The law of universal gravitation for dummies. Gravitational forces. The law of universal gravitation. Gravity. Subtle effects of gravity

Despite the fact that gravity is the weakest interaction between objects in the Universe, its importance in physics and astronomy is enormous, since it can influence physical objects at any distance in space.

If you are interested in astronomy, you have probably wondered what such a concept as gravity or the law of universal gravitation is. Gravity is the universal fundamental interaction between all objects in the Universe.

The discovery of the law of gravity is attributed to the famous English physicist Isaac Newton. Probably many of you know the story of the apple that fell on the head of the famous scientist. However, if you look deeper into history, you can see that the presence of gravity was thought about long before his era by philosophers and scientists of antiquity, for example, Epicurus. However, it was Newton who first described the gravitational interaction between physical bodies within the framework of classical mechanics. His theory was developed by another famous scientist, Albert Einstein, who in his general theory of relativity more accurately described the influence of gravity in space, as well as its role in the space-time continuum.

Newton's law of universal gravitation states that the force of gravitational attraction between two points of mass separated by a distance is inversely proportional to the square of the distance and directly proportional to both masses. The force of gravity is long-range. That is, regardless of how a body with mass moves in classical mechanics its gravitational potential will depend purely on the position of this object in this moment time. The greater the mass of an object, the greater its gravitational field - the more powerful the gravitational force it has. Space objects such as galaxies, stars and planets have greatest strength attraction and, accordingly, sufficiently strong gravitational fields.

Gravitational fields

Earth's gravitational field

The gravitational field is the distance within which gravitational interaction occurs between objects in the Universe. The greater the mass of an object, the stronger its gravitational field - the more noticeable its impact on other physical bodies within a certain space. The gravitational field of an object is potential. The essence of the previous statement is that if you introduce the potential energy of attraction between two bodies, then it will not change after the latter move along closed loop. From here emerges another famous law of conservation of the sum of potential and kinetic energy in a closed loop.

IN material world the gravitational field is of great importance. It is possessed by all material objects in the Universe that have mass. The gravitational field can influence not only matter, but also energy. It is due to the influence of the gravitational fields of such large cosmic objects as black holes, quasars and supermassive stars that solar systems, galaxies and other astronomical clusters are formed, which are characterized by a logical structure.

Recent scientific data show that the famous effect of the expansion of the Universe is also based on the laws gravitational interaction. In particular, the expansion of the Universe is facilitated by powerful gravitational fields, both of its small and largest objects.

Gravitational radiation in a binary system

Gravitational radiation or gravitational wave is a term first introduced into physics and cosmology by the famous scientist Albert Einstein. Gravitational radiation in the theory of gravitation is generated by the movement of material objects with variable acceleration. During the acceleration of an object, a gravitational wave seems to “break away” from it, which leads to oscillations of the gravitational field in the surrounding space. This is called the effect gravitational wave.

Although gravitational waves are predicted by Einstein's general theory of relativity as well as other theories of gravity, they have never been directly detected. This is due primarily to their extreme smallness. However, in astronomy there is indirect evidence that can confirm this effect. Thus, the effect of a gravitational wave can be observed in the example of the approach double stars. Observations confirm that the rate of convergence of double stars depends to some extent on the loss of energy from these cosmic objects, which is presumably spent on gravitational radiation. Scientists will be able to reliably confirm this hypothesis in the near future using the new generation of Advanced LIGO and VIRGO telescopes.

IN modern physics There are two concepts of mechanics: classical and quantum. Quantum mechanics was developed relatively recently and is fundamentally different from classical mechanics. IN quantum mechanics objects (quanta) do not have definite positions and speeds; everything here is based on probability. That is, an object can occupy a certain place in space at a certain point in time. Where he will move next cannot be reliably determined, but only with a high degree of probability.

An interesting effect of gravity is that it can bend the space-time continuum. Einstein's theory states that in the space around a bunch of energy or any material substance, space-time is curved. Accordingly, the trajectory of particles that fall under the influence of the gravitational field of this substance changes, which makes it possible to predict the trajectory of their movement with a high degree of probability.

