The force of gravity between two bodies is formula. What is gravity for dummies: definition and theory in simple words. How accurate are the calculations?

03.07.2023

It's no secret that the law of universal gravitation was discovered by the great English scientist Isaac Newton, according to legend, walking in the evening garden and thinking about the problems of physics. At that moment, an apple fell from the tree (according to one version, directly on the physicist’s head, according to another, it simply fell), which later became Newton’s famous apple, as it led the scientist to an insight, a eureka. The apple that fell on Newton’s head inspired him to discover the law of universal gravitation, because the Moon in the night sky remained motionless, but the apple fell, perhaps the scientist thought that some force was acting on the Moon (causing it to rotate in orbit), so on the apple, causing it to fall to the ground.

Now, according to some historians of science, this whole story about the apple is just a beautiful fiction. In fact, whether the apple fell or not is not so important; what is important is that the scientist actually discovered and formulated the law of universal gravitation, which is now one of the cornerstones of both physics and astronomy.

Of course, long before Newton, people observed both things falling to the ground and stars in the sky, but before him they believed that there were two types of gravity: terrestrial (acting exclusively within the Earth, causing bodies to fall) and celestial (acting on stars and moon). Newton was the first to combine these two types of gravity in his head, the first to understand that there is only one gravity and its action can be described by a universal physical law.

Definition of the law of universal gravitation

According to this law, all material bodies attract each other, and the force of attraction does not depend on physical or chemical properties tel. It depends, if everything is simplified as much as possible, only on the weight of the bodies and the distance between them. You also need to additionally take into account the fact that all bodies on Earth are affected by the gravitational force of our planet itself, which is called gravity (from Latin the word “gravitas” is translated as heaviness).

Let us now try to formulate and write down the law of universal gravitation as briefly as possible: the force of attraction between two bodies with masses m1 and m2 and separated by a distance R is directly proportional to both masses and inversely proportional to the square of the distance between them.

Formula for the law of universal gravitation

Below we present to your attention the formula of the law of universal gravitation.

G in this formula is the gravitational constant, equal to 6.67408(31) 10 −11, this is the magnitude of the impact of the gravitational force of our planet on any material object.

The law of universal gravitation and weightlessness of bodies

The law of universal gravitation discovered by Newton, as well as the accompanying mathematical apparatus, later formed the basis of celestial mechanics and astronomy, because with its help it is possible to explain the nature of the movement of celestial bodies, as well as the phenomenon of weightlessness. Being in outer space at a considerable distance from the force of attraction-gravity of such big body like a planet, any material object (for example, a spaceship with astronauts on board) will be in a state of weightlessness, since the force of the gravitational influence of the Earth (G in the formula for the law of gravity) or some other planet will no longer influence it.

Law of universal gravitation, video

And in conclusion, an instructive video about the discovery of the law of universal gravitation.

Gravitational force is the foundation on which the Universe rests. Thanks to gravity, the Sun does not explode, the atmosphere does not escape into space, people and animals move freely on the surface, and plants bear fruit.

Celestial mechanics and theory of relativity

The law of universal gravitation is studied in grades 8-9 high school. Diligent students know about the famous apple that fell on the head of the great Isaac Newton and about the discoveries that followed. In fact, giving a clear definition of gravity is much more difficult. Modern scientists continue discussions on how bodies interact in outer space and whether antigravity exists. It is extremely difficult to study this phenomenon in earthly laboratories, so there are several basic theories gravity:

Newtonian gravity

In 1687, Newton laid the foundations of celestial mechanics, which studies the motion of bodies in empty space. He calculated the force of gravity of the Moon on the Earth. According to the formula, this force directly depends on their mass and the distance between objects.

F = (G m1 m2)/r2
Gravitational constant G=6.67*10-11

The equation is not entirely relevant when analyzing a strong gravitational field or the attraction of more than two objects.

Einstein's theory of gravity

In the course of various experiments, scientists came to the conclusion that there are some errors in Newton's formula. The basis of celestial mechanics is a long-range force that operates instantly regardless of distance, which does not correspond to the theory of relativity.

According to A. Einstein’s theory developed at the beginning of the 20th century, information does not travel faster than the speed of light in a vacuum, therefore gravitational effects arise as a result of the deformation of space-time. The greater the mass of the object, the greater the curvature into which lighter objects roll.

Quantum gravity

A very controversial and not fully formed theory that explains the interaction of bodies as the exchange of special particles - gravitons.

At the beginning of the 21st century, scientists managed to conduct several significant experiments, including using the Hadron Collider, and develop the theory of loop quantum gravity and string theory.

