Sir Isaac Newton, having been hit on the head with an apple, deduced the law of universal gravitation, which reads:
Any two bodies are attracted to each other with a force directly proportional to the product of the masses of the body and inversely proportional to the square of the distance between them:
F = (Gm 1 m 2)/R 2 , where
m1, m2- masses of bodies
R- distance between the centers of bodies
G \u003d 6.67 10 -11 Nm 2 / kg- constant
Let us determine the acceleration of free fall on the surface of the Earth:
F g = m body g = (Gm body m Earth)/R 2
R (radius of the Earth) = 6.38 10 6 m
m Earth = 5.97 10 24 kg
m body g = (Gm body m Earth)/R 2 or g \u003d (Gm Earth) / R 2
Note that the acceleration due to gravity does not depend on the mass of the body!
g \u003d 6.67 10 -11 5.97 10 24 / (6.38 10 6) \u003d 398.2 / 40.7 \u003d 9.8 m / s 2
We said earlier that the force of gravity (gravitational attraction) is called weighing.
On the surface of the Earth, weight and mass of a body have the same meaning. But as you move away from the Earth, the weight of the body will decrease (since the distance between the center of the Earth and the body will increase), and the mass will remain constant (since mass is an expression of the inertia of the body). Mass is measured in kilograms, weight - in newtons.
Thanks to the force of gravity, celestial bodies rotate relative to each other: the Moon around the Earth; Earth around the Sun; The Sun around the center of our Galaxy, etc. While the bodies are held centrifugal force provided by the force of gravity.
The same applies to artificial bodies (satellites) revolving around the Earth. The circle along which the satellite revolves is called the orbit of rotation.
In this case, the centrifugal force acts on the satellite:
F c \u003d (m satellite V 2) / R
Gravity force:
F g \u003d (Gm satellite m of the Earth) / R 2
F c \u003d F g \u003d (m satellite V 2) / R \u003d (Gm satellite m Earth) / R 2
V2 = (Gm Earth)/R; V = √(Gm Earth)/R
Using this formula, you can calculate the speed of any body rotating in an orbit with a radius R around the Earth.
The natural satellite of the Earth is the Moon. Let us determine its linear velocity in orbit:
Mass of the Earth = 5.97 10 24 kg
R is the distance between the center of the earth and the center of the moon. To determine this distance, we need to add three quantities: the radius of the Earth; the radius of the moon; distance from the earth to the moon.
R moon = 1738 km = 1.74 10 6 m
R earth \u003d 6371 km \u003d 6.37 10 6 m
R zl \u003d 384400 km \u003d 384.4 10 6 m
The total distance between the centers of the planets: R = 392.5 10 6 m
Linear speed of the moon:
V \u003d √ (Gm of the Earth) / R \u003d √6.67 10 -11 5.98 10 24 / 392.5 10 6 \u003d 1000 m / s \u003d 3600 km / h
The moon moves in a circular orbit around the earth with a linear velocity of 3600 km/h!
Let us now determine the period of revolution of the Moon around the Earth. During the period of revolution, the Moon overcomes a distance equal to the length of the orbit - 2πR. Orbital speed of the moon: V = 2πR/T; on the other side: V = √(Gm Earth)/R:
2πR/T = √(Gm Earth)/R hence T = 2π√R 3 /Gm Earth
T \u003d 6.28 √ (60.7 10 24) / 6.67 10 -11 5.98 10 24 \u003d 3.9 10 5 s
The period of revolution of the Moon around the Earth is 2,449,200 seconds, or 40,820 minutes, or 680 hours, or 28.3 days.
1. Vertical rotation
Earlier in circuses there was a very popular trick in which a cyclist (motorcyclist) made a full turn inside a circle located vertically.
What is the minimum speed the trickster must have in order not to fall down at the top point?
To pass the top point without falling, the body must have a speed that creates such a centrifugal force that would compensate for the force of gravity.
Centrifugal force: F c \u003d mV 2 / R
Gravity: F g = mg
F c \u003d F g; mV 2 /R = mg; V = √Rg
And again, note that there is no body mass in the calculations! It should be noted that this is the speed that the body should have at the top!
