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  • The center of gravity of a rigid body and methods for finding its position Determining the coordinates of the center of gravity of a rigid body
  • Determination of the moment of inertia
  • Distribution law of a discrete random variable
  • Simpson's method for computing
  • The formula for the numerical integration of the simpson method has the form
  • Continuity of a function of two variables Determining the continuity of a function of two variables at a point
  • Basic research. The influence of the Earth's rotation on the balance and motion of bodies The influence of the Earth's rotation on the balance

    Basic research. The influence of the Earth's rotation on the balance and motion of bodies The influence of the Earth's rotation on the balance

    The Earth, rotating from west to east (as viewed from the North Pole), makes a complete revolution around its axis in 24 hours. The angular speed of rotation of all points of the Earth is the same (15 ° per hour). The linear speed of rotation of points depends on the distance that they must travel during the period of the Earth's daily rotation. Only the exit points of the imaginary axis - the points of the geographical poles (North and South) - remain stationary on the surface of the Earth. With the highest speed (464 m / s) points rotate on the equator line, on the line of the great circle formed by the intersection of the Earth by a plane perpendicular to the axis of rotation. If you mentally cross the Earth with a number of planes parallel to the equator, lines appear on the earth's surface with a west-east direction, called parallels... The length of the parallels decreases from the equator to the poles, and the linear speed of rotation of the parallels decreases accordingly. The linear speed of rotation of all points on one parallel is the same.
    When the Earth intersects with planes passing through the Earth's axis of rotation, lines appear on its surface with a north-south direction, meridians (meridianus, lat. - noon). The linear speed of rotation of all points on one meridian is not the same: it decreases from the equator to the poles.
    An experiment with a swinging pendulum (Foucault's experiment) serves as convincing proof of the rotation of the Earth around its axis.
    According to the laws of mechanics, any swinging body tends to keep the swing plane. A freely suspended swinging pendulum does not change the swing plane, and at the same time, if a circle with divisions is placed with a pendulum on the surface of the Earth, it turns out that in relation to this circle (i.e., relative to the Earth's surface) the position of the swing plane of the pendulum changes. This can only happen due to the fact that the surface of the Earth rotates under the pendulum. At the pole, the apparent rotation of the swinging plane of the pendulum will be 15 ° per hour; at the equator, the position of the swinging plane of the pendulum does not change, since it always coincides with the meridian; at intermediate latitudes, the apparent rotation of the swing plane is 15 ° sin φ per hour (φ is the geographic latitude of the observation site).
    Deflection action of the Earth's rotation (Coriolis force) is one of the most important consequences of the Earth's rotation. We usually orient the direction of motion of bodies in relation to the sides of the horizon (north, south, east, west), that is, in relation to the lines of meridians and parallels, forgetting that these lines, due to the rotation of the Earth, continuously change their orientation in world space ... A body in motion, according to the law of inertia, seeks to maintain the direction and speed of its movement relative to world space. For example, let a rocket be launched from point A (in the northern hemisphere) towards the North Pole (Fig. 13). At the moment of launch, the direction of its movement (AB) coincides with the direction of the meridian. Ho already at the next moment, point A, as a result of the Earth's rotation, will move to the right, to point B. The direction of the meridian in space will change, the meridian will deviate to the left. The rocket, on the contrary, will retain the direction of movement, while it seems to an observer watching its movement that it has deviated to the right under the influence of some force. It is easy to understand that this force is fictitious, for the rocket only seems to deviate due to a change in the direction of the meridian, along which the observer orients the direction of its movement. If the body moves in the northern hemisphere from north to south, the meridian changes its direction, moving to the left, and the observer sees the moving body deviating, as well as when moving from south to north, to the right.


