The apparent movement of the planets in the sky. The laws of motion of the planets of the solar system

Apparent movement of the planets Movements of the Sun and planets along celestial sphere reflect only their visible, that is, movements that seem to an earthly observer. Moreover, any movements of the luminaries in the celestial sphere are not associated with the daily rotation of the Earth, since the latter is reproduced by the rotation of the celestial sphere itself.

Loop-like movement of the planets Five planets can be seen with the naked eye - Mercury, Venus, Mars, Jupiter and Saturn. By appearance they are not easily distinguished from stars, especially since they are not always significantly bright.

If you follow the movement of a planet, for example Mars, monthly marking its position on a star chart, then the main feature of the visible movement of the planet may come to light: the planet describes a loop against the background of the starry sky.

Configuration of the planets Planets whose orbits are located inside the earth's orbit are called inferior, and planets whose orbits are located outside the earth's orbit are called superior. The characteristic mutual arrangements of the planets relative to the Sun and the Earth are called planetary configurations.

The configurations of the lower and upper planets are different. For the lower planets, this is. For the upper planets - conjunctions (upper and squares (eastern lower) and elongations and western), conjunction and (eastern and western). confrontation. Apparent motion The upper planets are best seen near the lower planets, reminiscent of oppositions, when all movements around the Sun are directed to the oscillatory Earth. hemisphere of the planet illuminated by the Sun.

Sidereal and synodic periods of the planets. The period of time during which the planet makes a complete revolution around the Sun in orbit is called the sidereal (or stellar) period of revolution (T), and the period of time between two identical planet configurations is called the synodic period (S).

slide 2

Composition of the solar system

Planets - 8 large planets with satellites and rings: Mercury, Venus, Earth (with the Moon), Mars (with Phobos and Deimos), Jupiter (with a ring and at least 63 satellites), Saturn (with a powerful ring and at least 55 satellites) – these planets are visible to the naked eye; Uranus (discovered in 1781, with a ring and at least 29 satellites), Neptune (discovered in 1846, with a ring and at least 13 satellites). Dwarf planets - Pluto (discovered in 1930, its satellite Charon - was a planet until 08/24/2006), Ceres (the first asteroid discovered in 1801), and Kuiper belt objects: Eris (136199, discovered in 2003) and Sedna (90377, discovered in 2003). Minor planets - asteroids = (the first Ceres was discovered in 1801 - transferred to the category of dwarf planets), located mainly in 4 belts: the main one - between the orbits of Mars and Jupiter, the Kuiper belt - beyond the orbit of Neptune, the Trojans: in the orbit of Jupiter and Neptune . Dimensions less than 800 km. Almost 300,000 are known. Comets are small bodies up to 100 km in diameter, a conglomerate of dust and ice, moving in very elongated orbits. Oort cloud (reservoir of comets) on the periphery of the solar system (3000 - 160000 AU). Meteor bodies - small bodies from grains of sand to stones several meters in diameter (formed from comets and crushing of asteroids). Small ones burn up when entering the earth's atmosphere, and those that reach the Earth are meteorites. Interplanetary dust - from comets and crushing asteroids. Interplanetary gas - from the Sun and planets, very rarefied. Electromagnetic radiation and gravitational waves.

slide 3

The looping motion of the planets

More than 2000 years before the NE, people noticed that some stars moved around the sky - they were later called "wandering" by the Greeks - planets. The current name of the planets is borrowed from the ancient Romans. It turned out that the planets wander in the zodiac constellations. Since, when observed from the Earth, the movement of the planets around the Sun is also superimposed on the movement of the Earth in its orbit, the planets move against the background of the stars either from west to east (direct movement), or from east to west (reverse movement). By 1539, the Polish astronomer Nicolaus Copernicus (1473-1543) was able to explain this movement. For internal, Venus For external, Mars The nature of the visible movement of the planet depends on which group it belongs to.

