The force of universal gravity. Gravitational forces What determines the attraction between bodies

Isaac Newton suggested that there are forces of mutual attraction between any bodies in nature. These forces are called by gravitational forces or forces of universal gravity. The force of unnatural gravity manifests itself in space, the solar system and on Earth.

Law of Gravity

Newton generalized the laws of motion of celestial bodies and found out that the force \(F\) is equal to:

\[ F = G \dfrac(m_1 m_2)(R^2) \]

where \(m_1\) and \(m_2\) are the masses of interacting bodies, \(R\) is the distance between them, \(G\) is the proportionality coefficient, which is called gravitational constant. The numerical value of the gravitational constant was experimentally determined by Cavendish by measuring the force of interaction between lead balls.

The physical meaning of the gravitational constant follows from the law of universal gravitation. If \(m_1 = m_2 = 1 \text(kg)\), \(R = 1 \text(m) \) , then \(G = F \) , i.e. the gravitational constant is equal to the force with which two bodies of 1 kg each are attracted at a distance of 1 m.

Numerical value:

\(G = 6.67 \cdot() 10^(-11) N \cdot() m^2/ kg^2 \) .

The forces of universal gravity act between any bodies in nature, but they become noticeable at large masses (or if at least the mass of one of the bodies is large). The law of universal gravitation is satisfied only for material points and balls (in this case, the distance between the centers of the balls is taken as the distance).

Gravity

A particular type of universal gravitational force is the force of attraction of bodies towards the Earth (or to another planet). This force is called gravity. Under the influence of this force, all bodies acquire free fall acceleration.

In accordance with Newton's second law \(g = F_T /m\) , therefore, \(F_T = mg \) .

If M is the mass of the Earth, R is its radius, m is the mass of a given body, then the force of gravity is equal to

\(F = G \dfrac(M)(R^2)m = mg \) .

The force of gravity is always directed towards the center of the Earth. Depending on the height \(h\) above the Earth's surface and the geographic latitude of the body's position, the acceleration of gravity takes on different values. On the Earth's surface and in mid-latitudes, the acceleration of gravity is 9.831 m/s 2 .

Body weight

The concept of body weight is widely used in technology and everyday life.

Body weight denoted by \(P\) . The unit of weight is newton (N). Since weight is equal to the force with which the body acts on the support, then, in accordance with Newton’s third law, the largest weight of the body is equal to the reaction force of the support. Therefore, in order to find the weight of the body, it is necessary to determine what the support reaction force is equal to.

In this case, it is assumed that the body is motionless relative to the support or suspension.

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

The state of a body in which its weight is zero is called weightlessness. The state of weightlessness is observed in an airplane or spacecraft when moving with free fall acceleration, regardless of the direction and value of the speed of their movement. Outside the Earth's atmosphere, when the jet engines are turned off, only the force of universal gravity acts on the spacecraft. Under the influence of this force, the spaceship and all the bodies in it move with the same acceleration, therefore a state of weightlessness is observed in the ship.

DEFINITION

The law of universal gravitation was discovered by I. Newton:

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

Description of the law of universal gravitation

The coefficient is the gravitational constant. In the SI system, the gravitational constant has the meaning:

This constant, as can be seen, is very small, therefore the gravitational forces between bodies with small masses are also small and practically not felt. However, the movement of cosmic bodies is completely determined by gravity. The presence of universal gravitation or, in other words, gravitational interaction explains what the Earth and planets are “supported” by, and why they move around the Sun along certain trajectories, and do not fly away from it. The law of universal gravitation allows us to determine many characteristics of celestial bodies - the masses of planets, stars, galaxies and even black holes. This law makes it possible to calculate the orbits of planets with great accuracy and create a mathematical model of the Universe.

Using the law of universal gravitation, cosmic velocities can also be calculated. For example, the minimum speed at which a body moving horizontally above the Earth’s surface will not fall on it, but will move in a circular orbit is 7.9 km/s (first escape velocity). In order to leave the Earth, i.e. to overcome its gravitational attraction, the body must have a speed of 11.2 km/s (second escape velocity).

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

Gravity

A special case of the manifestation of gravitational forces is the force of gravity.

Gravity is always directed vertically downward (toward the center of the Earth).

If the force of gravity acts on a body, then the body does . The type of movement depends on the direction and magnitude of the initial speed.

We encounter the effects of gravity every day. , after a while he finds himself on the ground. The book, released from the hands, falls down. Having jumped, a person does not fly into outer space, but falls down to the ground.

Considering the free fall of a body near the Earth's surface as a result of the gravitational interaction of this body with the Earth, we can write:

where does the acceleration of free fall come from:

The acceleration of gravity does not depend on the mass of the body, but depends on the height of the body above the Earth. The globe is slightly flattened at the poles, so bodies located near the poles are located a little closer to the center of the Earth. In this regard, the acceleration of gravity depends on the latitude of the area: at the pole it is slightly greater than at the equator and other latitudes (at the equator m/s, at the North Pole equator m/s.

The same formula allows you to find the acceleration of gravity on the surface of any planet with mass and radius.

Examples of problem solving

EXAMPLE 1 (problem about “weighing” the Earth)

EXAMPLE 2

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 what has potential energy, where is it 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 contributing 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. Although the massive Sun 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 a quantitative characteristic of 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 gravity is truly a constant value, since its formula includes constant quantities - 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 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 simpler 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 must 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 gravity 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)? This is exactly the speed 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 the universal law of gravity.

Between any bodies in nature there is a force of mutual attraction called force of universal gravity(or gravitational forces). was discovered by Isaac Newton in 1682. When he was still 23 years old, he suggested that the forces that keep the Moon in its orbit are of the same nature as the forces that make an apple fall to Earth.

Gravity (mg) is directed vertically strictly to the center of the earth; Depending on the distance to the surface of the globe, the acceleration of gravity is different. At the Earth's surface in mid-latitudes its value is about 9.8 m/s 2 . as you move away from the Earth's surface g decreases.

Body weight (weight strength) – is the force with which a body acts onhorizontal support or stretches the suspension. It is assumed that the body motionless relative to the support or suspension. Let the body lie on a horizontal table motionless relative to the Earth. Denoted by the letter R.

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

If acceleration a = 0 , then the weight is equal to the force with which the body is attracted to the Earth, namely . [P] = N.

If the condition is different, then the weight changes:

• if acceleration A not equal 0 , then the weight P = mg - ma (down) or P = mg + ma (up);
• if the body falls freely or moves with free fall acceleration, i.e. a =g(Fig. 2), then the body weight is equal to 0 (P=0 ). The state of a body in which its weight is zero is called weightlessness.

IN weightlessness There are also astronauts. IN weightlessness For a moment, you too find yourself when you jump while playing basketball or dancing.

Home experiment: A plastic bottle with a hole at the bottom is filled with water. We release it from our hands from a certain height. While the bottle falls, water does not flow out of the hole.

Weight of a body moving with acceleration (in an elevator) A body in an elevator experiences overloads