    The deviation will be greatest at the poles, since there the meridian changes its direction in world space by 360 ° per day. The deviation from the poles and the equator decreases, and at the equator, where the meridians are parallel to each other and their direction in space does not change, the deviation is 0.
    In the southern hemisphere, the deflecting action of the Earth's rotation is manifested in the deflection of moving bodies to the left.
    Bodies moving in any direction deviate from the direction of movement to the right in the northern hemisphere and to the left in the southern hemisphere.
    The deflecting force of the Earth's rotation (Coriolis force), acting on a unit of mass (1 g) moving at a speed of V m / s, is expressed by the formula F \u003d 2ω * v * sin φ, where φ is the angular speed of the Earth's rotation, φ is latitude. The Coriolis force does not depend on the direction of motion of the body and does not affect its speed.
    The deflecting effect of the Earth's rotation has a constant effect on the direction of movement of all bodies on the Earth, in particular, it significantly affects the direction of air and sea currents.
    Change of day and night on Earth. The sun's rays always illuminate only half of the Earth facing the Sun. The rotation of the Earth around its axis causes the rapid movement of solar illumination across the earth's surface from east to west, i.e., the change of day and night.

    If the earth's axis were perpendicular to the plane of the orbit, the light-dividing plane (the plane dividing the earth into illuminated and unlit halves) would divide all latitudes into two equal parts and at all latitudes, day and night would always be equal. When the axis is tilted to the plane of the earth's orbit, day and night can be equal at all latitudes only at the moment when the earth's axis lies in the dividing plane and when the dividing line (the line formed by the intersection of the earth's surface with the dividing plane) passes through the geographic poles. When the earth's axis is tilted with its northern end to the Sun (Fig. 14, a), the dividing plane, crossing the earth's axis at the center of the Earth, divides the Earth into two halves so that most of the northern hemisphere is illuminated, and the smaller part falls into the shadow, and vice versa most of the southern hemisphere is in shadow. If the axis of the Earth is tilted toward the Sun by its southern end (Fig. 14, b), the southern hemisphere is illuminated more than the northern one. Since the dividing line in both cases does not pass through the geographic poles and divides all latitudes, except 0 °, into two unequal parts - illuminated and unlit, day and night at all latitudes, except for the equator, are not equal. In the hemisphere that is tilted towards the Sun, the day is longer than the night, in the opposite hemisphere, on the contrary, the night is longer than the day. At those latitudes that are not crossed by the dividing line and for some time find themselves completely on the illuminated or unlit side of the Earth, during the corresponding period (up to six months at the poles) the change of day and night does not occur. If the change of day and night is determined by the rotation of the Earth about the axis, and their inequality is determined by the inclination of the axis to the Earth's orbit, then the constant change in the duration of day and night at all latitudes, except for the equator, is the result of the constant position of the Earth's axis in space when the Earth revolves around the Sun. 1

    Bayrashev K.A.

    An exact solution to the problem of the influence of the Earth's rotation on the motion of a material point in the Northern Hemisphere is obtained without taking into account air resistance at nonzero initial conditions. Several specific options for specifying the initial point speed are considered. It is shown that at the initial velocity directed to the east, the deflection of the point to the south is proportional to the first power of the angular velocity of the Earth's rotation. When the initial speed is directed to the north or down the plumb line, the deviation of the point to the east is greater than when falling without initial speed. The solution obtained in the work can be applied to assess the influence of the rotation of the planets of the solar system on the motion of a material point near their surfaces.

    1. We consider the problem of the influence of the Earth's rotation on the fall of a heavy material point in the Northern Hemisphere, also known as the problem of the deviation of falling bodies to the east. The movement of a point is determined relative to the non-inertial frame of reference Oxyz, fastened to the rotating Earth. The origin of coordinates is generally located at a certain height above the spherical surface of the Earth.

    The Oz axis is plumb down, the Ox axis is in the meridian plane to the north, the Oy axis is parallel to the east (Fig. 1).

    When a material point moves near the surface of the Earth, it is acted upon by the force of gravity, the portable and Coriolis forces of inertia. Air resistance is not considered. Replacing the sum of the gravitational force and the transportable inertia force by the force of gravity, and the Coriolis force of inertia by the formula

    We have the following equation for the relative motion of a material point in vector form

    (1)

    Here m, and are the mass, velocity and acceleration of point M, respectively, is the vector of the Earth's angular velocity, is the acceleration of gravity.

