The Earth is constantly in motion, rotating around the Sun and around its own axis. This movement and the constant tilt of the Earth's axis (23.5°) determines many of the effects that we observe as normal phenomena: night and day (due to the rotation of the Earth on its axis), the change of seasons (due to the tilt of the Earth's axis), and different climate in different areas. Globes can be rotated and their axis is tilted like the Earth’s axis (23.5°), so with the help of a globe you can trace the movement of the Earth around its axis quite accurately, and with the help of the Earth-Sun system you can trace the movement of the Earth around the Sun.

Rotation of the Earth around its axis

The Earth rotates on its own axis from west to east (counterclockwise when viewed from the North Pole). It takes the Earth 23 hours, 56 minutes, and 4.09 seconds to complete one full rotation on its own axis. Day and night are caused by the rotation of the Earth. The angular velocity of the Earth's rotation around its axis, or the angle through which any point on the Earth's surface rotates, is the same. It is 15 degrees in one hour. But the linear speed of rotation anywhere at the equator is approximately 1,669 kilometers per hour (464 m/s), decreasing to zero at the poles. For example, the rotation speed at latitude 30° is 1445 km/h (400 m/s).
We do not notice the rotation of the Earth for the simple reason that in parallel and simultaneously with us all objects around us move at the same speed and there are no “relative” movements of objects around us. If, for example, a ship moves uniformly, without acceleration or braking, through the sea in calm weather without waves on the surface of the water, we will not feel at all how such a ship is moving if we are in a cabin without a porthole, since all objects inside the cabin will be move parallel with us and the ship.

Movement of the Earth around the Sun

While the Earth rotates on its own axis, it also rotates around the Sun from west to east counterclockwise when viewed from the north pole. It takes the Earth one sidereal year (about 365.2564 days) to complete one full revolution around the Sun. The path of the Earth around the Sun is called the Earth's orbit and this orbit is not perfectly round. The average distance from the Earth to the Sun is approximately 150 million kilometers, and this distance varies up to 5 million kilometers, forming a small oval orbit (ellipse). The point in the Earth's orbit closest to the Sun is called Perihelion. The earth passes this point in early January. The point of the Earth's orbit farthest from the Sun is called Aphelion. The earth passes this point in early July.
Since our Earth moves around the Sun along an elliptical path, the speed along the orbit changes. In July, the speed is minimal (29.27 km/sec) and after passing aphelion (upper red dot in the animation) it begins to accelerate, and in January the speed is maximum (30.27 km/sec) and begins to slow down after passing perihelion (lower red dot ).
While the Earth makes one revolution around the Sun, it covers a distance equal to 942 million kilometers in 365 days, 6 hours, 9 minutes and 9.5 seconds, that is, we rush along with the Earth around the Sun at an average speed of 30 km per second (or 107,460 km per hour), and at the same time the Earth rotates around its own axis once every 24 hours (365 times per year).
In fact, if we consider the movement of the Earth more scrupulously, it is much more complex, since the Earth is influenced by various factors: the rotation of the Moon around the Earth, the attraction of other planets and stars.

Our planet is in constant motion, it rotates around the Sun and its own axis. The Earth's axis is an imaginary line drawn from the North to the South Pole (they remain motionless during rotation) at an angle of 66 0 33 ꞌ relative to the plane of the Earth. People cannot notice the moment of rotation, because all objects move in parallel, their speed is the same. It would look exactly the same as if we were sailing on a ship and did not notice the movement of objects and objects on it.

A full revolution around the axis is completed within one sidereal day, consisting of 23 hours 56 minutes and 4 seconds. During this period, first one or the other side of the planet turns towards the Sun, receiving different amounts of heat and light from it. In addition, the rotation of the Earth around its axis affects its shape (flattened poles are the result of the planet’s rotation around its axis) and the deviation when bodies move in the horizontal plane (rivers, currents and winds of the Southern Hemisphere deviate to the left, of the Northern Hemisphere to the right).

