You already know that between all bodies there are attractive forces called forces of gravity.

Their action is manifested, for example, in the fact that bodies fall to the Earth, the Moon revolves around the Earth, and the planets revolve around the Sun. If the forces of gravity disappeared, the Earth would fly away from the Sun (Fig. 14.1).

The law of universal gravitation was formulated in the second half of the 17th century by Isaac Newton.
Two material points of mass m 1 and m 2 located at a distance R attract with forces directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The modulus of each force

The coefficient of proportionality G is called gravitational constant. (From the Latin "gravitas" - gravity.) Measurements showed that

G \u003d 6.67 * 10 -11 N * m 2 / kg 2. (2)

The law of universal gravitation reveals another important property of the mass of a body: it is a measure not only of the body's inertia, but also of its gravitational properties.

1. What are the attractive forces of two material points with a mass of 1 kg each, located at a distance of 1 m from each other? How many times is this force greater or less than the weight of a mosquito, whose mass is 2.5 mg?

Such a small value of the gravitational constant explains why we do not notice the gravitational attraction between the objects around us.

Gravitational forces noticeably manifest themselves only when at least one of the interacting bodies has a huge mass - for example, it is a star or a planet.

3. How will the force of attraction between two material points change if the distance between them is increased by 3 times?

4. Two material points of mass m each are attracted with force F. With what force are material points of mass 2m and 3m located at the same distance attracted?

2. Movement of planets around the Sun

The distance from the Sun to any planet is many times greater than the size of the Sun and the planet. Therefore, when considering the motion of the planets, they can be considered material points. Therefore, the gravitational force of the planet to the Sun

where m is the mass of the planet, M С is the mass of the Sun, R is the distance from the Sun to the planet.

We will assume that the planet moves around the Sun uniformly in a circle. Then the speed of the planet can be found if we take into account that the acceleration of the planet a = v 2 /R is due to the action of the force F of the attraction of the Sun and the fact that, according to Newton's second law, F = ma.

5. Prove that the speed of the planet

the larger the radius of the orbit, the lower the speed of the planet.

6. The radius of Saturn's orbit is about 9 times the radius of the Earth's orbit. Find verbally, what is the approximate speed of Saturn if the Earth moves in its orbit at a speed of 30 km / s?

In a time equal to one revolution period T, the planet, moving at a speed v, covers a path equal to the circumference of a circle of radius R.

7. Prove that the orbital period of the planet

From this formula it follows that the larger the radius of the orbit, the longer the period of revolution of the planet.

9. Prove that for all planets of the solar system

Clue. Use formula (5).
From formula (6) it follows that for all the planets of the solar system, the ratio of the cube of the radius of the orbit to the square of the period of revolution is the same. This regularity (it is called Kepler's third law) was discovered by the German scientist Johannes Kepler on the basis of the results of many years of observations by the Danish astronomer Tycho Brahe.

3. Conditions for the applicability of the formula for the law of universal gravitation

Newton proved that the formula

F \u003d G (m 1 m 2 / R 2)

for the force of attraction of two material points, you can also apply:
- for homogeneous balls and spheres (R is the distance between the centers of balls or spheres, Fig. 14.2, a);

- for a homogeneous ball (sphere) and a material point (R is the distance from the center of the ball (sphere) to the material point, Fig. 14.2, b).

4. Gravity and the law of universal gravitation

The second of the above conditions means that by formula (1) one can find the force of attraction of a body of any shape to a homogeneous ball, which is much larger than this body. Therefore, according to formula (1), it is possible to calculate the force of attraction to the Earth of a body located on its surface (Fig. 14.3, a). We get the expression for gravity:

(The earth is not a uniform sphere, but it can be considered spherically symmetrical. This is sufficient for formula (1) to be applicable.)

10. Prove that near the surface of the Earth

Where M Earth is the mass of the Earth, R Earth is its radius.
Clue. Use formula (7) and that F t = mg.

Using formula (1), you can find the acceleration of free fall at a height h above the Earth's surface (Fig. 14.3, b).

11. Prove that

12. What is the free fall acceleration at a height above the Earth's surface equal to its radius?

13. How many times is the acceleration of free fall on the surface of the Moon less than on the surface of the Earth?
Clue. Use formula (8), in which the mass and radius of the Earth are replaced by the mass and radius of the Moon.

14. The radius of a white dwarf star can be equal to the radius of the Earth, and its mass can be equal to the mass of the Sun. What is the weight of a kilogram weight on the surface of such a "dwarf"?

5. First space velocity

Let us imagine that a huge cannon has been set up on a very high mountain and fired from it in a horizontal direction (Fig. 14.4).

The greater the initial velocity of the projectile, the further it will fall. It will not fall at all if its initial speed is chosen so that it moves around the Earth in a circle. Flying in a circular orbit, the projectile will then become an artificial satellite of the Earth.