Theories of gravity

Today scientists know over a dozen different theories of gravity. They are divided into classical and alternative theories. Most well-known representatives The first is the classical theory of gravity by Isaac Newton, which was invented by the famous British physicist back in 1666. Its essence lies in the fact that a massive body in mechanics generates a gravitational field around itself, which attracts smaller objects. In turn, the latter also have gravitational field, like any other material objects in the Universe.

The next popular theory of gravity was invented by the world famous German scientist Albert Einstein at the beginning of the 20th century. Einstein was able to more accurately describe gravity as a phenomenon, and also explain its action not only in classical mechanics, but also in the quantum world. His general theory relativity describes the ability of a force such as gravity to influence the space-time continuum, as well as the trajectory of movement elementary particles in space.

Among alternative theories In gravity, the relativistic theory, which was invented by our compatriot, the famous physicist A.A., perhaps deserves the greatest attention. Logunov. Unlike Einstein, Logunov argued that gravity is not a geometric, but a real, fairly strong physical force field. Among the alternative theories of gravity, scalar, bimetric, quasilinear and others are also known.

1. For people who have been in space and returned to Earth, it is quite difficult at first to get used to the strength of the gravitational influence of our planet. Sometimes this takes several weeks.
2. It has been proven that human body in a state of weightlessness can lose up to 1% of bone marrow mass per month.
3. The least attractive force in solar system Among the planets, Mars has the largest, and Jupiter has the largest.
4. The known salmonella bacteria, which cause intestinal diseases, behave more actively in a state of weightlessness and are capable of causing to the human body much more harm.
5. Among all known astronomical objects in the Universe, black holes have the greatest gravitational force. A black hole the size of a golf ball could have the same gravitational force as our entire planet.
6. The force of gravity on Earth is not the same in all corners of our planet. For example, in the Hudson Bay region of Canada it is lower than in other regions of the globe.

In nature, there are various forces that characterize the interaction of bodies. Let us consider the forces that occur in mechanics.

Gravitational forces. Probably the very first force the existence of which man became aware of was force of gravity, acting on bodies from the Earth.

And it took many centuries for people to understand that the force of gravity acts between any bodies. And it took many centuries for people to understand that the force of gravity acts between any bodies. The English physicist Newton was the first to understand this fact. Analyzing the laws that govern the motion of planets (Kepler's laws), he came to the conclusion that the observed laws of motion of planets can be fulfilled only if there is an attractive force between them, directly proportional to their masses and inversely proportional to the square of the distance between them.

Newton formulated law of universal gravitation. Any two bodies attract each other. The force of attraction between point bodies is directed along the straight line connecting them, is directly proportional to the masses of both and inversely proportional to the square of the distance between them:

Under the point bodies in in this case understand bodies whose dimensions are many times smaller than the distance between them.

The forces of universal gravity are called gravitational forces. The proportionality coefficient G is called the gravitational constant. Its value was determined experimentally: G = 6.7 10¯¹¹ N m² / kg².

Gravity acting near the surface of the Earth is directed towards its center and is calculated by the formula:

where g is the acceleration of gravity (g = 9.8 m/s²).

The role of gravity in living nature is very significant, since the size, shape and proportions of living beings largely depend on its magnitude.

Body weight. Consider what happens when some weight is placed on horizontal plane(support). At the first moment after the load is lowered, it begins to move downward under the influence of gravity (Fig. 8).

The plane bends and an elastic force (support reaction) directed upward appears. After the elastic force (Fу) balances the force of gravity, the lowering of the body and the deflection of the support will stop.

The deflection of the support arose under the action of the body, therefore, a certain force (P) acts on the support from the side of the body, which is called the weight of the body (Fig. 8, b). According to Newton's third law, the weight of a body is equal in magnitude to the ground reaction force and is directed in the opposite direction.

P = - Fу = Fheavy.

Body weight is called the force P with which a body acts on a horizontal support that is motionless relative to it.

Since the force of gravity (weight) is applied to the support, it is deformed and, due to its elasticity, counteracts the force of gravity. The forces developed in this case from the side of the support are called support reaction forces, and the very phenomenon of the development of counteraction is called the support reaction. According to Newton's third law, the support reaction force is equal in magnitude to the force of gravity of the body and opposite in direction.

If a person on a support moves with the acceleration of the parts of his body directed from the support, then the reaction force of the support increases by the amount ma, where m is the mass of the person, and is the acceleration with which the parts of his body move. These dynamic effects can be recorded using strain gauge devices (dynamograms).