Linear and angular rotation speed

(Earth Rotation)

The linear speed of rotation of the Earth around its axis is 465 m/s or 1674 km/h in the equator zone; as you move away from it, the speed gradually slows down, at the North and South Poles it is zero. For example, for citizens of the equatorial city of Quito (the capital of Ecuador in South America), the rotation speed is exactly 465 m/s, and for Muscovites living at the 55th parallel north of the equator, it is 260 m/s (almost half as much) .

Every year, the speed of rotation around the axis decreases by 4 milliseconds, which is due to the influence of the Moon on the strength of sea and ocean tides. The Moon's gravity "pulls" the water in the opposite direction to the Earth's axial rotation, creating a slight frictional force that slows the rotation speed by 4 milliseconds. The speed of angular rotation remains the same everywhere, its value is 15 degrees per hour.

Why does day give way to night?

(The change of night and day)

The time for a complete revolution of the Earth around its axis is one sidereal day (23 hours 56 minutes 4 seconds), during this time period the side illuminated by the Sun is first “in the power” of the day, the shadow side is under the control of the night, and then vice versa.

If the Earth rotated differently and one side of it was constantly turned towards the Sun, then there would be a high temperature (up to 100 degrees Celsius) and all the water would evaporate; on the other side, on the contrary, frost would rage and the water would be under a thick layer of ice. Both the first and second conditions would be unacceptable for the development of life and the existence of the human species.

Why do the seasons change?

(Change of seasons on Earth)

Due to the fact that the axis is tilted relative to the earth's surface at a certain angle, its parts receive different amounts of heat and light at different times, which causes the change of seasons. According to the astronomical parameters necessary to determine the time of year, certain points in time are taken as reference points: for summer and winter these are the Solstice Days (June 21 and December 22), for spring and autumn - the Equinoxes (March 20 and September 23). From September to March, the Northern Hemisphere faces the Sun for less time and, accordingly, receives less heat and light, hello winter-winter, the Southern Hemisphere at this time receives a lot of heat and light, long live summer! 6 months pass and the Earth moves to the opposite point of its orbit and the Northern Hemisphere receives more heat and light, the days become longer, the Sun rises higher - summer comes.

If the Earth were located in relation to the Sun in an exclusively vertical position, then the seasons would not exist at all, because all points on the half illuminated by the Sun would receive the same and uniform amount of heat and light.

Movement around an axis of rotation is one of the common types of movement of objects in nature. In this article we will consider this type of movement from the point of view of dynamics and kinematics. We also present formulas connecting the basic physical quantities.

What kind of movement are we talking about?

In the literal sense, we will talk about the movement of bodies in a circle, that is, about their rotation. A striking example of such movement is the rotation of a car or bicycle wheel while the vehicle is moving. Rotation around its axis by a figure skater performing complex pirouettes on ice. Or the rotation of our planet around the Sun and around its own axis, inclined to the ecliptic plane.

As you can see, an important element of the type of movement under consideration is the axis of rotation. Each point of a body of arbitrary shape makes circular movements around it. The distance from a point to an axis is called the radius of rotation. Many properties of the entire mechanical system, such as moment of inertia, linear speed and others, depend on its value.

If the reason for the linear translational movement of bodies in space is the external force acting on them, then the reason for the movement around the axis of rotation is the external moment of force. This quantity is described as the vector product of the applied force F¯ and the distance vector from the point of its application to the r¯ axis, that is:

The action of the moment M¯ leads to the appearance of angular acceleration α¯ in the system. Both quantities are related to each other through a certain coefficient I by the following equality:

The quantity I is called the moment of inertia. It depends both on the shape of the body and on the distribution of mass inside it and on the distance to the axis of rotation. For a material point it is calculated by the formula:

If the external one is zero, then the system retains its angular momentum L¯. This is another vector quantity, which, according to definition, is equal to:

Here p¯ is a linear impulse.

The law of conservation of torque L¯ is usually written in the following form:

Where ω is the angular velocity. It will be discussed further in the article.

Kinematics of rotation

Unlike dynamics, this branch of physics considers exclusively practical important quantities associated with changes in time in the position of bodies in space. That is, the objects of study of rotation kinematics are velocities, accelerations and rotation angles.

