactly to the center of gravity O, and the other is perpendicular to it, and directed along the tangent to the orbit. It is this component of the pushing force that causes the planet to move in orbit during the rotation of the massive body S.

Thus, around the rotating massive body, a kind of “broom” or “spinner” appears, pushing each elementary mass of the planet tangentially to the orbit in the direction of rotation of the main mass. Since the impact is made on each elementary part of the planet, the action of the “broom” is proportional to the mass of the body it carries in orbit.

But if the matter were limited to this, then the speeds of the planets would continuously increase, and circular orbits could not be stable. Obviously, there is a braking factor, and it should also be proportional to the mass. Such a factor is most likely the graviton gas itself, that is, the gravitons themselves, penetrating the body from all sides. No matter how high the speed of gravitons is, if they influence the elementary masses, as explained earlier, then the elementary masses themselves will experience a certain resistance when moving through the graviton gas.

It is interesting to note that R. Feynman in one of his lectures, considering the possibility of explaining gravity by “pushing,” puts forward as the main objection against it precisely the braking effect of graviton gas, assuming its existence. Of course, Feynman is right if we limit our consideration to the very fact of the presence of such a “gas”, and do not understand in more detail the consequences of the graviton hypothesis, namely the existence of the “Cosmic Broom”. At a certain speed in a given orbit, equality arises between the accelerating force (from the side of the “broom”) and the braking force (from the side of the graviton gas). And thus Feynman's main objection is removed.

The force of the panicle decreases in proportion to the square of the angle at which the planet is visible from the Sun. The force of resistance to motion from the graviton gas practically does not depend on the distance, but depends only on the mass of the body moving in orbit. Thus, it does not matter what mass is in a given orbit. By increasing the mass, we increase the driving force, and at the same time increase the braking force. If the Earth were in Jupiter’s orbit, it would steadily move at the speed of Jupiter (in fact, Kepler talks about this). The orbital parameters do not depend on the mass of the planet (if its relative mass is sufficiently small). An important consequence follows from all this - a planet can have satellites only if it has not only a certain mass, but also a certain speed of rotation around its axis, creating the “space broom” effect. If the planet rotates slowly, then it cannot have satellites; the whisk “does not work.” This is why Venus and Mercury do not have satellites. The moons of Jupiter also do not have satellites, although some of them are comparable in size to the Earth.

That is why Phobos, the satellite of Mars, is gradually approaching Mars. Most likely, the parameters of Phobos are critical. The “broom” formed by Mars with its rotation speed of 24 hours and a mass of 0.107 Earth’s creates just the critical force for the 10,000 km semi-axis. Apparently all bodies that have a product of relative mass and relative rotation speed of less than 0.1 (like Mars) cannot have satellites. In theory, Deimos should behave the same way. On the other hand, since the Moon is moving away from the Earth, it can be assumed that the Earth has excess energy from the Broom, and it is accelerating the Moon.

On the reverse rotation of the distant satellites of Jupiter and Saturn

The reverse rotation of the outer satellites of Saturn and Jupiter is due to the fact that the “cosmic broom” at such distances ceases to effectively “revenge”. Nevertheless, the attraction of the central body takes place. But this attraction is quite weak, so the situation is somewhat different than in the case of an ordinary (“fast-flying”) satellite. As the satellite approaches, the planet seems to elude it. See Fig.2A (image on the left) For the same reason, objects located in the Solar System at a very large distance from the Sun can move along paths different from those calculated without taking into account the action of the “space broom”.