Let's say that a circle with a radius of 10 meters is set in the circus arena. Let's calculate the safe speed for the trick:
V = √Rg = √10 9.8 = 10 m/s = 36 km/h
Based on the interpretation of Newton's second law, we can conclude that the change in motion occurs through force. Mechanics considers forces of various physical nature. Many of them are determined by the action of gravitational forces.
In 1862, the law of universal gravitation was discovered by I. Newton. He suggested that the forces holding the moon were of the same nature as the forces that made the apple fall to the earth. The meaning of the hypothesis is the presence of the action of attractive forces directed along the line and connecting the centers of mass, as shown in Figure 1. ten . one . A spherical body has a center of mass coinciding with the center of the ball.
Picture 1 . 10 . 1 . Gravitational forces of attraction between bodies. F 1 → = - F 2 →.
Definition 1
At famous destinations movements of the planets Newton tried to find out what forces act on them. This process has been named inverse problem of mechanics.
The main task of mechanics is to determine the coordinates of a body of known mass with its speed at any time using known forces acting on the body and a given condition (direct problem). The reverse is performed with the determination of the acting forces on the body with its known direction. Such tasks led the scientist to the discovery of the definition of the law of universal gravitation.
Definition 2All bodies are attracted to each other with a force that is directly proportional to their masses and inversely proportional to the square of the distance between them.
F = G m 1 m 2 r 2 .
The value of G determines the coefficient of proportionality of all bodies in nature, called the gravitational constant and denoted by the formula G \u003d 6, 67 10 - 11 N m 2 / k g 2 (C I) .
Most phenomena in nature are explained by the presence of the force of universal gravitation. The movement of planets, artificial satellites of the Earth, the flight paths of ballistic missiles, the movement of bodies near the surface of the Earth - everything is explained by the law of gravity and dynamics.
Definition 3
The manifestation of the force of gravity is characterized by the presence gravity. This is the name of the force of attraction of bodies to the Earth and near its surface.
When M is denoted as the mass of the Earth, R З is the radius, m is the mass of the body, then the gravity formula takes the form:
F = G M R Z 2 m = m g .
Where g is the free fall acceleration equal to g = G M R З 2 .
Gravity is directed towards the center of the Earth, as shown in the Moon-Earth example. In the absence of the action of other forces, the body moves with the acceleration of free fall. Its average value is 9.81 m / s 2. With known G and radius R 3 \u003d 6, 38 10 6 m, the mass of the Earth M is calculated using the formula:
M \u003d g R 3 2 G \u003d 5.98 10 24 k
If the body moves away from the surface of the Earth, then the action of the force of gravity and the acceleration of free fall change inversely with the square of the distance r to the center. Picture 1 . ten . 2 shows how the gravitational force acting on the astronaut of the ship changes with distance from the Earth. It is obvious that F of its attraction to the Earth is 700 N.
Picture 1 . 10 . 2 . Change in the gravitational force acting on the astronaut when moving away from the Earth.
Example 1
The Earth-Moon is suitable as an example of the interaction of a two-body system.
The distance to the Moon is r L = 3, 84 10 6 m. It is 60 times greater than the radius of the Earth R З. Hence, in the presence of gravity, the free fall acceleration α L of the Moon's orbit will be α L = g R З r L 2 = 9.81 m/s 2 60 2 = 0.0027 m/s 2.
It is directed towards the center of the Earth and is called centripetal. The calculation is made according to the formula a L \u003d υ 2 r L \u003d 4 π 2 r L T 2 \u003d 0, 0027 m / s 2, where T \u003d 27, 3 days is the period of the Moon's revolution around the Earth. The results and calculations made in different ways show that Newton was right in his assumption of the same nature of the force that keeps the Moon in orbit and the force of gravity.
The moon has its own gravitational field, which determines the free fall acceleration g L on the surface. The mass of the Moon is 81 times less than the mass of the Earth, and the radius is 3.7 times. This shows that the acceleration g L should be determined from the expression:
g L \u003d G M L R L 2 \u003d G M W 3, 7 2 T 3 2 \u003d 0, 17 g \u003d 1, 66 m / s 2.
Such weak gravity characteristic of astronauts on the moon. Therefore, you can make huge jumps and steps. A jump up a meter on Earth corresponds to a jump of seven meters on the Moon.
