Period of revolution around the sun. Complete revolution of the planets. Equations of synodic motion

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

Since ancient times, humanity has believed that the Earth moves. But how it moves in the Universe has always been a controversial issue. It was assumed that the entire Universe revolves around our planet. N. Copernicus was the first to suggest that the Earth revolves around the Sun. Then other scientists tried to mathematically find the relationship and calculate the time of the Earth's movement.

Over time, reliable facts about the rotation of our planet have emerged:

• There are two periods of the year when the Earth is at a certain distance. The first period is when the Earth is as close as possible to the Sun. This time is called perihelion. The period when the Earth is at its maximum distance from the Sun is aphelion. Aphelion occurs at the beginning of July, perihelion at the beginning of January;
• The shape of our planetary orbit is not a perfect circle, but an ellipse. The first scientist to describe this was the German explorer, astronomer and mathematician Kepler;
• The Earth has an axial tilt of 23.4 degrees relative to the vertical axis, which explains the existence of seasons in two hemispheres. Solstice days are when a point in the orbit is tilted to the maximum in the direction from the Sun, equinox days are when these directions are perpendicular to each other.

The earth makes one revolution around its axis every twenty-four hours, the so-called day. In the area where sunlight falls, facing the Sun, there will be day, on the opposite side - night.

Earth Rotation

The period of revolution of the Earth around the Sun is a calendar year (365 days). Since this number does not exactly coincide with the number of hours in 365 days, but is slightly larger, a whole day accumulates in four years. Therefore, there are leap years, with 366 days and an extra day in the month of February.

Solstice days - December 22 (winter) - the shortest day, June 22 (summer) - the longest day. The equinox days are March 21 and September 23 - the length of day and night are equal in both the Northern and Southern Hemispheres.

Configurations – the relative positions of the bodies of the solar system visible in the sky.

Lower,(Mercury, Venus) - closer to the Sun than the Earth.

For lower planets: Bottom connection ( 1) - a planet between the Sun and Earth. (Figure 17.)

Fig 17. Diagram of the configurations of the lower planets, conjunction,

4 – greatest eastern elongation

Top connection (3) - the planet is farther from Earth than the Sun.

Western (2) and eastern (4) elongations– angular distance of the planet from the Earth-Sun line.

The order of passage: 1 – inferior connection, 2 – greatest western elongation, 3 – superior.

Figure 18. Diagram of configurations of the upper planets

For the top planets

Connection (1) – planet behind the Sun.

Confrontation (opposition) – p3. – The sun and the planet are on opposite sides of the Earth.

Western (2) and eastern quadratures (4).

For the lower planets it is possible passage across the solar disk(a rare event).

During western elongation, the planet appears above the horizon and goes below the horizon before the Sun. It is located above the horizon during the day and is not visible in the rays of the Sun - morning visibility. With eastern elongation – evening visibility,(the planet sets after the Sun).

For the upper planets, the most favorable era for observation is opposition. It is better during the winter opposition, when the planets move through the constellations of Taurus, Gemini and Cancer. The planets rise high and are visible above the horizon most of the day (the nights are longer).

Planetary orbital periods

Synodic (S) period – planets - the period of time between two successive configurations of the same name.

Sidereal (T) or sidereal planetary period - the period of time during which a planet completes a full revolution around the Sun.

The sidereal period of the Earth's revolution is called star year.

Equations of synodic motion.

For the lower planets(1)

For the upper planets - (2)

From observations, S and are determined.

Kepler's laws

Kepler was a supporter of the teachings of Copernicus and set himself the task of improving his system based on observations of Mars, which were carried out for 20 years by the Danish astronomer Tycho Brahe (1546 -1601) and for several years by Kepler himself.

In the beginning, Kepler shared the traditional belief that celestial bodies could only move in circles, and so he spent a lot of time trying to find a circular orbit for Mars.

After many years of very labor-intensive calculations, abandoning the general misconception about the circularity of motions, Kepler discovered three laws of planetary motions, which are currently formulated as follows:

1. All planets move in ellipses, in one of the focuses (common to all planets) is the Sun.

2. The radius vector of the planet describes equal areas in equal time intervals.

3. The squares of the sidereal periods of revolutions of the planets around the Sun are proportional to the cubes of the semimajor axes of their elliptical orbits.