Weight should not be confused with body weight. The mass of a body characterizes its inert properties and does not depend either on the force of gravity or on the acceleration with which it moves.

The weight of a body characterizes the force with which it acts on the support and depends on both the force of gravity and the acceleration of movement.

For example, on the Moon the weight of a body is approximately 6 times less than the weight of a body on Earth. Mass in both cases is the same and is determined by the amount of matter in the body.

In everyday life, technology, and sports, weight is often indicated not in newtons (N), but in kilograms of force (kgf). The transition from one unit to another is carried out according to the formula: 1 kgf = 9.8 N.

When the support and the body are motionless, then the mass of the body is equal to the gravity of this body. When the support and the body move with some acceleration, then, depending on its direction, the body can experience either weightlessness or overload. When the acceleration coincides in direction and is equal to the acceleration of gravity, the weight of the body will be zero, therefore a state of weightlessness arises (ISS, high-speed elevator when lowering down). When the acceleration of the support movement is opposite to the acceleration of free fall, the person experiences an overload (a manned launch from the surface of the Earth spaceship, High-speed elevator going up).

The law of universal gravitation was discovered by Newton in 1687 while studying the motion of the moon's satellite around the Earth. The English physicist clearly formulated a postulate characterizing the forces of attraction. In addition, by analyzing Kepler's laws, Newton calculated that gravitational forces must exist not only on our planet, but also in space.

Background

The law of universal gravitation was not born spontaneously. Since ancient times, people have studied the sky, mainly to compile agricultural calendars, calculate important dates, and religious holidays. Observations indicated that in the center of the “world” there is a Luminary (Sun), around which celestial bodies rotate in orbits. Subsequently, the dogmas of the church did not allow this to be considered, and people lost the knowledge accumulated over thousands of years.

In the 16th century, before the invention of telescopes, a galaxy of astronomers appeared who looked at the sky in a scientific way, discarding the prohibitions of the church. T. Brahe, having been observing space for many years, systematized the movements of the planets with special care. These highly accurate data helped I. Kepler subsequently discover his three laws.

By the time Isaac Newton discovered the law of gravitation (1667), the heliocentric system of the world of N. Copernicus was finally established in astronomy. According to it, each of the planets of the system rotates around the Sun in orbits that, with an approximation sufficient for many calculations, can be considered circular. At the beginning of the 17th century. I. Kepler, analyzing the works of T. Brahe, established kinematic laws characterizing the movements of the planets. The discovery became the foundation for elucidating the dynamics of planetary motion, that is, the forces that determine exactly this type of their motion.

Description of interaction

Unlike short-period weak and strong interactions, gravity and electromagnetic fields have properties long range: their influence manifests itself over gigantic distances. Mechanical phenomena in the macrocosm are affected by two forces: electromagnetic and gravitational. The influence of planets on satellites, the flight of an thrown or launched object, the floating of a body in a liquid - in each of these phenomena gravitational forces act. These objects are attracted by the planet and gravitate towards it, hence the name “law of universal gravitation”.

It has been proven that there is certainly a force of mutual attraction between physical bodies. Phenomena such as the fall of objects to the Earth, the rotation of the Moon and planets around the Sun, occurring under the influence of the forces of universal gravity, are called gravitational.

Law of universal gravitation: formula

Universal gravity is formulated as follows: any two material objects are attracted to each other with a certain force. The magnitude of this force is directly proportional to the product of the masses of these objects and inversely proportional to the square of the distance between them:

In the formula, m1 and m2 are the masses of the material objects being studied; r is the distance determined between the centers of mass of the calculated objects; G is a constant gravitational quantity expressing the force with which the mutual attraction of two objects weighing 1 kg each, located at a distance of 1 m, occurs.

What does the force of attraction depend on?

The law of gravity works differently depending on the region. Since the force of gravity depends on the values ​​of latitude in a certain area, similarly, the acceleration of gravity has different values ​​in different places. Maximum value the force of gravity and, accordingly, the acceleration of free fall is at the poles of the Earth - the force of gravity at these points is equal to the force of attraction. The minimum values ​​will be at the equator.