    Note that the speed of a freely falling point M, starting from a state of relative rest, is almost parallel to the plumb line. Therefore, the Coriolisian force of inertia is practically perpendicular to the plane of the meridian and is directed to the east.

    Projecting (1) onto the coordinate axes and following, we obtain a system of second-order ordinary differential equations

    (2)

    where the points above x, y, z denote their derivatives with respect to time, φ is the geographical latitude of the place, i.e. the angle of the plumb line to the equatorial plane. The initial conditions are as follows:

    those. at the initial moment of time, the point is at relative rest. Courses in theoretical mechanics usually provide an approximate solution to the problem of the influence of the Earth's rotation on the fall of a material point without an initial velocity. In the book of academician N.A. Kilchevsky, an exact solution of the system of equations is given, which coincides with (2) up to signs, with zero initial conditions (3). In this paper, an exact solution to system (2) is obtained for nonzero initial conditions (see Section 4.). Problem (2) - (3) is preliminarily solved (see item 2.).

    2. Integrating each of the equations of system (2), we find

    Taking into account (3), we obtain the values \u200b\u200bof the integration constants: c 1 \u003d c 2 \u003d c 3 \u003d 0.

    Expressing from (4) in terms of y and substituting into the second equation of system (2), we have

    (5)

    Differential equation (5) is linear inhomogeneous. Hence his solution

    y \u003d + Y,

    where is the general solution of the homogeneous equation, Y is the particular solution of the inhomogeneous equation. Roots of the characteristic equation

    purely imaginary Therefore, the general solution to the homogeneous equation

    depending on two constants of integration, can be written as

    Private solution

    where A and B are undefined coefficients. Substituting the right side (6) in (5)

    taking into account we get

    Reducing by 2ω and equating to each other the coefficients at the first powers of t and the free terms, we find

    So the general solution is

    Satisfying the initial condition y 0 \u003d 0, we obtain c 1 * \u003d 0. The condition gives

    Consequently,

    (7)


    It should be noted that in the expression for y contains a misprint - in the second term, the coefficient in the denominator at ω 2 is equal to one.

    Substituting the right-hand side of (7) instead of y into the first and third equations of system (4), integrating and satisfying the initial conditions x 0 = z 0 \u003d 0, we get

    Due to the fact that the orientation of the axes xand z is opposite to that adopted in, formulas (8) - (9) differ in signs from the corresponding formulas derived by N.A. Kilchevsky.

    Subtracting expression (8) from (9) at we will have

    Differentiating in time we get

    Based on (8), it is easy to prove that for a moving point, therefore, the inequality

    (11)

    Consequently, when the Coriolis force of inertia is taken into account, the vertical speed of falling of a point is less than without taking it into account. In other words, disregard of the Earth's rotation overestimates the vertical velocity of the point falling in comparison with the actual velocity in the void. This conclusion, which is only of theoretical interest, is valid for all φ from the interval.For example, the difference in the distances traveled by a point in 10 s of fall without taking into account and taking into account the Earth's rotation at latitude φ \u003d 450 does not exceed 5. ten -5 m, i.e. the value is negligible.

    3. Let us write the solution of problem (2) - (3) in the form of converging series. Let's use the expansion

    Substituting the right-hand sides of these formulas in (7) - (9), after transformations we obtain

    Setting ω \u003d 0 in (12), we have x \u003d y \u003d 0, The same result can be obtained from (7) - (9) as ω → 0.

    ,

    The solution to problem (2), (13) can be obtained by the method described in detail in Section 2. In the case of nonzero initial conditions, the calculations are more cumbersome, so they are omitted here. The solution has the form

    Substitution in (2) of the corresponding derivatives obtained from (14) shows that each of the equations of the system turns into an identity. The initial conditions (13) are also satisfied exactly. It is assumed that there is a unique solution to the Cauchy problem for system (2). Strictly speaking, solution (14) should agree well with experimental data only in such a neighborhood of the initial point M 0 (x 0 , y 0 , z 0 ) , where the latitude and gravity acceleration values \u200b\u200bdiffer little from those at this starting point. To expand the solution domain, one can organize a time-dependent iterative step-by-step procedure by introducing corrections in (14) at the next time step that take into account the changes φ , gand taking as the initial conditions the corresponding values \u200b\u200bcalculated in the previous step.