First, let's introduce angular velocity. It is understood as the angle through which a body rotates per unit time. The formula for instantaneous angular velocity is:

If the body rotates through equal angles at equal intervals of time, then the rotation is called uniform. The formula for the average angular velocity is valid for it:

ω is measured in radians per second, which in the SI system corresponds to reciprocal seconds (s -1).

In the case of uneven rotation, the concept of angular acceleration α is used. It determines the rate of change in time of the value ω, that is:

α = dω/dt = d 2 θ/dt 2

α is measured in radians per square second (in SI - s -2).

If the body initially rotated uniformly with a speed ω 0, and then began to increase its speed with constant acceleration α, then such motion can be described by the following formula:

θ = ω 0 *t + α*t 2 /2

This equality is obtained by integrating the angular velocity equations over time. The formula for θ allows you to calculate the number of revolutions that the system will make around the axis of rotation in time t.

Linear and angular velocities

Both speeds are related to each other. When they talk about the speed of rotation around an axis, they can mean both linear and angular characteristics.

Suppose that a certain material point rotates around an axis at a distance r with a speed ω. Then its linear speed v will be equal to:

The difference between linear and angular speed is significant. Thus, with uniform rotation, ω does not depend on the distance to the axis, but the value of v increases linearly with increasing r. The latter fact explains why, as the radius of rotation increases, it is more difficult to keep the body on a circular path (its linear speed and, as a consequence, inertial forces increase).

The task of calculating the speed of rotation around the Earth's axis

Everyone knows that our planet in the solar system undergoes two types of rotational motion:

• around its axis;
• around the star.

Let us calculate the velocities ω and v for the first of them.

Angular velocity is not difficult to determine. To do this, remember that the planet completes a full revolution equal to 2*pi radians in 24 hours (the exact value is 23 hours 56 minutes 4.1 seconds). Then the value of ω will be equal to:

ω = 2*pi/(24*3600) = 7.27*10 -5 rad/s

The calculated value is small. Let us now show how much the absolute value of ω differs from that of v.

Let us calculate the linear velocity v for points lying on the surface of the planet at the latitude of the equator. Since the Earth is an oblate ball, the equatorial radius is slightly larger than the polar one. It is 6378 km. Using the formula for connecting two speeds, we get:

v = ω*r = 7.27*10 -5 *6378000 ≈ 464 m/s

The resulting speed is 1670 km/h, which is greater than the speed of sound in air (1235 km/h).

The rotation of the Earth around its axis leads to the appearance of the so-called Coriolis force, which should be taken into account when flying ballistic missiles. It is also the cause of many atmospheric phenomena, such as the deviation of the trade winds to the west.

The movement of the planet in orbit is determined by two reasons:
- linear inertia of motion (it tends to rectilinear - tangential)
and the gravitational force of the Sun.

It is the force of gravity that will change the direction of movement from linear to circular. And gravitational forces applied to a smaller radius will act
stronger on the planet.
If we consider gravity as a force applied to the center, then this gives a change in the direction of movement to a circular one.
If we consider gravity as the sum of forces applied to the entire mass of the planet,
then this gives both a change in the motion vector to a circular one and rotation around an axis.

Look at the picture.
The planet has points located closer to the Sun and points more distant.
Point A will be closer to the Sun than point B.
And the attraction of point A will be greater than that of point B. Recall that the force of gravity depends on the radius squared.
When the planet moves clockwise, the gravitational force through point A will pull the planet away more than through point B. This difference in gravitational forces applied to diametrically opposite points of the planet, with simultaneous movement, creates rotation.

Thus, the period of revolution of the planet around its axis directly depends on the equatorial radius of the planet.
With large planets such as Jupiter and Saturn, the difference in the attraction of opposite points is greater and the planet rotates faster.