The globe is slightly flattened, its polar radius is approximately 21.5 km less than the equatorial radius. However, this dependence is less significant compared to the daily rotation of the Earth. Calculations show that due to the oblateness of the Earth at the equator, the magnitude of the acceleration due to gravity is slightly less than its value at the pole by 0.18%, and after daily rotation - by 0.34%.

However, in the same place on Earth, the angle between the direction vectors is small, so the discrepancy between the force of attraction and the force of gravity is insignificant, and it can be neglected in calculations. That is, we can assume that the modules of these forces are the same - the acceleration of gravity near the Earth’s surface is the same everywhere and is approximately 9.8 m/s².

Conclusion

Isaac Newton was a scientist who made a scientific revolution, completely rebuilt the principles of dynamics and based on them created scientific picture peace. His discovery influenced the development of science and the creation of material and spiritual culture. It fell to Newton's fate to revise the results of the idea of ​​the world. In the 17th century Scientists have completed the grandiose work of building the foundation of a new science - physics.

To the question “What is force?” physics answers this way: “Force is a measure of the interaction of material bodies with each other or between bodies and other material objects - physical fields" All forces in nature can be classified into four fundamental types of interactions: strong, weak, electromagnetic and gravitational. Our article talks about what gravitational forces are - a measure of the last and, perhaps, most widespread type of these interactions in nature.

Let's start with the gravity of the earth

Everyone alive knows that there is a force that attracts objects to the earth. It is commonly referred to as gravity, gravity, or gravity. Thanks to its presence, a person developed the concepts of “up” and “down”, which determine the direction of movement or the location of something relative to earth's surface. So in a particular case, on the surface of the earth or near it, gravitational forces manifest themselves, which attract objects with mass to each other, manifesting their effect at any distance, both small and very large, even by cosmic standards.

Gravity and Newton's third law

As is known, any force, if it is considered as a measure of the interaction of physical bodies, is always applied to one of them. So in the gravitational interaction of bodies with each other, each of them experiences such types of gravitational forces that are caused by the influence of each of them. If there are only two bodies (it is assumed that the action of all others can be neglected), then each of them, according to Newton’s third law, will attract the other body with the same force. So the Moon and the Earth attract each other, resulting in the ebb and flow of the Earth's seas.

Each planet in the solar system experiences several gravitational forces from the Sun and other planets. Of course, it is the force of gravity of the Sun that determines the shape and size of its orbit, but also the influence of other celestial bodies astronomers take into account their movement trajectories in their calculations.

Which will fall to the ground faster from a height?

The main feature of this force is that all objects fall to the ground at the same speed, regardless of their mass. Once upon a time, right up to the 16th century, it was believed that everything was the other way around - heavier bodies should fall faster than lighter ones. To dispel this misconception, Galileo Galilei had to perform his famous experiment of simultaneously dropping two cannonballs of different weights from the leaning Tower of Pisa. Contrary to the expectations of witnesses to the experiment, both nuclei reached the surface at the same time. Today, every schoolchild knows that this happened due to the fact that gravity imparts to any body the same acceleration of free fall g = 9.81 m/s 2 regardless of the mass m of this body, and its value according to Newton’s second law is equal to F = mg.

Gravitational forces on the Moon and other planets have different meanings this acceleration. However, the nature of the action of gravity on them is the same.

Gravity and body weight

If the first force is applied directly to the body itself, then the second to its support or suspension. In this situation, elastic forces always act on the bodies from the supports and suspensions. Gravitational forces applied to the same bodies act towards them.

Imagine a weight suspended above the ground by a spring. Two forces are applied to it: the elastic force of the stretched spring and the force of gravity. According to Newton's third law, a load acts on a spring with a force equal and opposite to the elastic force. This force will be its weight. A load weighing 1 kg has a weight of P = 1 kg ∙ 9.81 m/s 2 = 9.81 N (newton).

Gravitational forces: definition

The first quantitative theory of gravity, based on observations of planetary motion, was formulated by Isaac Newton in 1687 in his famous “Principles of Natural Philosophy.” He wrote that the gravitational forces that act on the Sun and planets depend on the amount of matter they contain. They spread over long distances and always decrease as the reciprocal of the square of the distance. How can we calculate these gravitational forces? The formula for the force F between two objects with masses m 1 and m 2 located at a distance r is:

• F=Gm 1 m 2 /r 2 ,
  where G is a constant of proportionality, a gravitational constant.