    It is easy to see that, for, equalities (7) - (9) follow from (14). Letting ω to zero (ω → 0), from (14) it is possible to obtain a solution to the problem for nonzero initial conditions without taking into account the Earth's rotation:

    In this case, the trajectory of the point is a flat curve - a parabola, so usually two equations are sufficient.

    5. Consider six more options for specifying the initial conditions, in all of them, for simplicity, we assume x 0 = y 0 \u003dz 0 = 0.

    Variant I. Let, i.e. the initial velocity is directed to the east. Then the Coriolis inertial force acting on the point at the initial moment of time lies in the plane of parallel and is directed from the axis of rotation of the Earth. From (14), following the approach of item 3., leaving explicitly only a few first terms of the series, we obtain

    The point deviates to the east and to the south (southeast). Formula (15) shows that the deviation of the trajectory of the point to the south is proportional to the first degree of the angular velocity ω . For example, for t \u003d10cit is about 5 cm. In the absence of an initial velocity, the deviation of the trajectory of a point to the south due to the rotation of the Earth is proportional to the square of the angular velocity. This well-known result follows from the formula for x of system (12).

    Option II. Let, i.e. the initial velocity of the point is directed to the north, therefore, the Coriolis force of inertia acting on the material point at t \u003d 0 is directed to the east. Carrying out the same calculations as in the previous case, we will have

    The point deviates north and east (northeast). From formula (19) it can be seen that there are two positive terms proportional to the first power of the angular velocity ω, and the second term appears due to the initial velocity directed to the north. Consequently, the deviation to the east is greater than when a point falls in the void without an initial velocity. This conclusion is made taking into account the fact that the angular velocity of the Earth's rotation is small in comparison with the unit value Therefore, terms containing ω to a power higher than the second for small t and υ 0 can be neglected.

    Option III. Let, i.e. the initial speed is directed down the plumb line. The Coriolis force of inertia for the entire time of the point falling is directed to the east. The solution obtained similarly to the previous two options has the form

    From (21) it is seen that the deviation of the point to the south is negligible. Formula (22) shows that, as in the previous version, the deviation of the point to the east is greater than when falling without an initial velocity.

    Option IV. Let be those. the initial velocity is westward. Coriolis force of inertia at t = 0 lies in the plane of parallel and is directed to the axis of rotation of the Earth. The solution is given by formulas (15 - 17) taking into account the negative sign . If the sum of the first two terms in (16) is negative, the point deviates at the considered moment to the west and north (north - west), if positive, then - to the north and east (north - east). For the latter case to take place, the point must free fall over a relatively long period of time. For example, for g = 9,81 m / spoint must fall more than 77 from, i.e. from a height of more than 29.1 km.The point begins to fall in the westerly direction, under the action of the Coriolis force of inertia it turns to the right, crosses the meridian plane and changes direction to the north-east.

    where the plus and minus signs are chosen in the same way as in (24) and (25).

    Variant V. Let those. the initial velocity is directed to the south. Coriolis force of inertia at t \u003d 0 directed west. The solution is given by formulas (18) - (20) taking into account the sign .

    Option VI. Point is thrown vertically upwards: ... The Coriolis force of inertia when a point rises is almost perpendicular to the meridian plane and is directed to the west. As a solution, you can use formulas (21) - (23), only you need to take into account that the conditions must be satisfied .

    In this work, it was assumed, as is usually accepted, that the point is located in the Northern Hemisphere. You can similarly solve the problem of the motion of a material point in a void near the Earth's surface in the Southern Hemisphere.

    Finally, we note that formulas (14) - (23) can be applied to assess the influence of the rotation of the planets of the solar system on the motion of a material point near their surfaces.

    BIBLIOGRAPHY

    1. Kilchevsky N.A. Course of theoretical mechanics, vol. I (kinematics, statics, dynamics of a point). - 2nd ed. - M .: Nauka, Main edition of physical and mathematical literature, 1977.
    2. Mathematical analysis tasks and exercises. Under the editorship of Demidovich B.P. - M .: Nauka, Main edition of physical and mathematical literature, 1978 .-- 480 p.

