According to Newton's laws, the movement of the body with acceleration is possible only under the action of force. Because Falling bodies move with acceleration aimed down, then they have the strength of attraction to Earth. But not only the land has a property to act on all the body of the force of attraction. Isaac Newton suggested that the strengths of attraction are applied between all bodies. These forces are called forces of worldy gravityor gravitationalforces.

By distributing the established patterns - the dependence of the force of attraction of bodies to the Earth from the distances between the bodies and the masses of the interacting bodies obtained as a result of observations - Newton opened in 1682 the Law of the World Health:All the bodies are attracted to each other, the world's strength is directly proportional to the mass of mass bodies and inversely proportional to the square of the distance between them:

The vectors of the world's strengths are directed along a direct connecting body. The ratio of proportionality is girtimized gravitational constant (permanent worldy gravity)and equal

.

Force of gravityit is called the force of attraction, acting on the part of the earth for all bodies:

.

Let be
- Earth weight, and
- Earth radius. Consider the dependence of the acceleration of the free fall on the height of the lifting above the surface of the Earth:

Body weight. Weightlessness

Body weight -the force with which the body presses on the support or suspension due to the attraction of this body to the ground. Body weight is applied to the support (suspension). The weight of the body weight depends on how the body is moving with a support (suspension).

Body weight, i.e. The force with which the body acts on the support is and the strength of elasticity with which the support acts on the body, in accordance with the third law of Newton, is equal to the absolute value and are opposite to the direction.

If the body is alone on the horizontal support or evenly moves, only the strength of gravity and the force of elasticity on the part side act on it, therefore the body weight is equal to the strength of gravity (but these forces are applied to different bodies):

.

With accelerated motion, the body weight will not be equal to the power of gravity. Consider the movement of the body weighing the MPO effect of gravity and elasticity with acceleration. On the 2nd Newton law:

If the acceleration of the body is directed down, the body weight is less gravity; If the acceleration of the body is directed up, then all the bodies are more gravity.

Increased body weight caused by the accelerated movement of support or suspension, called overload.

If the body falls freely, then from the formula * it follows that the body weight is zero. The disappearance of the weight when moving support with acceleration of free fall is called uncomfortable.

The state of weightlessness is observed in an airplane or a spacecraft when they move them with an acceleration of free fall regardless of their speed. Outside the earth's atmosphere, when turning off the jet engines to the spacecraft, only the world's strength is valid. Under the action of this force, the spacecraft and all the bodies in it move with the same acceleration; Therefore, in the ship there is a phenomenon of weightlessness.

Body movement under the action of gravity. Movement of artificial satellites. First cosmic speed

If the body movement module is much less than the distance to the center of the Earth, then we can consider the strength of the global gravity during the constant movement, and the movement of the body is equivalent. The easiest case of body movement under the action of gravity is free drop with zero initial speed. In this case, the body moves with the acceleration of free fall to the center of the Earth. If there is an initial speed directed by vertical, then the body moves along the curvilinear trajectory (Parabola, if you do not take into account the resistance of the air).

With some initial speed, the body thrown on the surface of the earth, under the action of gravity, in the absence of an atmosphere, can move around the circumference around the Earth, without falling on it and without removing from it. Such speed is called the first space speedand the body moving in this way - artificial Earth Satellite (UES).

We define the first space speed for the Earth. If the body under the action of gravity moves around the earth is evenly around the circumference, then the acceleration of the free fall is its centripetal acceleration:

.

Hence the first cosmic speed is equal

.

The first cosmic speed for any celestial body is determined in the same way. The acceleration of the free fall at a distance of R from the center of the celestial body can be found using the second Newton law and the World Act:

.

Consequently, the first cosmic speed at a distance of R from the center of the celestial body massm is equal

.

To launch an exemplary orbit, it is necessary to first take out the atmosphere. Therefore, space ships start upright. At an altitude of 200 - 300 km from the surface of the Earth, where the atmosphere is cleaned and almost does not affect the movement of the USS, the rocket makes the turn and reports the first space speed in the direction perpendicular to the vertical.