As is known, in an ellipse, the sum of the distances from any of its points to two fixed points f1 and f2, lying on its axis AP and called foci, is a constant value equal to the major axis AP (Fig. 19). Distance PO (or OA), where O is the center of the ellipse is called the semimajor axis a, and the ratio = e is the eccentricity of the ellipse. The latter characterizes deviations from the circle, e=0.

Figure 19. a) Elliptical orbit, b) illustration of Kepler’s second law.

The orbits of the planets differ little from circles, i.e. their eccentricities are small. The orbit of Venus has the smallest eccentricity (e=0.007), the greatest eccentricity is the orbit of Pluto (e=0.249). The eccentricity of the earth's orbit is e=0.017.

According to Kepler's first law, the Sun is at one of the foci of the planet's elliptical orbit. Let in Fig. 19, and this be the focus f 1 (C – Sun). Then the point of the orbit P closest to the Sun is called perihelion, and the point A most distant from the Sun is called aphelion. The major axis of the AP's orbit is called the apsidal line, and the line f 1 P, connecting the Sun and planet P in its orbit, is the radius - the vector of the planet.

Distance of the planet from the Sun at perihelion

q = a (1-e), (2.3)

Q = a (1 + e). (2.4)

The average distance of the planet from the Sun is taken to be the semimajor axis of the orbit.

Thus, according to modern concepts in the solar system, bodies move in ellipses, at one of the foci of which the Sun is located.

The Earth is a cosmic object involved in the continuous movement of the Universe. It rotates around its axis, travels millions of kilometers in orbit around the Sun, and, together with the entire planetary system, slowly circles the center of the Milky Way galaxy. The first two movements of the Earth are clearly noticeable to its inhabitants by changes in daily and seasonal illumination, changes in temperature conditions, and characteristics of the seasons. Today our focus is on the characteristics and period of the Earth’s revolution around the Sun, its influence on the life of the planet.

General information

Our planet moves in the third orbit farthest from the star. On average, the Earth is separated from the Sun by 149.5 million kilometers. The orbital length is approximately 940 million km. The planet covers this distance in 365 days and 6 hours (one sidereal, or sidereal, year - the period of revolution of the Earth around the Sun relative to distant luminaries). Its speed during orbital movement reaches an average of 30 km/s.

For an observer on earth, the revolution of a planet around a star is expressed in a change in the position of the Sun in the sky. It moves one degree per day eastward relative to the stars.

Orbit of planet Earth

The trajectory of our planet is not a perfect circle. It is an ellipse with the Sun at one of its focuses. This form of orbit “forces” the Earth to either approach the star or move away from it. The point at which the distance from the planet to the Sun is minimal is called perihelion. Aphelion is the part of the orbit where the Earth is as far away from the star as possible. In our time, the first point is reached by the planet around January 3, and the second on July 4. At the same time, the Earth does not move around the Sun at a constant speed: after passing aphelion, it accelerates and slows down, having overcome perihelion.

The minimum distance separating two cosmic bodies in January is 147 million km, the maximum is 152 million km.

Satellite

Together with the Earth, the Moon also moves around the Sun. When observed from the north pole, the satellite moves counterclockwise. The Earth's orbit and the Moon's orbit lie in different planes. The angle between them is approximately 5º. This discrepancy significantly reduces the number of lunar and solar eclipses. If the orbital planes were identical, then one of these phenomena would occur once every two weeks.

The Earth's orbit is designed in such a way that both objects rotate around a common center of mass with a period of approximately 27.3 days. At the same time, the tidal forces of the satellite gradually slow down the movement of our planet around its axis, thereby slightly increasing the length of the day.

Consequences

The axis of our planet is not perpendicular to the plane of its orbit. This tilt, as well as the movement around the star, leads to certain climate changes throughout the year. The sun rises higher above the territory of our country at a time when the planet’s north pole is inclined towards it. The days are getting longer, the temperature is rising. When it deviates from the luminary, the warmth is replaced by cooling. Similar climate changes are characteristic of the southern hemisphere.