The movement of artificial satellites is fixed outside the Earth's atmosphere, so they are affected by the Earth's gravitational forces. The trajectory of a space body can change depending on the initial speed. Motion artificial satellite on earth orbit is approximately taken as the distance to the center of the Earth, equal to the radius R З. They fly at altitudes of 200 - 300 km.
Definition 4
It follows that the centripetal acceleration of the satellite, which is reported by the forces of gravity, is equal to the free fall acceleration g. The speed of the satellite will take the designation υ 1 . They call her first cosmic speed.
Applying the kinematic formula for centripetal acceleration, we obtain
a n \u003d υ 1 2 R З \u003d g, υ 1 \u003d g R З \u003d 7, 91 10 3 m / s.
At this speed, the satellite was able to fly around the Earth in a time equal to T 1 = 2 πR W υ 1 = 84 m and n 12 s.
But the period of revolution of the satellite in a circular orbit near the Earth is much longer than indicated above, since there is a difference between the radius of the real orbit and the radius of the Earth.
The satellite moves according to the principle of free fall, vaguely similar to the trajectory of a projectile or ballistic missile. The difference lies in the high speed of the satellite, and the radius of curvature of its trajectory reaches the length of the radius of the Earth.
Satellites that move in circular trajectories over long distances have a weakened terrestrial gravity that is inversely proportional to the square of the radius r of the trajectory. Then finding the speed of the satellite follows the condition:
υ 2 k \u003d g R 3 2 r 2, υ \u003d g R 3 R Z r \u003d u 1 R 3 r.
Therefore, the presence of satellites in high orbits indicates a lower speed of their movement than from near-Earth orbit. The formula for the period of revolution is:
T \u003d 2 πr υ \u003d 2 πr υ 1 r R Z \u003d 2 πR Z υ 1 r R 3 3 / 2 \u003d T 1 2 π R Z.
T 1 takes the value of the period of revolution of the satellite in near-Earth orbit. T increases with the size of the orbit radius. If r is 6 , 6 R 3 then the T of the satellite is 24 hours. When it is launched in the plane of the equator, it will be observed how it hangs over a certain point on the earth's surface. The use of such satellites is known in the space radio communication system. An orbit with a radius r = 6 , 6 R З is called geostationary.
Picture 1 . 10 . 3 . Satellite movement model.
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The most important phenomenon constantly studied by physicists is motion. Electromagnetic Phenomena, the 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 familiar 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 up and down.
In this article, we will consider what Newton's universal attraction is - the classical theory of gravity. However, before moving on to formulas and examples, let's talk about the essence of the problem of attraction and give it a definition.
Perhaps the study of gravity was 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 gravity of bodies interested in ancient Greece.
Movement was understood as the essence of the sensual characteristics of the body, or rather, the body moved while the observer sees it. If we cannot measure, weigh, feel a phenomenon, does this mean that this phenomenon does not exist? Naturally, it doesn't. And since Aristotle understood this, reflections on the essence of gravity began.
As it turned out today, after many tens of centuries, gravity is the basis not only of the earth's attraction and the attraction of our planet to, but also the basis of the origin of the Universe and almost all existing elementary particles.
Movement task
Let's do a thought experiment. Take a small ball in your left hand. Let's take the same one on the right. Let's release the right ball, and it will start 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 must 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 it fixed in it?
This is the task set by Aristotle, Newton and Albert Einstein. And all three brilliant thinkers partly solved this problem for themselves, but today there are a number of issues that need to be resolved.
Newtonian gravity
In 1666, the greatest English physicist and mechanic I. Newton discovered a law capable of quantitatively calculating the force due to which all matter in the universe tends to each other. This phenomenon is called universal gravitation. When 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 in direct proportion to the masses of these bodies and inversely proportional 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 with 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 point is that the distance between their centers r1+r2 is nonzero. On a cosmic scale, this refinement 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 is the force of attraction,
- - masses,
- r - distance,
- G is the gravitational constant, equal to 6.67 10−11 m³ / (kg s²).
What is weight, if we have just considered the force of attraction?
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 ratio should be understood 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 there is nothing surprising in the fact that we personally we feel the attraction of the sun is much weaker than the earth's. The massive Sun, although it has a large mass, is very far from us. also far from the Sun, but it is attracted to it, as it has a large mass. How to find the force of attraction of two bodies, namely, how to calculate the gravitational force of the Sun, the 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 free fall acceleration of the Earth (9.81 m/s 2).