The XVI - XVII century, many are rightly called one of the most glorious periods at that time, those foundations were largely laid, without which the further development of this science would be simply unthinkable. Copernicus, Galilee, Kepler did a great job to declare physics as a science that can answer almost any question. A global law is worth a mansion in a whole series of discovery, the final formulation of which belongs to the outstanding English scientist Isaac Newton.

The main importance of the work of this scientist was not in the opening of the world's strength - about the presence of this magnitude before Newton, Galilee, and Kepler, and in the fact that he was the first to prove that on Earth, and in outer space there are alone and those The same strengths of interaction between bodies.

Newton in practice confirmed and theoretically substantiated the fact that absolutely all bodies in the universe, including those that are located on Earth interact with each other. This interaction got the name of the gravitational, while the process of global gravity itself is gravity.
This interaction occurs between the bodies because there is a special, unlike others, the type of matter, which in science received the name of the gravitational field. This field exists and acts around an absolutely any subject, while no protection from it does not exist, as it has no matter what the ability to penetrate any materials.

The world's strength, the definition and wording of which gave is directly dependent on the product of the masses of interacting bodies, and in the back dependence on the square of the distance between the intercom objects. According to Newton, irrefutably confirmed by practical surveys, the world's strength is located on the following formula:

It has a particular importance to the gravitational constant G, which is approximately equal to 6.67 * 10-11 (H * m2) / kg2.

The world's strength with which the bodies are attracted to the Earth is private case Newton's law is called forceful gravity. In this case, the gravitational constant and mass of the earth itself can be neglected, so the formula for finding gravity will look like this:

Here G is nothing but acceleration numeric value which is approximately 9.8 m / s2.

Newton's law explains not only the processes occurring directly on Earth, it gives an answer to many questions related to the device Solar system. In particular, the world's strength between has a decisive effect on the movement of the planets in its orbits. The theoretical description of this movement was still given to Kepler, but it was only possible just after Newton formulated his famous law.

Newton himself associated the phenomena of earth and extraterrestrial gravity on simple example: When shooting out of flies, it is not directly, but along the arcuate trajectory. At the same time, with an increase in the charge of gunpowder and the mass of the nucleus, the latter will fly farther and further. Finally, if we assume that it is possible to get so much powder and construct such a gun so that the kernel will fly around around the globe, then, having done this movement, it will not stop, but will continue its circular (ellipsed) movement, turning into artificial as a result, the power of the World The same is the same in nature and on Earth, and in outer space.

Definition

The law of world community opened by I. Newton:

Two bodies are attracted to each other with, directly proportional to the product and inversely proportional to the square of the distance between them:

Description of the law of world

The coefficient is a gravitational constant. In the SI system, the gravitational constant matters:

This constant, as can be seen, is very small, so the forces between bodies having small masses are also small and practically not felt. However, the movement of cosmic bodies is fully determined by gravity. The presence of global or, in other words, the gravitational interaction explains what the land and planets "hold" "and why they move around the sun according to certain trajectories, and they do not fly away from it. The law of global gravity allows you to identify many characteristics. heavenly Tel - mass planets, stars, galaxies and even black holes. This law makes it possible to calculate the orbits of the planets and create a mathematical model of the universe.

With the help of the world of world, you can also calculate cosmic speeds. For example, minimum speedIn which the body moving horizontally over the surface of the Earth does not fall on it, and will move along a circular orbit - 7.9 km / s (first cosmic speed). In order to leave the Earth, i.e. To overcome its gravitational attraction, the body must have a speed of 11.2 km / s, (second cosmic speed).

Gravity is one of the most amazing phenomena of nature. In the absence of gravity forces, the existence of the universe would be impossible, the universe could not even arise. Gravity is responsible for many of the processes in the Universe - her birth, the existence of order instead of chaos. The nature of gravity is still not even enough. To date, no one has been able to develop a decent mechanism and a model of gravitational interaction.

Gravity

A special occasion of the manifestation of gravitational forces is the power of gravity.

Gravity strength is always directed vertically down (towards the center of the Earth).

If the body acts on the body, the body makes. The type of motion depends on the direction and module of the initial speed.

With the action of gravity, we are confronted every day. After some time it turns out on Earth. The book released from the hands falls down. By bouncing, the person does not fly into open space, but it falls down, to the ground.