Table of solar days for planets and equatorial radius:

Mercury..... - 175.9421 .... - 0.3825
Venus..... - 116.7490 ... ... - 0.9488
Earth...... - 1.0 .... .. - 1.0
M a r s.... - 1.0275 ... .... - 0.5326
Jupiter..... - 0.41358 ... - 11.209
Saturn..... - 0.44403 .... - 9.4491
U r a n..... - 0.71835 ... - 4.0073
Neptune..... - 0.67126 ... - 3.8826
Pluto..... - 6.38766 .... - 0.1807

The first number is the period of rotation of the planet around its axis in Earth days, the second number is similar - the equatorial radius of the planet. And it is clear that the largest planet, Jupiter, rotates the fastest, and the smallest, Mercury, rotates the slowest.

In general, the reason for the rotation of the Earth can be explained simply.
As the planet moves in orbit, there is a constant change in the direction of its motion from straight to circular. And at the same time, a simultaneous rotation of the planet occurs, due to the fact that the points of attraction of planets located closer to the Sun will pull the planet more strongly than those further away.

For example, on Jupiter, where the planet is not a monolith, rotation occurs in layers. The equatorial movement of the layers is especially noticeable.

Reviews

Dear Nikolay!
There is no gravity. Newton's and Einstein's laws do not work.
Using such methods, it is impossible to substantiate the causes of rotation.
But the topic is interesting.
I hope that through joint efforts, and not on this site, we will solve it.

No. Gravity is all there! But we have not yet established the reasons for its appearance.
“Gravitational force,” a term conventionally accepted hereinafter, means an external influence on the body. Conventionally, in physics this is called the “force” of gravity.

And rotation occurs from the action of two forces: the inertia of rectilinear motion and its change to circular motion under the influence of the force of gravity, which in vector is perpendicular to the vector of inertia.

Dear Nikolay!

Dear Nikolay!
Your works already contain calculations, I won’t say, that substantiate the absence of gravity. These works aroused my interest in you, because it is clear that there is a large statistical material and on it, together and quickly we will build a science for ourselves, where many things will fall into place. And whether they accept it or not, it shouldn’t concern us. Let Volosatov prove it, and we will do it.

I can formulate my position on gravity like this.
Gravity, as an attractive force that arises between two bodies, does not exist.
There is an external influence on bodies, the consequence of which is the appearance of force, causing them to move towards each other. Force does not lead to the appearance of another force, but to movement. In this case, the vector of this force is directed along the line connecting these two bodies.
Not attraction, but movement towards.
And not the force arising in the bodies themselves, but the force of external influence.
Like the wind blows on a sail.
In general, I understand force as a factor of external influence.

Dear Nikolay!
Having refuted the forces and their reactions, you return to them again.
Yes, these are the “weights” of our teachings. It’s difficult to break away from them. I am still tearing myself away from the remnants of the teachings of the “institute”. But the physics of the world is completely different. You intuitively felt it. The rest is in personal correspondence.

The Earth rotates around an axis from west to east, that is, counterclockwise when looking at the Earth from the North Star (North Pole). In this case, the angular velocity of rotation, i.e. the angle through which any point on the Earth’s surface rotates, is the same and amounts to 15° per hour. Linear speed depends on latitude: at the equator it is highest - 464 m/s, and the geographic poles are stationary.

The main physical proof of the Earth's rotation around its axis is the experiment with Foucault's swinging pendulum. After the French physicist J. Foucault carried out his famous experiment in the Paris Pantheon in 1851, the rotation of the Earth around its axis became an immutable truth. Physical evidence of the Earth’s axial rotation is also provided by measurements of the arc of the 1° meridian, which is 110.6 km at the equator and 111.7 km at the poles (Fig. 15). These measurements prove the compression of the Earth at the poles, and this is characteristic only of rotating bodies. And finally, the third evidence is the deviation of falling bodies from the plumb line at all latitudes except the poles (Fig. 16). The reason for this deviation is due to their inertia maintaining a higher linear velocity of the point A(at height) compared to point IN(near the earth's surface). When falling, objects are deflected to the east on the Earth because it rotates from west to east. The magnitude of the deviation is maximum at the equator. At the poles, bodies fall vertically, without deviating from the direction of the earth's axis.