Physical mechanism of gravity

Newton was not completely satisfied with his theory, since it assumed interaction between attracting bodies at a distance. The great Englishman himself was sure that there must be some physical agent responsible for transferring the action of one body to another, which he quite clearly stated in one of his letters. But the time when the concept of a gravitational field that permeates all space was introduced came only four centuries later. Today, speaking about gravity, we can talk about the interaction of any (cosmic) body with the gravitational field of other bodies, the measure of which is the gravitational forces arising between each pair of bodies. The law of universal gravitation, formulated by Newton in the above form, remains true and is confirmed by many facts.

Gravity theory and astronomy

It was very successfully applied to solving problems of celestial mechanics during the 18th and early XIX century. For example, mathematicians D. Adams and W. Le Verrier, analyzing disturbances in the orbit of Uranus, suggested that it is subject to gravitational forces of interaction with an as yet unknown planet. They indicated its expected position, and soon Neptune was discovered there by astronomer I. Galle.

There was still one problem though. Le Verrier in 1845 calculated that the orbit of Mercury precesses by 35" per century, in contrast to the zero value of this precession obtained from Newton's theory. Subsequent measurements gave a more accurate value of 43". (The observed precession is actually 570"/century, but a careful calculation to subtract the influence from all other planets gives a value of 43".)

It was not until 1915 that Albert Einstein was able to explain this discrepancy within the framework of his theory of gravity. It turned out that the massive Sun, like any other massive body, bends space-time in its vicinity. These effects cause deviations in the orbits of planets, but on Mercury, as the smallest planet and closest to our star, they are most pronounced.

Inertial and gravitational masses

As noted above, Galileo was the first to observe that objects fall to the ground at the same speed, regardless of their mass. In Newton's formulas the concept of mass comes from two different equations. His second law says that a force F applied to a body with mass m gives acceleration according to the equation F = ma.

However, the force of gravity F applied to a body satisfies the formula F = mg, where g depends on the other body interacting with the one in question (the earth usually when we talk about gravity). In both equations m is a coefficient of proportionality, but in the first case it is inertial mass, and in the second it is gravitational mass, and there is no obvious reason that they should be the same for any physical object.

However, all experiments show that this is indeed the case.

Einstein's theory of gravity

He took the fact of equality of inertial and gravitational mass as a starting point for his theory. He managed to construct the equations of the gravitational field, the famous Einstein equations, and with their help calculate correct value for the precession of Mercury's orbit. They also give a measured value for the deflection of light rays that pass near the Sun, and there is no doubt that they give the correct results for macroscopic gravity. Einstein's theory of gravity, or general theory of relativity (GR) as he called it, is one of the greatest triumphs of modern science.

Are gravitational forces acceleration?

If you cannot distinguish inertial mass from gravitational mass, then you cannot distinguish gravity from acceleration. The gravitational field experiment can instead be performed in an accelerating elevator in the absence of gravity. When an astronaut in a rocket accelerates away from the earth, he experiences a force of gravity that is several times greater than Earth's, with the vast majority of it coming from acceleration.

If no one can distinguish gravity from acceleration, then the former can always be reproduced by acceleration. A system in which acceleration replaces gravity is called inertial. Therefore, the Moon in near-Earth orbit can also be considered as an inertial system. However, this system will differ from point to point as the gravitational field changes. (In the example of the Moon, the gravitational field changes direction from one point to another.) The principle that one can always find an inertial system at any point in space and time at which physics obeys the laws in the absence of gravity is called the equivalence principle.

Gravity as a manifestation of the geometric properties of space-time

The fact that gravitational forces can be thought of as accelerations in inertial coordinate systems that differ from point to point means that gravity is a geometric concept.

We say that spacetime is curved. Consider a ball on a flat surface. It will rest or, if there is no friction, move uniformly in the absence of any forces acting on it. If the surface is curved, the ball will accelerate and move to the lowest point, taking the shortest path. Similarly, Einstein's theory states that four-dimensional space-time is curved, and a body moves in this curved space along a geodesic line that corresponds to the shortest path. Therefore, the gravitational field and the gravitational forces acting in it on physical bodies are geometric quantities that depend on the properties of space-time, which change most strongly near massive bodies.