Considering the free drop in the body near the surface of the Earth as the result of the gravitational interaction of this body with the Earth, you can write:

where to accelerate free fall:

Acceleration of free fall does not depend on body weight, and depends on the height of the body above the ground. The globe is a little flattened by the poles, so the bodies located near the poles are located a little closer to the center of the Earth. In this regard, the acceleration of free fall depends on the latitude of the terrain: it is a little more on the pole than the equator and other latitudes (at the Equator M / C, on the North Pole, the Equator M / s.

The same formula allows you to find an acceleration of free fall on the surface of any planet weighing and radius.

Examples of solving problems

Example 1 (task about "weighing" land)

The task	The radius of the Earth KM, accelerate the free fall on the surface of the planet M / s. Using this data, evaluate the approximate mass of the Earth.
Decision	Acceleration of free fall at the surface of the Earth: from where the mass of the Earth: In the system SI radius m. Substituting in the formula numerical values \u200b\u200bof physical quantities, we estimate the mass of the earth:
Answer	Mass of the Earth kg.

Example 2.

The task

The satellite of the Earth moves along a circular orbit at an altitude of 1000 km from the surface of the Earth. How fast is the satellite moving? For what time the satellite will make one full turn around the earth?

Decision

According to, the force acting on the satellite from the ground is equal to the product of the mass of the satellite to the acceleration, with which it moves: On the part of the Earth on the satellite, the strength of gravitational attraction is valid, which, according to the world of world, is equal to: where and the masses of the satellite and land, respectively. Since the satellite is at some height above the ground surface, the distance from it to the center of the Earth: where the radius of the earth.

Between any bodies in nature, there is a power of mutual attraction, called by the power of the world (or gravity forces). Isaac Newton was opened in 1682. When he was still 23 years old, he suggested that the forces holding the moon on her orbit, the same nature as the strength forcing the apple to fall on the ground.

Gravity (mG.) directed vertically strictly to the land center; Depending on the distance to the surface globe Acceleration of free fall differently. The surface of the Earth in medium latitudes is about 9.8 m / s 2. As removal from the surface of the Earth g. decreases.

Body weight (weight weight) – this is the power with which the body acts onhorizontal support or stretching suspension.It is assumed that the body motionless about support or suspension. Let the body lies on a fixed relative to the earth horizontal table. Denotes letter R.

The weight of the body and the power of gravity differ in nature: the body weight is a manifestation of the action of intermolecular forces, and gravity has a gravitational nature.

If acceleration a \u003d 0. , the weight is equal to the power, with which the body is attracted to the ground, namely. [P] \u003d n.

If another condition, the weight changes:

• if acceleration but not equal 0 , then weight P \u003d MG - MA (down) or P \u003d Mg + Ma (up);
• if the body falls freely or moves with an acceleration of free fall, i.e. a \u003d.g.(Fig.2), then the body weight is equal 0 (P \u003d 0. ). Body condition in which its weight is zero, called uncomfortable.

IN justice There are also astronauts. IN justice For a moment, you are, when you jump during a game of basketball or dance.

Home Experiment: Plastic bottle With the opening at the bottom is filled with water. We produce from hands from some height. While the bottle drops, the water from the hole does not follow.

Body weight moving with acceleration (in elevator) body in the elevator is experiencing overload