The geographic significance of the Earth's axial rotation is extremely large. First of all, it affects the figure of the Earth. The compression of the Earth at the poles is the result of its axial rotation. Previously, when the Earth rotated at a higher angular velocity, the polar compression was greater. The lengthening of the day and, as a consequence, a decrease in the equatorial radius and an increase in the polar one is accompanied by tectonic deformations of the earth's crust (faults, folds) and a restructuring of the Earth's macrorelief.

An important consequence of the Earth’s axial rotation is the deflection of bodies moving in a horizontal plane (winds, rivers, sea currents, etc.). from their original direction: in the northern hemisphere – right, in the south - left(this is one of the forces of inertia, called the Coriolis acceleration in honor of the French scientist who first explained this phenomenon). According to the law of inertia, every moving body strives to maintain unchanged the direction and speed of its movement in world space (Fig. 17). Deflection is the result of the body participating in both translational and rotational movements simultaneously. At the equator, where the meridians are parallel to each other, their direction in world space does not change during rotation and the deviation is zero. Toward the poles, the deviation increases and becomes greatest at the poles, since there each meridian changes its direction in space by 360° per day. The Coriolis force is calculated by the formula F = m x 2ω x υ x sin φ, where F – Coriolis force, T– mass of a moving body, ω – angular velocity, υ – speed of a moving body, φ – geographical latitude. The manifestation of the Coriolis force in natural processes is very diverse. It is because of it that vortices of different scales arise in the atmosphere, including cyclones and anticyclones, winds and sea currents deviate from the gradient direction, influencing the climate and through it the natural zonality and regionality; The asymmetry of large river valleys is associated with it: in the northern hemisphere, many rivers (Dnieper, Volga, etc.) for this reason have steep right banks, left banks are flat, and in the southern hemisphere it’s the other way around.

Associated with the rotation of the Earth is a natural unit of time measurement - day and it happens the change of night and day. There are sidereal and sunny days. Sidereal day– the time interval between two successive upper culminations of a star through the meridian of the observation point. During a sidereal day, the Earth makes a complete rotation around its axis. They are equal to 23 hours 56 minutes 4 seconds. Sidereal days are used for astronomical observations. True solar days– the period of time between two successive upper culminations of the center of the Sun through the meridian of the observation point. The length of the true solar day varies throughout the year, primarily due to the uneven movement of the Earth along its elliptical orbit. Therefore, they are also inconvenient for measuring time. For practical purposes they use average sunny days. Mean solar time is measured by the so-called mean Sun - an imaginary point that moves evenly along the ecliptic and makes a full revolution per year, like the true Sun. The average solar day is 24 hours long. They are longer than sidereal days, since the Earth rotates around its axis in the same direction in which it moves in its orbit around the Sun with an angular velocity of about 1° per day. Because of this, the Sun moves against the background of the stars, and the Earth still needs to “turn” by about 1° for the Sun to “come” to the same meridian. Thus, during a solar day, the Earth rotates approximately 361°. To convert true solar time to mean solar time, a correction is introduced - the so-called equation of time. Its maximum positive value is + 14 minutes on February 11, its maximum negative value is –16 minutes on November 3. The beginning of the average solar day is taken to be the moment of the lowest culmination of the average Sun - midnight. This kind of time counting is called civil time.

In everyday life, it is also inconvenient to use mean solar time, since it is different for each meridian, local time. For example, on two adjacent meridians, drawn with an interval of 1°, the local time differs by 4 minutes. The presence of different local times at different points lying on different meridians led to many inconveniences. Therefore, at the International Astronomical Congress in 1884, zone time was adopted. To do this, the entire surface of the globe was divided into 24 time zones, 15° each. Behind standard time The local time of the middle meridian of each zone is accepted. To convert local time to standard time and back, there is a formula T n – m = N – λ °, Where T P – standard time, m - local time, N– number of hours equal to the belt number, λ ° – longitude expressed in hourly units. The zero (also known as the 24th) belt is the one through the middle of which the zero (Greenwich) meridian passes. His time is taken as universal time. Knowing universal time, it is easy to calculate standard time using the formula T n = T 0 + N, Where T 0 - universal time. The belts are counted to the east. In two neighboring zones, the standard time differs by exactly 1 hour. For convenience, the boundaries of time zones on land are drawn not strictly along meridians, but along natural boundaries (rivers, mountains) or state and administrative boundaries.