The most important phenomenon constantly studied by physicists is movement. Electromagnetic phenomena, laws of mechanics, thermodynamic and quantum processes - all this is a wide range of fragments of the universe studied by physics. And all these processes come down, one way or another, to one thing - to.

In contact with

Everything in the Universe moves. Gravity is a common phenomenon for all people since childhood, we were born in the gravitational field of our planet, this physical phenomenon is perceived by us at the deepest intuitive level and, it would seem, does not even require study.

But, alas, the question is why and how do all bodies attract each other, remains to this day not fully disclosed, although it has been studied far and wide.

In this article we will look at what universal attraction is according to Newton - the classical theory of gravity. However, before moving on to formulas and examples, we will talk about the essence of the problem of attraction and give it a definition.

Perhaps the study of gravity became the beginning of natural philosophy (the science of understanding the essence of things), perhaps natural philosophy gave rise to the question of the essence of gravity, but, one way or another, the question of the gravitation of bodies became interested in ancient Greece.

Movement was understood as the essence of the sensory characteristic of the body, or rather, the body moved while the observer saw it. If we cannot measure, weigh, or feel a phenomenon, does this mean that this phenomenon does not exist? Naturally, it doesn't mean that. And since Aristotle understood this, reflections began on the essence of gravity.

As it turns out today, after many tens of centuries, gravity is the basis not only of gravity and the attraction of our planet to, but also the basis for the origin of the Universe and almost all existing elementary particles.

Movement task

Let's conduct a thought experiment. Let's take a small ball in our left hand. Let's take the same one on the right. Let's release the right ball and it will begin to fall down. The left one remains in the hand, it is still motionless.

Let's mentally stop the passage of time. The falling right ball “hangs” in the air, the left one still remains in the hand. The right ball is endowed with the “energy” of movement, the left one is not. But what is the deep, meaningful difference between them?

Where, in what part of the falling ball is it written that it should move? It has the same mass, the same volume. It has the same atoms, and they are no different from the atoms of a ball at rest. Ball has? Yes, this is the correct answer, but how does the ball know that it has potential energy, where is this recorded in it?

This is precisely the task that Aristotle, Newton and Albert Einstein set themselves. And all three brilliant thinkers partly solved this problem for themselves, but today there are a number of issues that require resolution.

Newton's gravity

In 1666, the greatest English physicist and mechanic I. Newton discovered a law that can quantitatively calculate the force due to which all matter in the Universe tends to each other. This phenomenon is called universal gravity. When you are asked: “Formulate the law of universal gravitation,” your answer should sound like this:

The force of gravitational interaction, which contributes to the attraction of two bodies, is located in direct proportion to the masses of these bodies and in inverse proportion to the distance between them.

Important! Newton's law of attraction uses the term "distance". This term should be understood not as the distance between the surfaces of bodies, but as the distance between their centers of gravity. For example, if two balls of radii r1 and r2 lie on top of each other, then the distance between their surfaces is zero, but there is an attractive force. The thing is that the distance between their centers r1+r2 is different from zero. On a cosmic scale, this clarification is not important, but for a satellite in orbit, this distance is equal to the height above the surface plus the radius of our planet. The distance between the Earth and the Moon is also measured as the distance between their centers, not their surfaces.

For the law of gravity the formula is as follows:

,

• F – force of attraction,
• – masses,
• r – distance,
• G – gravitational constant equal to 6.67·10−11 m³/(kg·s²).

What is weight, if we just looked at the force of gravity?

Force is a vector quantity, but in the law of universal gravitation it is traditionally written as a scalar. In a vector picture, the law will look like this:

.

But this does not mean that the force is inversely proportional to the cube of the distance between the centers. The relation should be perceived as a unit vector directed from one center to another:

.

Law of Gravitational Interaction

Weight and gravity

Having considered the law of gravity, one can understand that it is not surprising that we personally we feel the Sun's gravity much weaker than the Earth's. Massive Sun Although it has a large mass, it is very far from us. is also far from the Sun, but it is attracted to it, since it has a large mass. How to find the gravitational force of two bodies, namely, how to calculate the gravitational force of the Sun, Earth and you and me - we will deal with this issue a little later.