In this paragraph, we will tell about the amazing guappy of Newton, who led to the discovery of the law of the world.
Why the stone released from the hands falls to the ground? Because the earth attracts him, each of you will say. In fact, the stone falls on the ground with an acceleration of free fall. Consequently, the stone on the ground is the power aimed towards the Earth. According to the third law of Newton and the stone acts on Earth with the same module by force, on-grounded to the stone. In other words, the strength of mutual attraction act between the Earth and Stone.
Caught Newton
Newton was the first one who first guessed, and then strictly proved that the reason that causes the fall of the stone to the ground, the movement of the moon around the earth and the planets around the Sun, the same. This is the force of gravity acting between any bodies of the universe. Here is the course of his arguments given in Newton's main work "Mathematical starts of natural philosophy": "Abandoned horizontal stone will reject
, \\
1
/ /
W.
Fig. 3.2
under the action of gravity from the rectilinear path and, describing the trajectory curve, will fall finally on the ground. If you quit it with a greater speed,! it will fall further "(Fig. 3.2). Pro Justing these arguments, Newton \\ comes to the conclusion that if it were not for the resistance of the air, then the trajectory of the stone abandoned with high mountain At a certain speed, it could be that he would never achieve the surface of the Earth at all, and moved around it "just as the planets describe their orbits in the heavenly space."
Now we have become so familiar to the movement of satellites around the Earth, which is not necessary to explain the idea of \u200b\u200bNewton.
So, according to Newton, the movement of the moon around the Earth or the planets around the Sun is also a free fall, but only a fall that lasts, without stopping, billions of years. The reason for such a "fall" (whether it is really about the fall of ordinary stone on earth or the movement of the planets on their orbits) is the power of global. What does this power depends on?
The dependence of the force of body mass
In § 1.23 it was referred to a free drop of tel. Galilee's experiments were mentioned, which proved that the Earth reports to all the bodies in this place the same acceleration regardless of their mass. This is possible only if the force of attraction to the ground is directly proportional to the mass of the body. It is in this case that the acceleration of free fall equal to the ratio of the power of the earth's attraction to the mass of the body is a constant value.
Indeed, in this case, the increase in the mass of t, for example, halvery will lead to an increase in the force module F, too, twice as well as
F.
rhenium, which is equal to attitude - will remain unchanged.
Summarizing this conclusion for the forces of gravity between any bodies, we conclude that the world's strength is directly proportional to the mass of the body, which this force is valid. But in mutual attraction, at least two bodies participate. For each of them, according to the third law of Newton, the same in the module of the force is valid. Therefore, each of these forces should be proportional to both the mass of one body and the mass of another body.
Therefore, the world's strength between two bodies is directly proportional to the product of their masses:
F - here2. (3.2.1)
What does the force acting on this body on the part of another body depends?
The dependence of the force against the distance between the bodies
It can be assumed that the force of gravity should depend on the distance between the bodies. To verify the correctness of this assumption and find the dependence of the force from the distance between the bodies, Newton turned to the movement of the Earth's satellite - the Moon. Its movement was much more accurate in those days than the movement of the planets.
The appeal of the moon around the Earth occurs under the influence of the force between them. An approximate orbit of the moon can be considered a circle. Consequently, the Earth reports the moon centripetal acceleration. It is calculated by the formula
l 2.
a \u003d - TG
where B is a radius of the lunar orbit equal to about 60 radius of the Earth, T \u003d 27 days 7 h 43 min \u003d 2.4 106 C - the period of circulation of the moon around the Earth. Considering that the radius of the earth is R3 \u003d 6.4 106 m, we obtain that the centripetal acceleration of the moon is:
2 6 4K 60 | 6.4 | 10
M "" ". , about
a \u003d 2 ~ 0.0027 m / s *.
(2.4 | 106 s)
The foundation of the acceleration is less than accelerating the free fall of the bodies at the surface of the Earth (9.8 m / s2) approximately 3600 \u003d 602 times.
Thus, the increase in the distance between the body and the ground 60 times led to a decrease in the acceleration, reported by the earthly attraction, and therefore, the forces of attraction in 602 times.
This implies an important conclusion: acceleration, which informs the bodies of attraction to the ground, decreases inversely in the square of the distance to the center of the Earth:
cI
a \u003dK, (3.2.2)
R.
where CJ is a permanent coefficient, the same for all bodies.
Kepler laws
The study of the motion of the planets showed that this movement caused by the force of attraction to the Sun. Using thorough perennial observations of the Danish astronomer Quiet Brage, non-Metsky scientist Johann Kepler at the beginning of the XVII century. Called the Ki-Loatic Laws of Movement Planets - the so-called laws of Kepler.
First law of Kepler
All planets move along the ellipses, in one of the focus of which the sun is located.
The ellipse (Fig. 3.3) is called a flat closed curve, the amount of distances from any point of which up to two fixed points, called focus, is constant. This amount of distances is equal to the length of the large axis of AB ellipses, i.e.
FG + F2P \u003d 2B,
where Fl and F2 are the focuses of the ellipse, and B \u003d ^^ - its large half; About the center of the ellipse. The nearest point of the orbit is called the periecelium, and the most distant point from it - p