slide 4

The apparent movement of Mars among the stars in the period from 10/1/2007 to 04/1/2008 Venus and Jupiter in the rays of the evening dawn. A rare celestial phenomenon: five planets of the solar system (all that can be seen with the naked eye) meet in the evening sky! From May 13 to May 16, 2002, a crescent of the young Moon was present near the "wandering luminaries".

slide 5

Planet configuration

For the lower (inner) conjunction, the planet is on the direct Sun-Earth. the upper one is the planet behind the Sun (V2). the lower one is the planet in front of the Sun (V4). elongation is the angular distance of a planet from the sun. poppy: Mercury-28o, Venus-48o. east - the planet is visible in the east before sunrise in the rays of dawn (V1). western - the planet is visible in the west in the rays of the evening dawn after sunset (V3). Inferior (inner) - planets whose orbits are located inside the earth's orbit. Upper (outer) - planets whose orbits are beyond the orbit of the Earth. Configuration - the characteristic relative position of the planet, the Sun and the Earth. For the upper (external) connection, the planet behind the Sun, on the straight line Sun-Earth (M1). opposition - a planet behind the Earth from the Sun - the best time to observe the outer planets, it is completely illuminated by the Sun (M3). quadrature - a quarter of a circle western - the planet is observed in the western side (M4). eastern - observed in the eastern side (M2). Species The outer planet can be at any angular distance from the Sun.

slide 6

Visibility conditions for the inner planets The inner planets are best seen at the maximum distance from the Sun (in elongation), which is 28o for Mercury and 48o for Venus.

Slide 7

Periods of the planets

During the development of the heliocentric system of the structure of the world, Nicolaus Copernicus by 1539 received formulas (equations of the synodic period) for calculating the periods of revolution of the planets and calculated them for the first time. The lower (inner) planets orbit faster than the Earth, and the upper (outer) planets slower. Sidereal (T - stellar) - the period of time during which the planet makes a complete revolution around the Sun in its orbit relative to the stars. Synodic (S) - the period of time between two successive identical configurations of the planet. for internal for external

Slide 8

At the zenith, refraction is minimal - it increases with inclination to the horizon up to 35 "and strongly depends on physical characteristics atmosphere: composition, density, pressure, temperature. Due to refraction, the true height of the celestial bodies is always less than their apparent height. The shape and angular dimensions of the luminaries are distorted: at sunrise and sunset, the disks of the Sun and Moon "flatten" near the horizon, since the lower edge of the disk rises by refraction more than the upper one. The refraction of rays of starlight in atmospheric layers (streams) of different density causes the twinkling of stars - uneven increases and decreases in their brilliance, accompanied by changes in their color. Astronomical refraction - the phenomenon of refraction (curvature) of light rays when passing through the atmosphere, caused by the optical inhomogeneity of the atmosphere. Refraction changes the zenithal distance (height) of the luminaries, "raising" the images of the luminaries above their true positions.

View all slides

− rectangular coordinates of the point P

− spherical coordinates of the point P

Horizontal coordinate system

When constructing any system of celestial coordinates on the celestial sphere, one chooses big circle(the main circle of the coordinate system) and two diametrically opposite points on an axis perpendicular to the plane of this circle (the poles of the coordinate system).

The true horizon is taken as the main circle of the horizontal coordinate system, the zenith (Z) and nadir (Z 1) serve as poles, through which large semicircles are drawn, called height circles or verticals.

heavenly body

True horizon

vertical

The instantaneous position of the star M relative to the horizon and the celestial meridian is determined by two coordinates: height (h) and azimuth (A), which are called horizontal.

Zenith distance

0° ≤ h ≤ 90°

0° ≤ A ≤ 360°

The southern half of the celestial meridian (ZSZ 1) is the initial vertical, and the height circles ZEZ 1 and ZWZ 1 passing through the east E and west W points are called the first vertical.
Small circles (ab, cd) parallel to the plane of the true horizon are called circles of equal height or almucantars.

During the day, the azimuth and height of the luminaries are constantly changing.
Therefore, the horizontal coordinate system is unsuitable for compiling star charts and catalogs.
For this purpose, a system is needed in which the rotation of the celestial sphere does not affect the values of the coordinates of the luminaries.