Let our projectile-satellite move in a low near-Earth orbit (the so-called orbit, the radius of which can be taken equal to the radius of the Earth R Earth).
When moving uniformly along a circle, the satellite moves with centripetal acceleration a = v2/Rzem, where v is the speed of the satellite. This acceleration is due to the action of gravity. Consequently, the satellite moves with free fall acceleration directed towards the center of the Earth (Fig. 14.4). Therefore a = g.

15. Prove that when moving in low Earth orbit, the speed of the satellite

Clue. Use the formula a \u003d v 2 /r for centripetal acceleration and the fact that when moving along an orbit of radius R Earth, the satellite's acceleration is equal to the acceleration of free fall.

The speed v 1 that must be reported to the body so that it moves under the action of gravity in a circular orbit near the surface of the Earth is called the first cosmic velocity. It is approximately equal to 8 km/s.

16. Express the first cosmic velocity in terms of the gravitational constant, mass and radius of the Earth.

Clue. In the formula obtained from the previous task, replace the mass and radius of the Earth with the mass and radius of the Moon.

In order for a body to forever leave the vicinity of the Earth, it must be informed of a speed equal to approximately 11.2 km / s. It is called the second space velocity.

6. How the gravitational constant was measured

If we assume that the free fall acceleration g near the Earth's surface, the mass and radius of the Earth are known, then the value of the gravitational constant G can be easily determined using formula (7). The problem, however, is that until the end of the 18th century, the mass of the Earth could not be measured.

Therefore, to find the value of the gravitational constant G, it was necessary to measure the force of attraction of two bodies of known mass, located at a certain distance from each other. At the end of the 18th century, the English scientist Henry Cavendish was able to put such an experiment.

He hung a light horizontal rod with small metal balls a and b on a thin elastic thread, and measured the attractive forces acting on these balls from large metal balls A and B by the angle of rotation of the thread (Fig. 14.5). The scientist measured the small angles of rotation of the thread by the displacement of the "bunny" from the mirror attached to the thread.

This experiment of Cavendish was figuratively called "weighing the Earth", because this experiment for the first time made it possible to measure the mass of the Earth.

18. Express the mass of the Earth in terms of G, g and R Earth.

Additional questions and tasks

19. Two ships weighing 6000 tons each are attracted with forces of 2 mN. What is the distance between ships?

20. With what force does the Sun attract the Earth?

21. With what force does a person weighing 60 kg attract the Sun?

22. What is the free fall acceleration at a distance from the Earth's surface equal to its diameter?

23. How many times the acceleration of the Moon, due to the attraction of the Earth, is less than the acceleration of free fall on the surface of the Earth?

24. Acceleration of free fall on the surface of Mars is 2.65 times less than the acceleration of free fall on the surface of the Earth. The radius of Mars is approximately 3400 km. How many times the mass of Mars is less than the mass of the Earth?

25. What is the period of revolution of an artificial Earth satellite in low Earth orbit?

26. What is the first space velocity for Mars? The mass of Mars is 6.4 * 10 23 kg, and the radius is 3400 km.

The 16th-17th centuries are rightfully called by many one of the most glorious periods in the world. It was at this time that the foundations were largely laid, without which the further development of this science would be simply unthinkable. Copernicus, Galileo, Kepler have done a great job to declare physics as a science that can answer almost any question. Standing apart in a whole series of discoveries is the law of universal gravitation, the final formulation of which belongs to the outstanding English scientist Isaac Newton.

The main significance of the works of this scientist was not in his discovery of the force of universal gravitation - both Galileo and Kepler spoke about the presence of this quantity even before Newton, but in the fact that he was the first to prove that the same forces act both on Earth and in outer space. same forces of interaction between bodies.

Newton in practice confirmed and theoretically substantiated the fact that absolutely all bodies in the Universe, including those located on the Earth, interact with each other. This interaction is called gravitational, while the process of universal gravitation itself is called gravity.
This interaction occurs between bodies because there is a special type of matter, unlike others, which in science is called the gravitational field. This field exists and acts around absolutely any object, while there is no protection from it, since it has an unparalleled ability to penetrate any materials.

The force of universal gravitation, the definition and formulation of which he gave, is directly dependent on the product of the masses of interacting bodies, and inversely on the square of the distance between these objects. According to Newton, irrefutably confirmed by practical research, the force of universal gravitation is found by the following formula:

In it, of particular importance belongs to the gravitational constant G, which is approximately equal to 6.67 * 10-11 (N * m2) / kg2.

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

Here g is nothing more than an acceleration whose numerical value is approximately equal to 9.8 m/s2.

Newton's law explains not only the processes occurring directly on the Earth, it gives an answer to many questions related to the structure of the entire solar system. In particular, the force of universal gravitation between has a decisive influence on the motion of the planets in their orbits. The theoretical description of this motion was given by Kepler, but its justification became possible only after Newton formulated his famous law.

Newton himself connected the phenomena of terrestrial and extraterrestrial gravitation using a simple example: when fired from it, it does not fly straight, but along an arcuate trajectory. At the same time, with an increase in the charge of gunpowder and the mass of the nucleus, the latter will fly farther and farther. Finally, if we assume that it is possible to obtain so much gunpowder and construct such a cannon that the cannonball will fly around the globe, then, having made this movement, it will not stop, but will continue its circular (ellipsoidal) movement, turning into an artificial one. As a result, the force of the universal gravity is the same in nature both on Earth and in outer space.