Important! There are no two, three, ten kinds of forces of attraction. Gravity is the only force that quantifies attraction. Weight (P = mg) and gravitational force are one and the same.
If m is our mass, M is the mass of the globe, R is its radius, then the gravitational force acting on us is:
Thus, since F = mg:
.
The masses m cancel out, leaving the expression for the free fall acceleration:
As you can see, the acceleration of free fall is indeed a constant value, since its formula includes constant values - the radius, the mass of the Earth and the gravitational constant. Substituting the values of these constants, we will make sure that the acceleration of free fall is equal to 9.81 m / s 2.
At different latitudes, the radius of the planet is somewhat different, since the Earth is still not a perfect sphere. Because of this, the acceleration of free fall at different points on the globe is different.
Let's return to the attraction of the Earth and the Sun. Let's try to prove by example that the globe attracts us stronger 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 the Earth:
This result is quite obvious from more simple expression for weight (P = mg).
The force of gravitational attraction between man and the Sun:
As you 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 pulls on our planet more than a billion billion times stronger than the planet pulls you and me.
first cosmic speed
After Isaac Newton discovered the law of universal gravitation, he became interested in how fast a body should be thrown so that it, having overcome the gravitational field, left the globe forever.
True, he imagined it a little differently, in his understanding there was not a vertically standing rocket directed into the sky, but a body that horizontally makes a jump from the top of a mountain. It 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 gravity will not be the usual 9.8 m / s 2, but almost m / s 2. It is for this reason that there is so rarefied, the air particles are no longer as attached to gravity as those that "fell" to the surface.
Let's try to find out what cosmic speed is.
The first cosmic velocity v1 is the velocity 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 quantity for our planet.
Let's write Newton's second law for a body that revolves around the 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, centrifugal acceleration acts on the body, thus:
.
The masses are reduced, we get:
,
This speed is called the first cosmic speed:
As you can see, the space velocity is absolutely independent of the mass of the body. Thus, any object accelerated to a speed of 7.9 km / s will leave our planet and enter its orbit.
first cosmic speed
Second space velocity
However, even having accelerated the body to the first cosmic speed, we will not be able to completely break its gravitational connection with the Earth. For this, the second cosmic velocity is needed. Upon reaching this speed, the body leaves the gravitational field of the planet and all possible closed orbits.
Important! By mistake, it is often believed that in order to get to the moon, astronauts had to reach the second cosmic 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, we set the problem a little differently. Suppose a body flies from infinity to a planet. Question: what speed will be achieved on the surface upon landing (without taking into account the atmosphere, of course)? It is this speed and it will take the body to leave the planet.
The law of universal gravitation. Physics Grade 9
The law of universal gravitation.
Conclusion
We have learned that although gravity is the main force in the universe, many of the reasons for this phenomenon are still a mystery. We learned what Newton's universal gravitational force is, learned how to calculate it for various bodies, and also studied some useful consequences that follow from such a phenomenon as the universal law of gravitation.
Obi-Wan Kenobi said that strength holds the galaxy together. The same can be said about gravity. The fact is that gravity allows us to walk on the Earth, the Earth to revolve around the Sun, and the Sun to revolve around the supermassive black hole at the center of our galaxy. How to understand gravity? About this - in our article.
Let's say right away that you will not find here an unambiguously correct answer to the question "What is gravity." Because it just doesn't exist! Gravity is one of the most mysterious phenomena that scientists puzzle over and still cannot fully explain its nature.
There are many hypotheses and opinions. There are more than a dozen theories of gravity, alternative and classical. We will consider the most interesting, relevant and modern.
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Gravity is a physical fundamental interaction
There are 4 fundamental interactions in physics. Thanks to them, the world is exactly the way it is. Gravity is one of these forces.
Fundamental Interactions:
- gravity;
- electromagnetism;
- strong interaction;
- weak interaction.
At the moment, the current theory describing gravity is GR (general relativity). It was proposed by Albert Einstein in 1915-1916.
However, we know that it is too early to talk about the ultimate truth. After all, several centuries before the advent of general relativity in physics, Newtonian theory, which was significantly expanded, dominated to describe gravity.
Within the framework of the general relativity this moment it is impossible to explain and describe all the issues related to gravity.