Converting elliptical orbits to circular ones

The angle at which the planet is visible from the apogee of the satellite is significantly less than the angle at which it is visible from the perigee of the orbit. This leads to more than just that. that (as has already been said) the force of pushing (attraction) decreases, but in proportion to it the total flow of gravitons creating shading decreases, and therefore their relative number, which has a tangential speed shift. Therefore, at apogee the satellite is “pushed” forward by a smaller number of gravitons, and at perigee by a larger number. See Fig.3 (image on the left) It follows, in particular, that the perihelion of the orbit of any body rotating around a star must always shift, following the direction of rotation of the star itself. Therefore, in the presence of graviton (and any other) braking, the elliptical orbit should turn into a circular one - after all, the maximum braking will take place at high speed (at perigee), and the minimum at the apogee. Equilibrium must occur in a very specific orbit. Roughly speaking, first the elliptical orbit turns into a circular one, and then the radius of the circular orbit is gradually “brought” to a stable one. In fact, these processes can hardly be separated physically.

Asteroids

Any celestial body of small size that falls into the gravitational field (graviton shadow - see above) of a sufficiently massive rotating body (star), regardless of what orbit it had initially, will at the first stage move to a circular orbit, and then will be accelerated by a “broom” » to equilibrium linear speed. Therefore, any star should have an “asteroid belt,” even if it does not have a planetary system. These small fragments form into a layer at a certain distance from the Star, and this layer can be fractionated (consist of smaller distinct layers).

The planets of the solar system revolve around the sun in elliptical orbits (see. Kepler's laws) and are divided into two groups. Planets that are closer to the Sun than Earth are called lower. These are Mercury and Venus. Planets that are located further from the Sun than Earth are called top. These are Mars, Jupiter, Saturn, Uranus, Neptune and Pluto.

Planets in the process of revolving around the Sun can be located relative to the Earth and the Sun in an arbitrary manner. This mutual arrangement of the Earth, the Sun and the planet is called configuration. Some of the configurations are highlighted and have special names (see Fig. 19).

The lower planet can be located on the same line with the Sun and Earth: either between the Earth and the Sun - bottom connection, or behind the Sun - top connection. At the moment of inferior conjunction, a planet may pass across the disk of the Sun (the planet is projected onto the disk of the Sun). But due to the fact that the orbits of the planets do not lie in the same plane, such passages do not occur every inferior conjunction, but quite rarely. Configurations in which the planet, when observed from Earth, is at its maximum angular distance from the Sun (these are the most favorable periods for observing the lower planets) are called greatest elongations, western And eastern.

The upper planet can also be in line with the Earth and the Sun: behind the Sun - compound, and on the other side of the Sun - confrontation. Opposition is the most favorable time to observe the upper planet. Configurations in which the angle between the directions from the Earth to the planet and to the Sun is 90 o, are called quadratures, western And eastern.

The time interval between two successive planetary configurations of the same name is called its synodic circulation period P, in contrast to the true period of its revolution relative to the stars, therefore called sidereal S. The difference between these two periods arises due to the fact that the Earth also revolves around the Sun with a period T. The synodic and sidereal periods are interconnected:

10.2. Kepler's laws

The laws by which the planets revolve around the Sun were established empirically (i.e., from observations) by Kepler, and then theoretically justified on the basis of Newton's law of universal gravitation.

First law. Each planet moves in an ellipse, with the Sun at one focus.

Second law. When a planet moves, its radius vector describes equal areas in equal periods of time.

Third law. The squares of the sidereal revolution times of the planets are related to each other as the cubes of the semimajor axes of their orbits (as the cubes of their average distances from the Sun):

Kepler's third law is an approximate one; it was derived from the law of universal gravitation refined Kepler's third law:

Kepler's third law is satisfied with good accuracy only because the masses of the planets are much less than the mass of the Sun.

An ellipse is a geometric figure (see Fig. 20) that has two main points - tricks F 1 , F 2, and the sum of the distances from any point of the ellipse to each of the foci is a constant value equal to the major axis of the ellipse. The ellipse has center O, the distance from which to the most distant point of the ellipse is called semi-major shaft a, and the distance from the center to the nearest point is called minor axis b. The quantity that characterizes the oblateness of the ellipse is called eccentricity e:

A circle is a special case of an ellipse ( e=0).