    Bibliographic reference

    Bayrashev K.A. TO THE PROBLEM ON THE INFLUENCE OF EARTH ROTATION ON THE MOVEMENT OF A MATERIAL POINT // Fundamental Research. - 2006. - No. 10. - S. 9-15;
    URL: http://fundamental-research.ru/ru/article/view?id\u003d5388 (date of access: 15.01.2020). We bring to your attention the journals published by the "Academy of Natural Sciences"

    When solving most technical problems, the reference frame associated with the Earth is considered inertial (stationary). Thus, the diurnal rotation of the Earth with respect to the stars is not taken into account (for the influence of the Earth's motion in its orbit around the Sun, see § 99). This rotation (one revolution per day) occurs at an angular velocity

    Let us consider how such a rather slow rotation affects the equilibrium and motion of bodies near the earth's surface.

    1. The force of gravity. The concept of the force of gravity, which is part of the force of gravity (attraction to the Earth), is associated with the diurnal rotation of the Earth. A material point located near the earth's surface is affected by the force of gravity, decomposing into forces (Fig. 250).

    The force directed to the earth's axis gives the point the normal acceleration that the point should have, participating together with the Earth in its daily rotation; if the mass of a point, and its distance from the earth's axis, then numerically

    Another component of the gravitational force, the P force, is a quantity called gravity. In this way,

    that is, the force of gravity is equal to the difference between the entire force of gravity and that of its component, which ensures the participation of a point (body) in the daily rotation of the Earth.

    The direction of the force P determines the direction of the vertical at a given point on the earth's surface (this will be the direction of the thread on which some load is suspended; the tension of the thread is equal to P), and the plane perpendicular to the force P is a horizontal plane. Since where is very small, the force P, both numerically and in direction, differs little from the gravitational force FT. The modulus of force P is called the body weight.

    2. Relative rest and relative motion near the earth's surface. If we single out the gravitational force FT among the acting forces, then the equation of relative equilibrium (rest) of a point on the rotating Earth according to (57) will be

    But in this case. Then the equation will take on the form, that is, the same as the equilibrium equation has when the frame of reference associated with the Earth is considered stationary.

    Consequently, when drawing up the equations of equilibrium of bodies with respect to the Earth, additional corrections for the rotation of the Earth are not necessary (this rotation is taken into account by the presence of the force P in the equations).

    Now let's turn to the equation of relative motion (56), in which we also select the force of gravity. Then we get

    But, as in the previous case, the equation takes the form

    Hence it follows that when, when drawing up the equations of motion, the axes associated with the Earth are considered stationary, then only the Coriolis force of inertia is neglected, which is numerically equal to

    where a is the angle between the relative velocity v of the point and the earth's axis.

    Since the angular velocity of the Earth is very small, then if the velocity v is not very large, the magnitude in comparison with the force of gravity can be neglected. For example, at (the speed of a conventional artillery projectile) and the value of Fkop is only about 1% of the force P. Therefore, in most engineering calculations when studying the motion of bodies, the frame of reference associated with the Earth can really be considered inertial (stationary).

    Taking into account the Earth's rotation becomes of practical importance either at very high speeds (the flight speed of ballistic missiles), or for movements that last for a very long time (river currents, air and sea currents).

    3. Examples. Let us consider the qualitative effect of the Earth's rotation on the motion of bodies.

    Movement on the earth's surface. When a point moves along the meridian in the northern hemisphere from north to south, the Coriolis acceleration of akor is directed to the east (see § 67, problem 80), to the west. When moving from south to north, will be directed to the east. In both cases, as we see, the point deviates to the right from the direction of its motion due to the Earth's rotation.

    If the point moves along the parallel to the east, then the acceleration of the acor will be directed along the radius of the MC of the parallel (Fig. 251), and the force - in the opposite direction. The vertical component of this force, directed along the OM, will cause a slight change in body weight, and the horizontal component directed to the south will cause the point to deviate to the right from the direction of its movement. A similar result will be obtained when moving along the parallel to the west.