In our country, standard time was introduced on July 1, 1919. Russia is located in ten time zones: from the second to the eleventh. However, in order to more rationally use daylight in the summer in our country, in 1930, by a special government decree, the so-called maternity time, ahead of standard time by 1 hour. So, for example, Moscow is formally located in the second time zone, where standard time is calculated according to the local time of the meridian 30° east. etc. But in fact, time in winter in Moscow is set according to the time of the third time zone, corresponding to local time on the meridian 45° east. d. A similar “shift” operates throughout Russia, except for the Kaliningrad region, the time in which actually corresponds to the second time zone.

Rice. 17. Deviation of bodies moving along the meridian in the northern hemisphere - to the right, in the southern hemisphere - to the left

In a number of countries, time is moved forward one hour only in the summer. In Russia, since 1981, for the period from April to October, summer time by moving the time another hour ahead compared to maternity leave. Thus, in summer time in Moscow actually corresponds to local time on the meridian 60°E. d. The time according to which residents of Moscow and the second time zone in which it is located live is called Moscow. According to Moscow time, our country schedules trains and planes, and marks the time on telegrams.

In the middle of the twelfth zone, approximately along the 180° meridian, in 1884 a international date line. This is a conventional line on the surface of the globe, on both sides of which the hours and minutes coincide, and the calendar dates differ by one day. For example, on New Year’s Day at 0:00 a.m. to the west of this line it is already January 1 of the new year, and to the east it is only December 31 of the old year. When crossing the border of dates from west to east, one day is returned in the count of calendar days, and from east to west one day is skipped in the count of dates.

The change of day and night creates daily rhythm in living and inanimate nature. The circadian rhythm is associated with light and temperature conditions. The daily variation of temperature, day and night breezes, etc. are well known. The daily rhythm of living nature is very clearly manifested. It is known that photosynthesis is possible only during the day, in the presence of sunlight, and that many plants open their flowers at different hours. Animals can be divided into nocturnal and diurnal according to the time of their activity: most of them are awake during the day, but many (owls, bats, moths) are awake in the darkness of the night. Human life also flows in a circadian rhythm.

Rice. 18. Twilight and white nights

The period of smooth transition from daylight to night darkness and back is called at dusk. IN they are based on an optical phenomenon observed in the atmosphere before sunrise and after sunset, when the sun is still (or already) below the horizon, but illuminates the sky from which the light is reflected. The duration of twilight depends on the declination of the Sun (the angular distance of the Sun from the plane of the celestial equator) and the geographic latitude of the observation site. At the equator, twilight is short and increases with latitude. There are three periods of twilight. Civil twilight are observed when the center of the Sun plunges below the horizon shallowly (at an angle of up to 6°) and for a short time. This is actually White Nights, when the evening dawn meets the morning dawn. In summer they are observed at latitudes of 60° and more. For example, in St. Petersburg (latitude 59°56" N) they last from June 11 to July 2, in Arkhangelsk (64°33" N) - from May 13 to July 30. Navigational twilight observed when the center of the solar disk plunges 6–12° below the horizon. In this case, the horizon line is visible, and from the ship you can determine the angle of the stars above it. And finally, astronomical twilight are observed when the center of the solar disk plunges below the horizon by 12–18°. At the same time, the dawn in the sky still prevents astronomical observations of faint luminaries (Fig. 18).

The rotation of the Earth gives two fixed points - geographic poles(the points of intersection of the imaginary axis of rotation of the Earth with the earth's surface) - and thus allows us to construct a coordinate grid of parallels and meridians. Equator(lat. aequator - leveler) - the line of intersection of the globe with a plane passing through the center of the Earth perpendicular to its axis of rotation. Parallels(Greek parallelos – running side by side) – lines of intersection of the earth’s ellipsoid with planes parallel to the equatorial plane. Meridians(lat. meridlanus - midday) - the line of intersection of the earth's ellipsoid with planes passing through both of its poles. The length of the 1st meridian is on average 111.1 km.