Before Newton, it was widely believed that gravity on earth and celestial gravity were different things. It was believed that the planets move according to their own, different from earthly, ideal laws.
Newton discovered the law of universal gravitation in 1667. Of course, this law existed even during the dinosaurs and much earlier.
Ancient philosophers thought about the existence of gravity. Galileo experimentally calculated the acceleration of free fall on Earth, discovering that it is the same for bodies of any mass. Kepler studied the laws of motion of celestial bodies.
Newton was able to formulate and generalize the results of observations. Here's what he got:
Two bodies are attracted to each other with a force called gravitational force or gravitational force.
The formula for the force of attraction between bodies is:
G is the gravitational constant, m is the mass of the bodies, r is the distance between the centers of mass of the bodies.
What is the physical meaning of the gravitational constant? It is equal to the force with which bodies with masses of 1 kilogram each act on each other, being at a distance of 1 meter from each other.
According to Newton's theory, every object creates a gravitational field. The accuracy of Newton's law has been tested at distances of less than one centimeter. Of course, for small masses these forces are insignificant and can be neglected.
Newton's formula is applicable both for calculating the force of attraction of planets to the sun, and for small objects. We simply do not notice the force with which, say, the balls on the billiard table are attracted. Nevertheless, this force exists and can be calculated.
The force of attraction acts between any bodies in the universe. Its effect extends to any distance.
Newton's law of universal gravitation does not explain the nature of the force of attraction, but establishes quantitative patterns. Newton's theory does not contradict general relativity. It is sufficient to solve practical tasks on the scale of the Earth and to calculate the movement of celestial bodies.
Gravity in General Relativity
Despite the fact that Newton's theory is quite applicable in practice, it has a number of shortcomings. The law of universal gravitation is a mathematical description, but does not give an idea of the fundamental physical nature of things.
According to Newton, the force of attraction acts at any distance. And it works instantly. Considering that the fastest speed in the world is the speed of light, there is a discrepancy. How can gravity act instantaneously at any distance, when light needs not an instant, but several seconds or even years to overcome them?
Within the framework of general relativity, gravity is considered not as a force that acts on bodies, but as a curvature of space and time under the influence of mass. Thus, gravity is not a force interaction.
What is the effect of gravity? Let's try to describe it using an analogy.
Imagine space as an elastic sheet. If you put a light tennis ball on it, the surface will remain flat. But if you put a heavy weight next to the ball, it will push a hole in the surface, and the ball will begin to roll towards the large and heavy weight. This is "gravity".
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Discovery of gravitational waves
Gravitational waves were predicted by Albert Einstein back in 1916, but they were only discovered a hundred years later, in 2015.
What are gravitational waves? Let's draw an analogy again. If you throw a stone into calm water, circles will go on the surface of the water from the place of its fall. Gravitational waves are the same ripples, perturbations. Only not on the water, but in the world space-time.
Instead of water - space-time, and instead of stone, say, a black hole. Any accelerated movement of mass generates a gravitational wave. If the bodies are in a state of free fall, the distance between them will change when a gravitational wave passes.
Since gravity is a very weak force, the detection of gravitational waves has been associated with great technical difficulties. Modern technologies made it possible to detect a burst of gravitational waves only from supermassive sources.
A suitable event for registering a gravitational wave is the merger of black holes. Unfortunately or fortunately, this happens quite rarely. Nevertheless, scientists managed to register a wave that literally rolled through the space of the Universe.
To register gravitational waves, a detector with a diameter of 4 kilometers was built. During the passage of the wave, oscillations of mirrors on suspensions in vacuum and the interference of light reflected from them were recorded.
Gravitational waves confirmed the validity of general relativity.
Gravity and elementary particles
In the standard model, each interaction is responsible for certain elementary particles. We can say that particles are carriers of interactions.
The graviton is responsible for gravity - a hypothetical massless particle with energy. By the way, in our separate material, read more about the Higgs boson and other elementary particles that made a lot of noise.
Finally, here are some interesting facts about gravity.
10 facts about gravity
- To overcome the force of gravity of the Earth, the body must have a speed equal to 7.91 km / s. This is the first cosmic speed. It is enough for a body (for example, a space probe) to move in orbit around the planet.
- To break free from the Earth's gravity field, spaceship must have a speed of at least 11.2 km/s. This is the second space velocity.