Universe without gravity

Science fiction novels often describe various gravitational distortions, anti-gravity chambers and spaceships with an artificial gravitational field. Readers sometimes don’t even think about how unrealistic the plots of books are and what will happen if gravity decreases/increases or completely disappears.

Man is adapted to Earth's gravity, so in other conditions he will have to change radically. Weightlessness leads to muscle atrophy, a reduction in the number of red blood cells and a disruption in the functioning of all vital systems of the body, and with an increase in the gravitational field, people simply will not be able to move.
Air and water, plants and animals, houses and cars will fly away into open space. Even if people manage to stay, they will quickly die without oxygen and food. Low gravity on the Moon is the main reason for the absence of an atmosphere and, accordingly, life.
Our planet will fall apart as the pressure in the very center of the Earth disappears, all existing volcanoes will erupt and tectonic plates will diverge.
Stars will explode due to intense pressure and chaotic collisions of particles in the core.
The universe will become a formless stew of atoms and molecules that are unable to combine to create anything greater.

Fortunately for humanity, the shutdown of gravity and the terrible events that follow will never happen. The dark scenario simply demonstrates how important gravity is. She is much weaker than electromagnetism, strong or weak interactions, but in fact without it our world will cease to exist.

Gravity is a seemingly simple concept, known to every person since school. We all remember the story of how an apple fell on Newton's head and he discovered the law of universal gravitation. However, everything is not as simple as it seems. In that article we will try to give a clear and comprehensive answer to the question: what is gravity? We will also consider the main myths and misconceptions about this interesting phenomenon.

Speaking in simple words, gravity is the attraction between any two objects in the universe. Gravity can be determined by knowing the mass of bodies and the distance from one to another. The stronger the gravitational field, the greater the weight of the body and the higher its acceleration. For example, on the Moon the weight of an astronaut will be six times less than on Earth. The strength of the gravitational field depends on the size of the object it surrounds. Thus, the lunar gravity is six times lower than the earth’s. This was first scientifically substantiated and proven using mathematical calculations back in the 17th century by Isaac Newton.

What fell on Newton's head?

Despite the fact that the great English scientist himself partially confirmed the well-known legend about the apple and the head injury, nevertheless, now we can say with confidence that during the discovery of the law of universal gravitation there were no injuries or insights. The foundation that laid the foundation for a new era in the natural sciences was the work “ Mathematical principles natural philosophy." In it, Newton describes the law of gravity and important laws of mechanics that he discovered over many years of hard work. The famous physicist was a leisurely and judicious person, as befits a brilliant scientist. And therefore, from the beginning of thinking about the nature of gravity to the publication scientific work More than 20 years have passed about her. However, the legend about the fallen fruit could have some real basis, but the physicist’s head definitely remained intact.

The laws of attraction were studied before Isaac Newton by a variety of scientific figures. But only he was the first to mathematically prove the direct relationship between gravity and the movement of planets. That is, an apple falling from a branch and the rotation of the moon around the earth are controlled by the same force - gravity. And it acts on any two bodies in the universe. These discoveries laid the foundation for the so-called celestial mechanics, as well as the science of dynamics. The Newtonian model dominated science for more than two centuries until the advent of the theory of relativity and quantum mechanics.

What do modern scientists think about gravity?

Gravity is the weakest of the four known on this moment fundamental interactions to which all particles and bodies composed of them are subject. Besides gravitational interaction This also includes electromagnetic, strong and weak. They are studied on the basis of different theories, for example, in the approximate speeds of small gravity, Newton’s theory of gravity is used. In the general case, Einstein's general theory of relativity is used. In addition, the description of gravity in the quantum limit will have to be carried out using a quantum theory that has not yet appeared.

Of course, today physics is complex and goes far beyond ideas about the world around us ordinary person. But it is necessary to be interested in it at least at the level of basic concepts, because it is quite possible that in the near future we may witness amazing discoveries in this area that will radically change the life of mankind. It will be awkward if you don't understand what's going on at all.

Myths about gravity

Not only ignorance, but also constant new discoveries in this scientific field give rise to various absurdities and myths about gravity. So, a few common misconceptions about this unique phenomenon:

Artificial satellites will never leave the Earth's orbit and will forever revolve around it. It is not true. The fact is that in addition to gravity in space, there are various other factors that influence the orbit of bodies. This includes the braking of the atmosphere for low orbits and the gravitational fields of the Moon and other planets. Most likely, if a satellite is allowed to spin uncontrolled for a long time, its orbit will change, and eventually it will either fly off into space or fall onto the surface of a nearby body.
There is no gravity in space. Even at stations where astronauts are in weightlessness there is quite strong gravity, slightly less than on Earth. Why then don't they fall? We can say that the station employees seem to be in a state of constant falling, but they will not fall.
An object approaching black hole, will be torn apart. Quite a well-known myth. The gravitational force of a black hole will indeed increase as you approach it, but it is not at all necessary that the tidal forces will be so powerful. Most likely they have a finite value at the event horizon, since the distance is calculated from the center of the hole.