As far as we know, the force of gravity is:

where m is our mass, and g is the acceleration of free fall of the Earth (9.81 m/s 2).

Important! There are not two, three, ten types of attractive forces. Gravity is the only force that gives quantitative characteristics attraction. Weight (P = mg) and gravitational force are the same thing.

If m is our mass, M is the mass of the globe, R is its radius, then the gravitational force acting on us is equal to:

Thus, since F = mg:

.

The masses m are reduced, and the expression for the acceleration of free fall remains:

As we can see, the acceleration of free fall is indeed constant, since its formula includes constant quantities - radius, mass of the Earth and gravitational constant. Substituting the values ​​of these constants, we will make sure that the acceleration of gravity is equal to 9.81 m/s 2.

At different latitudes, the radius of the planet is slightly different, since the Earth is still not a perfect sphere. Because of this, the acceleration of free fall at individual points on the globe is different.

Let's return to the attraction of the Earth and the Sun. Let's try to prove with an example that the globe attracts you and me more strongly than the Sun.

For convenience, let’s take the mass of a person: m = 100 kg. Then:

• The distance between a person and the globe is equal to the radius of the planet: R = 6.4∙10 6 m.
• The mass of the Earth is: M ≈ 6∙10 24 kg.
• The mass of the Sun is: Mc ≈ 2∙10 30 kg.
• Distance between our planet and the Sun (between the Sun and man): r=15∙10 10 m.

Gravitational attraction between man and Earth:

This result is quite obvious from the more simple expression for weight (P = mg).

The force of gravitational attraction between man and the Sun:

As we can see, our planet attracts us almost 2000 times stronger.

How to find the force of attraction between the Earth and the Sun? In the following way:

Now we see that the Sun attracts our planet more than a billion billion times stronger than the planet attracts you and me.

First escape velocity

After Isaac Newton discovered the law of universal gravitation, he became interested in how fast a body needs to be thrown so that it, having overcome the gravitational field, leaves the globe forever.

True, he imagined it a little differently, in his understanding it was not a vertically standing rocket aimed at the sky, but a body that horizontally made a jump from the top of a mountain. This was a logical illustration because At the top of the mountain the force of gravity is slightly less.

So, at the top of Everest, the acceleration of free fall will not be the usual 9.8 m/s 2 , but almost m/s 2 . It is for this reason that the air there is so thin, the air particles are no longer as tied to gravity as those that “fell” to the surface.

Let's try to find out what escape velocity is.

The first escape velocity v1 is the speed at which the body leaves the surface of the Earth (or another planet) and enters a circular orbit.

Let's try to find out the numerical value of this value for our planet.

Let's write down Newton's second law for a body that rotates around a planet in a circular orbit:

,

where h is the height of the body above the surface, R is the radius of the Earth.

In orbit, a body is subject to centrifugal acceleration, thus:

.

The masses are reduced, we get:

,

This speed is called the first escape velocity:

As you can see, escape velocity is absolutely independent of body mass. Thus, any object accelerated to a speed of 7.9 km/s will leave our planet and enter its orbit.

First escape velocity

Second escape velocity

However, even having accelerated the body to the first escape velocity, we will not be able to completely break its gravitational connection with the Earth. This is why we need a second escape velocity. When this speed is reached the body leaves the planet's gravitational field and all possible closed orbits.

Important! It is often mistakenly believed that in order to get to the Moon, astronauts had to reach the second escape velocity, because they first had to “disconnect” from the gravitational field of the planet. This is not so: the Earth-Moon pair are in the Earth’s gravitational field. Their common center of gravity is inside the globe.

In order to find this speed, let's pose the problem a little differently. Let's say a body flies from infinity to a planet. Question: what speed will be reached on the surface upon landing (without taking into account the atmosphere, of course)? It is this speed that the body will need to leave the planet.

The law of universal gravitation. Physics 9th grade

Law of Universal Gravitation.

Conclusion

We learned that although gravity is the main force in the Universe, many of the reasons for this phenomenon still remain a mystery. We learned what Newton's force of universal gravitation is, learned to calculate it for various bodies, and also studied some useful consequences that follow from such a phenomenon as universal law gravity.