- Objects with the strongest gravity are black holes. Their gravity is so strong that they even attract light (photons).
- You will not find the force of gravity in any equation of quantum mechanics. The fact is that when you try to include gravity in the equations, they lose their relevance. This is one of the most important problems in modern physics.
- The word gravity comes from the Latin “gravis”, which means “heavy”.
- The more massive the object, the stronger the gravity. If a person who weighs 60 kilograms on Earth weighs on Jupiter, the scales will show 142 kilograms.
- NASA scientists are trying to develop a gravitational beam that will allow objects to be moved contactlessly, overcoming the force of gravity.
- Astronauts in orbit also experience gravity. More specifically, microgravity. They seem to fall endlessly along with the ship in which they are.
- Gravity always attracts and never repels.
- A tennis ball-sized black hole pulls objects with the same force as our planet.
Now you know the definition of gravity and you can say what formula is used to calculate the force of attraction. If the granite of science is holding you down harder than gravity, contact our student service. We will help you learn easily under the heaviest workloads!
Law of gravity
Gravity (universal gravitation, gravitation)(from lat. gravitas - “gravity”) - a long-range fundamental interaction in nature, to which all material bodies are subject. According to modern data, it is a universal interaction in the sense that, unlike any other forces, it gives the same acceleration to all bodies without exception, regardless of their mass. Primarily gravity plays a decisive role on a cosmic scale. Term gravity also used as the name of a branch of physics that studies the gravitational interaction. The most successful modern physical theory in classical physics, describing gravity, is the general theory of relativity, the quantum theory of gravitational interaction has not yet been built.
Gravitational interaction
Gravitational interaction is one of four fundamental interactions in our world. Within classical mechanics, the gravitational interaction is described by law of gravity Newton, who states that the force of gravitational attraction between two material points of mass m 1 and m 2 separated by distance R, is proportional to both masses and inversely proportional to the square of the distance - i.e.
.Here G- gravitational constant, equal to approximately 
m³/(kg s²). The minus sign means that the force acting on the body is always equal in direction to the radius vector directed to the body, that is, the gravitational interaction always leads to the attraction of any bodies.
The law of universal gravitation is one of the applications of the inverse square law, which is also encountered in the study of radiation (see, for example, Light Pressure), and which is a direct consequence of the quadratic increase in the area of the sphere with increasing radius, which leads to a quadratic decrease in the contribution of any unit area to the area of the entire sphere.
The simplest task of celestial mechanics is the gravitational interaction of two bodies in empty space. This problem is solved analytically to the end; the result of its solution is often formulated in the form of Kepler's three laws.
As the number of interacting bodies increases, the problem becomes much more complicated. So, the already famous three-body problem (that is, the motion of three bodies with non-zero masses) cannot be solved analytically in a general form. With a numerical solution, the instability of solutions with respect to the initial conditions sets in rather quickly. When applied to the solar system, this instability makes it impossible to predict the motion of the planets on scales exceeding a hundred million years.
In some special cases, it is possible to find an approximate solution. The most important is the case when the mass of one body is significantly more mass other bodies (examples: solar system and the dynamics of Saturn's rings). In this case, as a first approximation, we can assume that light bodies do not interact with each other and move along Keplerian trajectories around a massive body. Interactions between them can be taken into account in the framework of perturbation theory, and averaged over time. In this case, non-trivial phenomena may arise, such as resonances, attractors, randomness, etc. A good example of such phenomena is the non-trivial structure of Saturn's rings.
Despite attempts to describe the behavior of the system from a large number attracting bodies of approximately the same mass, this cannot be done due to the phenomenon of dynamic chaos.
Strong gravitational fields
In strong gravitational fields, when moving at relativistic speeds, the effects of general relativity begin to appear:
- deviation of the law of gravity from Newtonian;
- potential delay associated with the finite propagation velocity of gravitational perturbations; the appearance of gravitational waves;
- non-linear effects: gravitational waves tend to interact with each other, so the principle of superposition of waves in strong fields is no longer valid;
- change in the geometry of space-time;
- the emergence of black holes;
Gravitational radiation
One of the important predictions of general relativity is gravitational radiation, the presence of which has not yet been confirmed by direct observations. However, there is indirect observational evidence in favor of its existence, namely: the energy loss in the binary system with the PSR B1913+16 pulsar - the Hulse-Taylor pulsar - is in good agreement with the model in which this energy is carried away by gravitational radiation.