The change of seasons occurs at the points of equinox and solstices, which characterize a certain position of the earth's axis relative to the orbit. Let's look at this in more detail.

The longest and shortest day

Solstice is the moment in time when the planetary axis is maximally inclined towards the star or in the opposite direction. The Earth's orbit around the Sun has two such sections. In mid-latitudes, the point at which the sun appears at noon rises higher every day. This continues until the summer solstice, which falls on June 21 in the northern hemisphere. Then the location of the midday star begins to decrease until December 21-22. These days are the winter solstice in the northern hemisphere. In mid-latitudes, the shortest day arrives, and then it begins to increase. In the southern hemisphere, the axis tilt is opposite, so it falls here in June, and summer in December.

Day equals night

Equinox is the moment when the planet's axis becomes perpendicular to the orbital plane. At this time, the terminator, the boundary between the illuminated and dark half, runs strictly along the poles, that is, day is equal to night. There are also two such points in orbit. The spring equinox falls on March 20, the autumn equinox on September 23. These dates are valid for the northern hemisphere. In the southern one, similar to the solstices, the equinoxes change places: autumn is in March, and spring is in September.

Where is it warmer?

The circular orbit of the Earth - its features combined with the tilt of its axis - has another consequence. At the moment when the planet passes closest to the Sun, the south pole faces in its direction. It is summer in the corresponding hemisphere at this time. The planet at the moment of passing perihelion receives 6.9% more energy than when it passes aphelion. This difference occurs specifically in the southern hemisphere. During the year it receives slightly more solar heat than the northern one. However, this difference is insignificant, since a significant part of the “additional” energy falls on the water expanses of the southern hemisphere and is absorbed by them.

Tropical and sidereal year

The period of revolution of the Earth around the Sun relative to the stars, as already mentioned, is approximately 365 days 6 hours 9 minutes. This is a sidereal year. It is logical to assume that the change of seasons fits into this period. However, this is not entirely true: the time of the Earth’s revolution around the Sun does not coincide with the full period of the seasons. It makes up the so-called tropical year, lasting 365 days, 5 hours and 51 minutes. It is most often measured from one vernal equinox to the next. The reason for the twenty-minute difference between the duration of the two periods is the precession of the earth's axis.

Calendar year

For convenience, it is generally accepted that there are 365 days in a year. The remaining six and a half hours add up to a day during four revolutions of the Earth around the Sun. To compensate for this and in order to prevent the difference between the calendar and sidereal years from increasing, an “extra” day is introduced, February 29.

The Earth's only satellite, the Moon, has some influence on this process. It is expressed, as noted earlier, in the slowing down of the planet’s rotation. Every hundred years, the length of the day increases by about one thousandth.

Gregorian calendar

The counting of days we are accustomed to was introduced in 1582. unlike the Julian, over a long period of time allows the “civil” year to correspond to the full cycle of seasons. According to it, months, days of the week and dates are exactly repeated every four hundred years. The length of the year in the Gregorian calendar is very close to the tropical one.

The purpose of the reform was to return the day of the vernal equinox to its usual place - on March 21. The fact is that from the first century AD to the sixteenth century, the real date when day is equal to night moved to March 10. The main motivation for revising the calendar was the need to correctly calculate the day of Easter. To achieve this, it was important to keep March 21 a day close to the actual equinox. The Gregorian calendar copes with this task very well. The date of the vernal equinox will shift by one day no earlier than in 10,000 years.

If we compare the calendar, more significant changes are possible here. As a result of the peculiarities of the Earth's movement and the factors influencing it, over approximately 3,200 years, a discrepancy with the change of seasons of one day will accumulate. If at this time it is important to maintain the approximate equality of the tropical and calendar years, then a reform similar to that carried out in the 16th century will again be required.

The period of revolution of the Earth around the Sun thus correlates with the concepts of calendar, sidereal and tropical years. Methods for determining their duration have been improved since antiquity. New data on the interaction of objects in outer space allow us to make assumptions about the relevance of the modern understanding of the term “year” in two, three and even ten thousand years. The time of the Earth's revolution around the Sun and its connection with the change of seasons and the calendar is a good example of the influence of global astronomical processes on human social life, as well as the dependencies of individual elements within the global system of the Universe.