    Hence, we conclude that in the northern hemisphere, a body moving along the earth's surface in any direction will deviate to the right from the direction of motion due to the rotation of the earth. In the southern hemisphere, the deviation will occur to the left.

    This circumstance explains the fact that the rivers flowing in the northern hemisphere undermine the right bank (Baer's law). This is the same reason for the deviations of winds of constant direction (trade winds) and sea currents, as well as air masses in the cyclone and anticyclone, where, instead of moving to the center of the cyclone (area of \u200b\u200breduced pressure) or from the center of the anticyclone (area of \u200b\u200bincreased pressure), there is a circulation of air around the center cyclone (anticyclone).

    Vertical drop. To determine the direction of the Coriolis force of inertia in the case of a freely falling point, it is necessary to know the direction of the relative velocity v of the point. Since the force is very small in comparison with the force of gravity, then in the first approximation the vector v can be considered as directed vertically, that is, along the line MO (Fig. 251). Then the vector will be, as is easy to see, directed to the west, and the force to the east (that is, as in Fig. 251 the vector v is directed). Consequently, in the first approximation, a freely falling point (body) is deflected due to the rotation of the Earth from the vertical to the east. A body thrown vertically upward will obviously deviate to the west as it rises. The magnitudes of these deviations are very small and are noticeable only at a sufficiently large height of fall or rise, as can be seen from the calculations given in § 93.



    The earth makes 11 different movements, of which the following are of great geographic significance:

    Daily rotation around the axis,

    Annual revolution around the sun,

    Movement around the common center of gravity of the Earth-Moon system.

    As you know, the Earth rotates around its axis from west to east, turning in I second by 24.6Q.gQ \u003d wy part of a full revolution. SS

    The daily rotation of the Earth around its axis has a noticeable effect on any body freely moving along the surface of the earth and, in particular, on the movement of air.

    Imagine the horizon plane at the North Pole (Fig. 32). With the Earth's daily rotation, this plane will obviously rotate around the pole point P in the direction shown by the arrow.

    Let us assume that the air particle a, the motion of which is being considered, at a certain moment of time is at point b on the line of the meridian RA. Let the direction of motion of this particle, marked by an arrow, make a certain angle a with the direction of the meridian PA.

    Figure: 33. Deflecting action of the Earth's rotation in the northern and southern hemispheres.

    Consider the motion of a particle a relative to such a rotating horizon plane. Obviously, after some time the RA meridian will take the position of RAg. But a moving particle by inertia will tend to maintain the same direction

    Figure: 32. Deflecting action of the Earth's rotation at the pole.

    which she had at point b. Thus, the direction of motion of the particle at the point bx
    will be parallel to its movement at point b, which is indicated by the arrow. But this direction of movement is with the direction of the meridian RA1
    angle p, slightly larger than angle a.

    The movement will occur as if some force deflects the air particle to the right of the direction of its initial movement.

    We examined the motion of a particle near the pole. The same phenomenon will be observed, but only to a lesser extent, and at other latitudes of the northern hemisphere. In this case, the deviation will be the smaller, the smaller the latitude of the place. There is no such deviation at the equator.

    In the southern hemisphere, the deviation occurs to the left of the original direction of travel.

    In fig. 33 shows diagrams illustrating the deviation of p in the northern and southern hemispheres during the initial movement of the

    air particles along the meridian. The figure shows the cases of motion of a particle from pole to equator and from equator to pole - Here: AB and CD are the initial directions of motion of some air particles in the northern hemisphere, coinciding with the direction of the meridian; AHVX and C1D1 are the subsequent directions of motion of the corresponding particles, after points A and C, due to the rotation of the Earth, took position L, and Cѵ

    For the southern hemisphere, similar starting positions are represented by arrows A'B 'and C'D', followed by arrows AB and CD.

    As you can see, in these cases in the northern hemisphere there is a deviation to the right from the initial direction of movement, and in the southern hemisphere - to the left.