Equatorial coordinate system

For the invariance of spherical coordinates, it is necessary that the coordinate grid rotates along with the celestial sphere.
This condition is satisfied by the equatorial coordinate system.

The main plane in this system is the celestial equator, and the poles are the north and south poles of the world.

North Pole of the World

Celestial equator

South Pole of Peace

Large semicircles are drawn through the poles, called the circles of declination, and parallel to the plane of the equator are celestial parallels.

Celestial Parallel

Declension circle

The position of the luminary in the equatorial coordinate system is measured along the circle of declination (declination) and along the celestial equator (right ascension). The reference point of the coordinate is the vernal equinox.

Ecliptic

North Pole

ecliptic

Mood

ecliptic

Heavenly

South Pole

ecliptic

spring point

equinoxes

The circle of declination passing through the vernal equinox is called the equinox colure. Right ascension is the angle at the celestial pole between the equinoctial color and the circle of declination passing through the luminary. Declination is the angular distance of a star from the celestial equator.

Declension circle

Equinoctial

declination

Heavenly

right ascension

spring point

equinoxes

The vernal equinox is located in the constellation Pisces, and it serves as the starting point from which the right ascension coordinate is counted in a counterclockwise direction, which is usually denoted by the letter α . This coordinate is analogous to longitude in geographic coordinates.
In astronomy, right ascension is measured in hours, not degrees. In this case, it is assumed that the full circle is 24 hours.
The second coordinate of the luminary δ – declination - is an analogue of latitude, it is measured in degrees. Thus, the star Altair (α Eagle) has coordinates α = 19h48m18s, declination δ = +8°44".
The measured coordinates of the stars are stored in catalogs, they are used to build star maps that astronomers use when searching for the right stars.

On a dark night, we can see about 2500 stars in the sky (taking into account the invisible hemisphere 5000), which differ in brightness and color. It seems that they are attached to the celestial sphere and, together with it, revolve around the Earth. To navigate among them, the sky was divided into 88 constellations.
In the II century. BC e. Hipparchus divided the stars according to their brightness into magnitudes, he attributed the brightest to the stars of the first magnitude (1 m ), and the weakest, barely visible to the naked eye, to 6 m .
In the constellation, the stars are designated by Greek letters, some of the brightest stars have their own names. Yes, Polaris Ursa Minor has a shine 2 m. The most bright Star northern sky Vega - Lyra has a brilliance about 0 m .

Currently, astronomers use different systems of celestial coordinates to navigate among the stars. One of them - equatorial coordinate system (Fig. 1). It is based on celestial equator is the projection of the earth's equator onto the celestial sphere.
Ecliptic and equator intersect at two points: spring ( γ ) and autumn ( Ὠ ) equinoxes.

Apparent motion of the planets

were known in antiquity 5 similar to stars, but brighter luminaries, which, although they participate in the daily rotation of the sky, also make independent visible movements. The ancient Greeks called such luminaries planets(in Greek "planet" means "wandering").
With the naked eye you can see 5 wandering luminaries (planets) - Mercury, Venus, Mars, Jupiter and Saturn.

The planets are always located in the sky not far from the ecliptic, but unlike the Sun and the Moon, they change the direction of their movement at certain time intervals.
They move between stars mainly from west to east (like the Sun and Moon) - direct movement.
However, each planet at a certain time slows down its movement, stops and begins to move from east to west - backward movement.
Then the luminary stops again and resumes direct movement. So the apparent path of each planet in the sky- a complex line with zigzags and loops.

In the XVI century. Polish scientist Nicolaus Copernicus, rejecting the dogmatic idea of the immobility of the Earth, put it among the ordinary planets.
Copernicus pointed out that the Earth, occupying the third place from the Sun, just like other planets, moves in space around the Sun and simultaneously rotates around its axis. The heliocentric system of Copernicus very simply explained the loop-like motion of the planets.
The figure shows the movement of Mars on the celestial sphere, observed from Earth. Same digits the positions of Mars, the Earth and the points of the trajectory of Mars in the sky at the same moments of time are marked.