In nature, only four main fundamental forces are known (they are also called main interactions) - gravitational interaction, electromagnetic interaction, strong interaction and weak interaction.

Gravitational interaction is the weakest of all.Gravitational forcesconnect parts of the globe together and this same interaction determines large-scale events in the Universe.

Electromagnetic interaction holds electrons in atoms and bonds atoms into molecules. A particular manifestation of these forces isCoulomb forces, acting between stationary electric charges.

Strong interaction binds nucleons in nuclei. This interaction is the strongest, but it only acts over very short distances.

Weak interaction acts between elementary particles and has a very short range. It occurs during beta decay.

4.1.Newton's law of universal gravitation

Between two material points there is a force of mutual attraction, directly proportional to the product of the masses of these points ( m And M ) and inversely proportional to the square of the distance between them ( r 2 ) and directed along a straight line passing through the interacting bodiesF= (GmM/r 2) r o ,(1)

Here r o - unit vector drawn in the direction of the force F(Fig. 1a).

This force is called gravitational force(or force of universal gravity). Gravitational forces are always attractive forces. The force of interaction between two bodies does not depend on the environment in which the bodies are located.

g 1 g 2

Fig.1a Fig.1b Fig.1c

The constant G is called gravitational constant. Its value was established experimentally: G = 6.6720. 10 -11 N. m 2 / kg 2 - i.e. two point bodies weighing 1 kg each, located at a distance of 1 m from each other, are attracted with a force of 6.6720. 10 -11 N. The very small value of G just allows us to talk about the weakness of gravitational forces - they should be taken into account only in the case of large masses.

The masses included in equation (1) are called gravitational masses. This emphasizes that, in principle, the masses included in Newton’s second law ( F=m in a) and the law of universal gravitation ( F=(Gm gr M gr /r 2) r o), have a different nature. However, it has been established that the ratio m gr / m in for all bodies is the same with a relative error of up to 10 -10.

4.2.Gravitational field (gravitational field) of a material point

It is believed that gravitational interaction is carried out using gravitational field (gravitational field), which is generated by the bodies themselves. Two characteristics of this field are introduced: vector - and scalar - gravitational field potential.

4.2.1.Gravitational field strength

Let us have a material point with mass M. It is believed that a gravitational field arises around this mass. The strength characteristic of such a field is gravitational field strengthg, which is determined from the law of universal gravitation g= (GM/r 2) r o ,(2)

Where r o - a unit vector drawn from a material point in the direction of the gravitational force. Gravitational field strength gis a vector quantity and is the acceleration obtained by the point mass m, brought into the gravitational field created by a point mass M. Indeed, comparing (1) and (2), we obtain for the case of equality of gravitational and inertial masses F=m g.

Let us emphasize that the magnitude and direction of acceleration received by a body introduced into a gravitational field does not depend on the magnitude of the mass of the introduced body. Since the main task of dynamics is to determine the magnitude of the acceleration received by a body under the action of external forces, then, consequently, the strength of the gravitational field completely and unambiguously determines the force characteristics of the gravitational field. The g(r) dependence is shown in Fig. 2a.

Fig.2a Fig.2b Fig.2c

The field is called central, if at all points of the field the intensity vectors are directed along straight lines that intersect at one point, stationary with respect to any inertial reference system. In particular, the gravitational field of a material point is central: at all points of the field the vectors gAnd F=m g, acting on a body brought into the gravitational field are directed radially from the mass M , creating a field, to a point mass m (Fig. 1b).

The law of universal gravitation in the form (1) is established for bodies taken as material points, i.e. for such bodies whose dimensions are small compared to the distance between them. If the sizes of the bodies cannot be neglected, then the bodies should be divided into point elements, the forces of attraction between all elements taken in pairs should be calculated using formula (1), and then added geometrically. The gravitational field strength of a system consisting of material points with masses M 1, M 2, ..., M n is equal to the sum of the field strengths from each of these masses separately ( principle of superposition of gravitational fields ): g=g i, Where g i= (GM i /r i 2) r o i - field strength of one mass M i.