    Cases of such movement are considered here, when the initial direction of movement coincided with the direction of the meridian. In mechanics, it is proved that deflection is observed in any direction of motion and the deflecting force of the Earth's rotation is always directed perpendicular to the direction of motion. In the northern hemisphere, it ‘is directed to the right, at right angles to the direction of travel, and in the southern hemisphere to the left.

    In reality, there is no deflecting force, and the deviation of the particle from the initial direction of motion is due only to the daily rotation of the Earth.

    The influence of this deviation is manifested not only in the deviation of air movement, but also in a number of other phenomena. An example is that the right bank is steeper than the left in most of the large rivers of the northern hemisphere. This is due to the fact that the water, in its course, deviates all the time to the right and (continuously undermines the right bank.

    A deviation to the right in the northern hemisphere can be observed in the distribution of warm and cold ocean currents. Thus, the warm Gulfstrom current, starting off the coast of the Gulf of Mexico, deviates to the right when moving northward and reaches the coast of Scandinavia.

    Thus, any freely moving body moving in any direction, under the influence of the Earth's rotation, deviates in the northern hemisphere to the right, and in the southern hemisphere to the left.

    Astronomers have found that the Earth is simultaneously involved in several types of motion. For example, as part of it, it moves around the center of the Milky Way, and as part of our Galaxy, it participates in intergalactic movement. But there are two main types of movement known to mankind since ancient times. One of them is around its axis.

    A consequence of the axial rotation of the Earth

    Our planet rotates uniformly around an imaginary axis. This movement of the Earth is called axial rotation. All objects on the earth's surface rotate with the earth. Rotation occurs from west to east, that is, counterclockwise, if you look at the Earth from the North Pole. Due to this rotation of the planet, sunrise in the morning occurs in the east, and sunset in the evening - in the west.

    The Earth's axis is tilted at an angle of 66 1/2 ° to the orbital plane along which the planet moves around the Sun. Moreover, the axis is strictly in outer space: its northern end is constantly directed to the North Star. The axial rotation of the Earth determines the apparent movement of the stars and the Moon across the sky.

    The rotation of the Earth around its axis has a great impact on our planet. It determines the change of day and night and the emergence of a natural, given by nature, unit of time measurement - day. This is the period of a complete revolution of the planet around its axis. The length of the day depends on the speed of rotation of the planet. According to the existing time system, a day is divided into 24 hours, an hour - 60 minutes, a minute - 60 seconds.

    Due to the axial rotation of the Earth, all bodies moving along its surface deviate from the original direction in the Northern Hemisphere to the right in the course of their movement, and in the Southern Hemisphere - to the left. In rivers, the deflecting force pushes the water against one of the banks. Therefore, rivers in the Northern Hemisphere usually have a steeper right bank, and in the Southern Hemisphere, the left. The deflection affects the direction of winds in, currents in the World Ocean.

    Axial rotation affects the shape of the earth. Our planet is not a perfect ball, it is a little compressed. Therefore, the distance from the center of the Earth to the poles (polar radius) is 21 kilometers shorter than the distance from the center of the Earth to the equator (equatorial radius). For the same reason, the meridians are 72 kilometers shorter than the equator.

    Axial rotation causes diurnal changes in the flow of sunlight and heat to the earth's surface, explains the apparent movement of the stars and the moon across the sky. It also determines the difference in time in different parts of the world.

    World Time and Time Zones

    At the same time, in different parts of the world, the time of day may be different. But for all points located on the same meridian, the time is the same. It is called local time.

    For convenience of timing, the Earth's surface is conventionally divided into 24 (according to the number of hours in a day). The time within each zone is called standard time. The zones are counted from the zero time zone. This is the belt in the middle of which the Greenwich (zero) meridian passes. Time on this meridian is called universal. In two neighboring zones, the standard time differs by exactly 1 hour.

    In the middle of the twelfth time zone, approximately along the 180 meridian, there is a date line. On both sides of it, the hours and minutes coincide, and the calendar dates differ by one day. If the traveler crosses this line from east to west, then the date is moved forward one day, and if from west to east, then it goes back one day.