Mercury and Venus are always near the Sun, moving away from it alternately to the west and to the east. Due to their proximity to the Sun, these two planets are visible only in the eastern region of the sky in the morning, before sunrise, or in the western side in the evenings, shortly after sunset.
Thus, the apparent movement of Mercury and Venus differs significantly from the apparent path of Mars, Jupiter and Saturn.
The movement of the Sun and Moon against the background of stars occurs in large circles always in the forward direction.

Loop-like sections of the visible path of the planets can be located in different zodiac constellations, but there is a significant difference in their location.
The entire belt of the zodiacal constellations of Mars bypasses in 687 days, Jupiter in almost 12 years, and Saturn in 29.5 years. These three planets are periodically near the Sun and then are not visible, then gradually move away from it to the west and describe a loop in the region of the sky opposite to the Sun.
These planets are visible at various hours of the dark. Uranus, Neptune and Pluto move similarly.

Planets whose orbits are located inside earth orbit are called n i f n i m and , and the planets whose orbits are located in n e earth orbit, in e r x n and m and . The characteristic mutual positions of the planets relative to the Sun and the Earth are called k o n f i g u r a t i a m i planets .
The configurations of the lower and upper planets are different. In the lower planets it

connection (top and bottom) and e l o n g a ts i (eastern and western; is the greatest angular distance of the planet from the Sun).

At the upper planets - k v a d r a t u r y (eastern and western: the word "square" means "a quarter of a circle"), connection and p r o t i c o s t i o n .
The apparent movement of the lower planets resembles the oscillatory movement around the Sun. Inferior planets are best observed near elongation (Mercury's greatest elongation is 28° and Venus's is 48°). From the Earth at this time, not the entire hemisphere of the planet illuminated by the Sun is visible, but only part of it ( phase planets). At eastern elongation, the planet is visible in the west shortly after sunset, at western elongation - in the east shortly before sunrise.
The upper planets are best seen near oppositions, when the entire hemisphere of the planet illuminated by the Sun is facing the Earth.

In astronomy, the average distance from the Earth to the Sun is taken as a unit of distance and is called astronomical unit (a. e.), 1 a. e. = 1.5 10 8 km.
Thus, Mercury is located at a distance of 0.39 AU from the Earth. e., and Saturn - at a distance of 9.54 a. e.

The expression "the path of the Sun among the stars" will seem strange to someone. After all, you can't see the stars during the day. Therefore, it is not easy to notice that the Sun slowly, by about 1 ° per day, moves among the stars from right to left. But you can see how the appearance of the starry sky changes during the year. All this is a consequence of the revolution of the Earth around the Sun. The path of the apparent annual movement of the Sun against the background of stars is called the ecliptic (from the Greek "eclipsis" - "eclipse"), and the period of revolution along the ecliptic is called a stellar year. It is equal to 365 days 6 h 9 min 10 s, or 365.2564 mean solar days. The ecliptic and the celestial equator intersect at an angle of 23°26′ at the points of the spring and autumn equinoxes. At the first of these points, the Sun usually occurs on March 21, when it passes from the southern hemisphere of the sky to the northern hemisphere. In the second - on September 23, during the transition from the northern hemisphere to the southern. At the farthest point of the ecliptic to the north, the Sun occurs on June 22 (summer solstice), and to the south on December 22 (winter solstice). In a leap year, these dates are shifted by one day. Of the four points on the ecliptic, the main point is the vernal equinox. It is from her that one of the celestial coordinates is counted - right ascension. It also serves to count sidereal time and the tropical year - the time interval between two successive passages of the center of the Sun through the vernal equinox. The tropical year determines the change of seasons on our planet.