Graphic representation of the gravitational field using tension vectors g at different points of the field is very inconvenient: for systems consisting of many material points, the intensity vectors overlap each other and a very confusing picture is obtained. That's why for graphical representation of the gravitational field use lines of force (tension lines), which are carried out in such a way that the voltage vector is directed tangentially to the power line. Tension lines are considered to be directed in the same way as a vector g(Fig. 1c), those. lines of force end at a material point. Since at each point in space the tension vector has only one direction, That lines of tension never cross. For a material point, the lines of force are radial straight lines entering the point (Fig. 1b).

In order to use intensity lines to characterize not only the direction, but also the value of the field strength, these lines are drawn with a certain density: the number of intensity lines piercing a unit surface area perpendicular to the intensity lines must be equal to the absolute value of the vector g.

Every person in his life has come across this concept more than once, because gravity is the basis not only modern physics, but also a number of other related sciences.

Many scientists have been studying the attraction of bodies since ancient times, but the main discovery is attributed to Newton and is described as the well-known story of a fruit falling on one’s head.

What is gravity in simple words

Gravity is the attraction between several objects throughout the universe. The nature of the phenomenon varies, as it is determined by the mass of each of them and the extent between them, that is, the distance.

Newton's theory was based on the fact that both the falling fruit and the satellite of our planet are affected by the same force - gravity towards the Earth. But the satellite did not fall into earthly space precisely because of its mass and distance.

Gravity field

The gravitational field is the space within which the interaction of bodies occurs according to the laws of attraction.

Einstein's theory of relativity describes the field as a certain property of time and space, characteristically manifested when physical objects appear.

Gravity wave

These are certain types of field changes that are formed as a result of radiation from moving objects. They come off the object and spread in a wave effect.

Theories of gravity

The classical theory is Newtonian. However, it was imperfect and subsequently alternative options appeared.

These include:

metric theories;
non-metric;
vector;
Le Sage, who first described the phases;
quantum gravity.

Today there are several dozen different theories, all of them either complement each other or look at phenomena from a different perspective.

It is worth noting: There is no ideal solution yet, but ongoing developments are opening up more possible answers regarding the attraction of bodies.

The force of gravitational attraction

The basic calculation is as follows - the gravitational force is proportional to the multiplication of the mass of the body by another, between which it is determined. This formula is expressed this way: force is inversely proportional to the distance between objects squared.

The gravitational field is potential, which means it is conserved kinetic energy. This fact simplifies the solution of problems in which the force of attraction is measured.

Gravity in space

Despite the misconception of many, there is gravity in space. It is lower than on Earth, but still present.

As for the astronauts, who at first glance seem to be flying, they are actually in a state of slow decline. Visually, it seems that nothing attracts them, but in practice they experience gravity.

The strength of attraction depends on the distance, but no matter how large the distance between objects is, they will continue to be attracted to each other.

Mutual attraction will never be zero.

Gravity in the Solar System IN It's not just the Earth that has gravity. Planets, as well as the Sun, attract objects to themselves.

Since the force is determined by the mass of the object, then highest rate at the Sun. For example, if our planet has an indicator of one, then the luminary’s indicator will be almost twenty-eight.

Next in gravity after the Sun is Jupiter, so its gravitational force is three times higher than that of the Earth. Pluto has the smallest parameter.

For clarity, let’s denote this: in theory, on the Sun, the average person would weigh about two tons, but on the smallest planet of our system - only four kilograms.

What does the planet's gravity depend on?

Gravitational pull, as mentioned above, is the power with which the planet pulls toward itself objects located on its surface.

The force of gravity depends on the gravity of the object, the planet itself and the distance between them. If there are many kilometers, gravity is low, but it still keeps objects connected.

Several important and fascinating aspects related to gravity and its properties that are worth explaining to your child:

The phenomenon attracts everything, but never repels - this distinguishes it from other physical phenomena.
There is no such thing as zero. It is impossible to simulate a situation in which pressure does not apply, that is, gravity does not work.
The earth is falling from average speed 11.2 kilometers per second, having reached this speed you can leave the attracting well of the planet.
The existence of gravitational waves has not been scientifically proven, it is just a guess. If they ever become visible, then many mysteries of the cosmos related to the interaction of bodies will be revealed to humanity.

According to the theory of basic relativity of a scientist like Einstein, gravity is a curvature of the basic parameters of the existence of the material world, which represents the basis of the Universe.

Gravity is the mutual attraction of two objects. The strength of interaction depends on the gravity of the bodies and the distance between them. Not all the secrets of the phenomenon have been revealed yet, but today there are several dozen theories describing the concept and its properties.

The complexity of the objects being studied affects the research time. In most cases, the relationship between mass and distance is simply taken.