The distance from the planet to the Sun varies from the smallest, equal to

10.3. Movement of artificial celestial bodies

The movement of artificial celestial bodies is subject to the same laws as natural ones. However, a number of features need to be noted.

The main thing is that the size of the orbits of artificial satellites, as a rule, is comparable to the size of the planet around which they orbit, therefore they often talk about the height of the satellite above the surface of the planet (Fig. 21). It should be taken into account that the center of the planet is at the focus of the satellite’s orbit.

For artificial satellites, the concept of first and second escape velocity is introduced.

First escape velocity or circular velocity is the speed of circular orbital motion at the surface of the planet at altitude h:

Second escape velocity or parabolic speed is the speed that must be given to the spacecraft so that it can leave the sphere of gravity of a given planet in a parabolic orbit:

The speed of a celestial body at any point in the elliptical orbit at a distance R from the gravitating center can be calculated using the formula:

Questions

4. Could Mars pass across the solar disk? Transit of Mercury? Transit of Jupiter?

5. Is it possible to see Mercury in the east in the evening? And Jupiter?

Tasks

Solution: The orbits of all planets lie approximately in the same plane, so the planets move along the celestial sphere approximately along the ecliptic. At the moment of opposition, the right ascensions of Mars and the Sun differ by 180 o : . Let's calculate for May 19th. On March 21 it is 0 o. The sun's right ascension increases by about 1 per day o. 59 days passed from March 21 to May 19. So, , a . On the celestial map you can see that the ecliptic with such a right ascension passes through the constellations Libra and Scorpio, which means Mars was in one of these constellations.

47. The best evening visibility of Venus (its greatest distance east of the Sun) was on February 5th. When is Venus next visible under the same conditions, if its sidereal orbital period is 225 d ?

Solution: Venus's best evening visibility occurs during its eastern elongation. Therefore, the next best evening visibility will occur during the next easterly elongation. And the time interval between two successive eastern elongations is equal to the synodic period of revolution of Venus and can be easily calculated:

48. (663) Determine the mass of Uranus in units of the mass of the Earth, comparing the movement of the Moon around the Earth with the movement of the satellite of Uranus - Titania, orbiting around it with a period of 8 d.7 at a distance of 438,000 km. Orbital period of the Moon around the Earth 27 d.3, and its average distance from the Earth is 384,000 km.

Solution: To solve the problem, it is necessary to use Kepler's third refined law. Since for any body of mass m, orbiting another body of mass at an average distance a with period T:

(36)

Then we have the right to write down the equality for any pair of celestial bodies revolving around each other:

49. Taking the Moon's orbit as a circle and knowing the Moon's orbital speed v L = 1.02 km/s, determine the mass of the Earth.

Solution: Let us recall the formula for the square of circular velocity () and substitute the average distance of the Moon from the Earth a L (see previous problem):

50. Calculate the mass of the binary star Centauri, whose period of revolution of the components around the common center of mass is T = 79 years, and the distance between them is 23.5 astronomical units (AU). An astronomical unit is the distance from the Earth to the Sun, equal to approximately 150 million km.

Solution: The solution to this problem is similar to the solution to the problem of the mass of Uranus. Only when determining the masses of double stars are they compared with the Sun-Earth pair and their mass expressed in solar masses.

51. (1210) Calculate the linear velocities of the spacecraft at perigee and apogee if it flies above the Earth at perigee at an altitude of 227 km above the ocean surface and the major axis of its orbit is 13,900 km. The radius and mass of the Earth are 6371 km and 6.0 10 27 g.

Solution: Let's calculate the distance from the satellite to the Earth at apogee (the greatest distance from the Earth). To do this, it is necessary, knowing the distance at perigee (the shortest distance from the Earth), to calculate the eccentricity of the satellite’s orbit using formula () and then determine the required distance using formula (32). We get h a= 931 km.