IN
Fig. 3.4.
"2.
In a and aphelius. If the sun is in focus FR (see Fig. 3.3), then the point A is perigelius, and the point in the aphelius.
Second law of Kepler
The radius-vector of the planet for the same time intervals describes equal areas. So, if the shaded sectors (Fig. 3.4) have the same area, the path Si\u003e S2\u003e S3 will be passed with the planet in equal intervals. From the figure it is seen that SJ\u003e S2. Hence, line speed The movements of the planet at various points of its orbit are not the same. In the perihelion, the speed of the planet is the greatest, in Afe-Lii - the smallest.
The third law of Kepler
Squares of conversion periods of planets around the Sun belongs as cubes of large semi-axes of their orbits. Recalling the larger part of the orbit and the period of circulation of one of the planets through l and TV and the other - through b2 and T2, the third law of the Kepler can be written as follows:

From this formula it is clear that further Planet. From the sun, the more her period of treatment around the sun.
Based on the laws of the Kepler, certain conclusions on accelerations reported by the planets of the Sun can be made. For simplicity, we will consider orbits not elliptic, but circular. For the planets of the solar system, this replacement is not too rough approximation.
Then the strength of attraction from the Sun in this approximation should be directed for all planets to the center of the Sun.
If it means to designate the periods of circulation of planets, and through R radii their orbits, then, according to the third law of the Kepler, for two planets can be recorded
t \\ l? T2 R2.
Normal acceleration when driving around the circle A \u003d CO2R. Therefore, the ratio of acceleration planets
Q-I GLD.
7g \u003d -2 ~ - (3-2-5)
2 T: R0
Using equation (3.2.4), we get
T2.
Since the third law of Kepler is fair for all planets, thereto, the acceleration of each planet is inversely proportional to the square of her distance to the Sun:
About O.
a \u003d - |. (3.2.6)
T.
The permanent C2 is the same for all planets, but does not coincide with the C2 constant in the formula to accelerate, communicated by the bodies of the globe.
Expressions (3.2.2) and (3.2.6) show that the force of gravity in both cases (attraction to the ground and attraction to the Sun) informs all bodies acceleration, independent of their mass and decreasing inversely in proportion to the square of the distance between them:
F ~ A ~ -2. (3.2.7)
R.
The Law of the World Health
The existence of dependencies (3.2.1) and (3.2.7) means that the power of the world
TP.L Sh
F ~
R2? TT-I TPP
F \u003d G.
In 1667, Newton finally formulated the law of all-peaceful gravity:
(3.2.8) R
The power of mutual attraction of two bodies is directly proportional to the production of masses of these bodies and is inversely proportional to the square of the distance between them. The pro-specification coefficient G is called gravitational constant.
Interaction of point and extended bodies
The law of world community (3.2.8) is valid only for such bodies, the sizes of which are negligible compared to the distance between them. In other words, it is only valid for material points. In this case, the forces of gravitational interaction are directed along the line connecting these points (Fig. 3.5). This kind of force is called central.
To find the strength of the force acting on this body from the other, in the case when the sizes of bodies cannot neglect, they are applied as follows. Both bodies mentally once divided into such small elements so that each of them can be considered point. Folding the forces acting on each element of this body by all elements of another body receive the force acting on this element (Fig. 3.6). Having done such an operation for each element of this body and folding the forces obtained, find the full force acting on this body. The task is complicated.
There are, however, one is almost an important case, when Formula (3.2.8) is applicable to extended bodies. Can i
m ^
Fi rice. 3.5 Fig. 3.6.
it is depends on the spherical bodies that depends only on the distances to their centers, with randoms between them, the large amounts of their radii are attracted with the forces whose modules are determined by formula (3.2.8). In this case, R is the distance between the centers of the balls.
And finally, since the sizes of the body falling on the Earth less size Earth, these bodies can be viewed as point. Then under R in formula (3.2.8), it is necessary to understand the distance from this body to the center of the Earth.
Between all the bodies there are forces of mutual attraction, depending on the bodies themselves (their mass) and on the distance between them.
? 1. The distance from Mars to the Sun is 52% more than the distance from the ground to the Sun. What is the duration of the year on Mars? 2. How will the force of attraction between the balls change, if the aluminum balls (Fig. 3.7) are replaced with steel balls of the same mass? "of the same volume?