Uneven motion of the Sun among the stars

About 2 thousand years ago, when Hipparchus compiled his star catalog (the first to have come down to us in its entirety), the vernal equinox was in the constellation Aries.
By our time, it has moved almost 30 °, into the constellation of Pisces, and the autumnal equinox point has moved from the constellation of Libra to the constellation of Virgo. But according to tradition, the equinox points are indicated by the signs of the former "equinoctial" constellations - Aries 'Y' and Libra Ὠ.
The same thing happened with the solstices: summer in the constellation Taurus is marked by the sign of Cancer ®, and winter in the constellation of Sagittarius - by the sign of Capricorn ^.

Half of the ecliptic from the spring equinox to the autumn equinox (from March 21 to September 23) the Sun takes 186 days. The second half, from the autumn equinox to the spring, - for 179-180 days.
But the halves of the ecliptic are equal: each 180°. Therefore, the Sun moves along the ecliptic unevenly. This unevenness reflects changes in the speed of the Earth's movement in an elliptical orbit around the Sun.
The uneven movement of the Sun along the ecliptic leads to different lengths of the seasons.
For residents of the Northern Hemisphere, spring and summer are six days longer than autumn and winter. The Earth on July 2-4 is located 5 million kilometers further from the Sun than on January 2-3, and moves in its orbit more slowly in accordance with Kepler's second law.
In summer, the Earth receives less heat from the Sun, but summer in the Northern Hemisphere is longer than winter. Therefore, the Northern Hemisphere is warmer than the Southern Hemisphere.

At the end of the XVI century. Danish astronomer I. Kepler, studying the motion of the planets, discovered three laws of their motion. Based on these laws, I. Newton derived a formula for the law of universal gravitation. Later, using the laws of mechanics, I. Newton solved the problem of two bodies - he deduced the laws according to which one body moves in the gravitational field of another body. He received three generalized laws of Kepler.

Kepler's first law

Under the influence of the force of attraction, one celestial body moves in the gravitational field of another celestial body along one of the conic sections - a circle, ellipse, parabola or hyperbola.

The planets move around the Sun in an elliptical orbit (Fig. 15.6). The point in the orbit closest to the Sun is called perihelion, the most distant aphelion. The line connecting any point of the ellipse with the focus is called radius vector

The ratio of the distance between foci to the major axis (largest diameter) is called eccentricity e. The ellipse is the more elongated, the greater its eccentricity. The semi-major axis of the ellipse a is the average distance of the planet from the Sun.

Comets and asteroids move in elliptical orbits. A circle has e = 0, an ellipse has 0< е < 1, у параболы е = 1, у гиперболы е > 1.

The movement of natural and artificial satellites around the planets, the movement of one star around another in a binary system also obey this first generalized Kepler's law.

Kepler's second law

Each planet moves in such a way that the radius vector of the planet covers equal areas in equal periods of time.

The planet goes from point A to A" and from B to B" in the same time.

In other words, the planet moves fastest at perihelion, and slowest when at perihelion. farthest away(at aphelion). Thus, Kepler's second law determines the speed of the planet. It is the greater, the closer the planet is to the Sun. Thus, the speed of Halley's comet at perihelion is 55 km/s, and at aphelion 0.9 km/s.

Kepler's third law

The cube of the semi-major axis of the body's orbit, divided by the square of the period of its revolution and the sum of the masses of the bodies, is a constant value.

If T is the period of revolution of one body around another body at an average distance a then Kepler's third generalized law is written as

a 3 / [T 2 (M 1 + M 2)] \u003d G / 4π 2

where M 1 and M 2 are the masses of the attracted two bodies, and G is the gravitational constant. For the solar system, the mass of the Sun is the mass of any planet, and then

The right side of the equation is a constant for all bodies in the solar system, which is what Kepler's third law, obtained by the scientist from observations, claims.

Kepler's third generalized law makes it possible to determine the masses of planets from the motion of their satellites, and the masses double stars- by the elements of their orbits.

The movement of planets and other celestial bodies around the Sun under the influence of gravity occurs according to the three laws of Kepler. These laws make it possible to calculate the positions of the planets and determine their masses from the motion of the satellites around them.

Astronomy. Grade 11 - Abstracts from the textbook "Physics-11" (Myakishev, Bukhovtsev, Charugin) - Classroom physics