Gravitational radiation can only be generated by systems with variable quadrupole or higher multipole moments, this fact suggests that the gravitational radiation of most natural sources is directional, which greatly complicates its detection. Gravity power l-poly source is proportional (v / c) 2l + 2 , if the multipole is of electric type, and (v / c) 2l + 4 - if the multipole is magnetic type , where v is the characteristic velocity of sources in the radiating system, and c is the speed of light. Thus, the dominant moment will be the quadrupole moment of the electric type, and the power of the corresponding radiation is equal to:
where Q ij is the tensor of the quadrupole moment of the mass distribution of the radiating system. Constant 
(1/W) makes it possible to estimate the order of magnitude of the radiation power.
From 1969 (Weber's experiments) to the present day (February 2007), attempts have been made to directly detect gravitational radiation. In the USA, Europe and Japan, there are currently several operating ground-based detectors (GEO 600), as well as a project for a space gravitational detector of the Republic of Tatarstan.
Subtle effects of gravity
In addition to the classical effects of gravitational attraction and time dilation, the general theory of relativity predicts the existence of other manifestations of gravity, which are very weak under terrestrial conditions and their detection and experimental verification therefore very difficult. Until recently, overcoming these difficulties seemed beyond the capabilities of experimenters.
Among them, in particular, one can name the drag of inertial reference frames (or the Lense-Thirring effect) and the gravitomagnetic field. In 2005, NASA's Gravity Probe B conducted an experiment of unprecedented accuracy to measure these effects near the Earth, but the full results have not yet been published.
quantum theory of gravity
Despite more than half a century of attempts, gravity is the only fundamental interaction for which a consistent renormalizable quantum theory has not yet been built. However, at low energies, in the spirit of quantum field theory, the gravitational interaction can be represented as an exchange of gravitons - gauge bosons with spin 2.
Standard Theories of Gravity
Due to the fact that quantum effects gravitations are extremely small even under the most extreme experimental and observational conditions, there are still no reliable observations of them. Theoretical estimates show that in the overwhelming majority of cases one can confine oneself to the classical description of the gravitational interaction.
There is a modern canonical classical theory of gravity - the general theory of relativity, and many hypotheses that refine it and theories of varying degrees of development that compete with each other (see the article Alternative theories of gravity). All of these theories give very similar predictions within the approximation in which experimental tests are currently being carried out. The following are some of the major, most well developed or known theories of gravity.
- Gravity is not a geometric field, but a real physical force field described by a tensor.
- Gravitational phenomena should be considered within the framework of the flat Minkowski space, in which the laws of conservation of energy-momentum and angular momentum are unambiguously fulfilled. Then the motion of bodies in the Minkowski space is equivalent to the motion of these bodies in the effective Riemannian space.
- In tensor equations, to determine the metric, one should take into account the mass of the graviton, and also use the gauge conditions associated with the metric of the Minkowski space. This does not allow destroying the gravitational field even locally by choosing some suitable frame of reference.
As in general relativity, in RTG, matter refers to all forms of matter (including the electromagnetic field), with the exception of the gravitational field itself. The consequences of the RTG theory are as follows: black holes as physical objects predicted in general relativity do not exist; The universe is flat, homogeneous, isotropic, immobile and Euclidean.
On the other hand, there are no less convincing arguments of RTG opponents, which boil down to the following points:
A similar thing happens in RTG, where the second tensor equation is introduced to take into account the connection between the non-Euclidean space and the Minkowski space. Due to the presence of a dimensionless fitting parameter in the Jordan-Brans-Dicke theory, it becomes possible to choose it so that the results of the theory coincide with the results of gravitational experiments.
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Sources and notes
Literature
- Vizgin V.P. Relativistic theory of gravity (origins and formation, 1900-1915). M.: Nauka, 1981. - 352c.
- Vizgin V.P. Unified theories in the 1st third of the twentieth century. M.: Nauka, 1985. - 304c.
- Ivanenko D. D., Sardanashvili G. A. Gravity, 3rd ed. M.: URSS, 2008. - 200p.
see also
- gravimeter
Links
- The law of universal gravitation or "Why does the moon not fall to the Earth?" - Just about the complex
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