In the declining years of his life, he spoke of how he discovered law of gravity.

When young Isaac walked in the garden among the apple trees at his parents' estate, he saw the moon in the daytime sky. And next to him, an apple fell to the ground, breaking off a branch.

Since Newton was working on the laws of motion at the same time, he already knew that the apple fell under the influence of the Earth's gravitational field. And he knew that the Moon is not just in the sky, but revolves around the Earth in an orbit, and, therefore, some kind of force acts on it, which keeps it from breaking out of orbit and flying away in a straight line, into outer space. This is where the idea came to him that, perhaps, the same force makes the apple fall to the earth, and the moon remains in Earth orbit.

Before Newton, scientists believed that there were two types of gravity: terrestrial gravity (acting on Earth) and celestial gravity (acting in heaven). This idea was firmly entrenched in the minds of the people of that time.

Newton's epiphany was that he combined these two types of gravity in his mind. Since that historical moment, the artificial and false division of the Earth and the rest of the Universe has ceased to exist.

And so the law of universal gravitation was discovered, which is one of the universal laws of nature. According to the law, all material bodies attract each other, and the magnitude of the gravitational force does not depend on the chemical and physical properties of the bodies, on the state of their movement, on the properties of the environment where the bodies are located. Gravity on the Earth is manifested, first of all, in the existence of gravity, which is the result of the attraction of any material body by the Earth. Related to this is the term "gravity" (from lat. gravitas - gravity) , equivalent to the term "gravity".

The law of gravity states that the force of gravitational attraction between two material points of mass m1 and m2, separated by a distance R, is proportional to both masses and inversely proportional to the square of the distance between them.

The very idea of ​​a universal gravitational force was repeatedly expressed even before Newton. Previously, Huygens, Roberval, Descartes, Borelli, Kepler, Gassendi, Epicurus and others thought about it.

According to Kepler's assumption, gravity is inversely proportional to the distance to the Sun and extends only in the plane of the ecliptic; Descartes considered it the result of vortices in the ether.

There were, however, guesses with the correct dependence on distance, but before Newton, no one was able to clearly and mathematically conclusively connect the law of gravity (a force inversely proportional to the square of distance) and the laws of planetary motion (Kepler's laws).

In his main work "The Mathematical Principles of Natural Philosophy" (1687) Isaac Newton derived the law of gravity, based on the empirical laws of Kepler, known by that time.
He showed that:

• • the observed movements of the planets testify to the presence of a central force;
  • conversely, the central force of attraction leads to elliptical (or hyperbolic) orbits.

Unlike the hypotheses of its predecessors, Newton's theory had a number of significant differences. Sir Isaac published not only the proposed formula for the law of universal gravitation, but actually proposed a complete mathematical model:

• • law of gravitation;
  • the law of motion (Newton's second law);
  • system of methods for mathematical research (mathematical analysis).

Taken together, this triad is sufficient to fully explore the most complex movements of celestial bodies, thus creating the foundations of celestial mechanics.

But Isaac Newton left open the question of the nature of gravity. The assumption of the instantaneous propagation of gravity in space (i.e., the assumption that with a change in the positions of bodies the force of gravity between them instantly changes), which is closely related to the nature of gravity, was also not explained. For more than two hundred years after Newton, physicists have proposed various ways to improve Newton's theory of gravity. It was not until 1915 that these efforts were crowned with success by the creation Einstein's general theory of relativity in which all these difficulties were overcome.

The phenomenon of universal gravitation

The phenomenon of universal gravitation lies in the fact that between all bodies in the universe there are forces of attraction.

Newton came to the conclusion about the existence of universal gravitational pitchforks (they are also called gravitational pitchforks) as a result of studying the motion of the Moon around the Earth and planets around the Sun. These astronomical observations were made by the Danish astronomer Tycho Brahe. Tycho Brahe measured the position of all the known planets at that time and wrote down their coordinates, but Tycho Brahe did not succeed in finally deducing, creating the law of planetary motion relative to the Sun. This was done by his student Johannes Kepler. Johannes Kepler used not only the measurements of Tycho Brahe, but also by that time already sufficiently substantiated, used everywhere and everywhere, the heliocentric system of the world of Copernicus. The system in which it is believed that the Sun is at the center of our system and the planets revolve around it.

Figure 1. Heliocentric system of the world (Copernicus system)

First of all, Newton suggested that all bodies have the property of attraction, i.e. those bodies that have masses are attracted to each other. This phenomenon became known as universal gravitation. And bodies that attract others to each other create force. This force, with which bodies are attracted, began to be called gravitational (from the word gravitas - "gravity").

Law of gravity

Newton managed to obtain a formula for calculating the interaction force of bodies with masses. This formula is called law of gravity. It was discovered in $1667$. I. Newton substantiated his discovery on astronomical observations

The very "law of universal gravitation" sounds like this: two bodies are attracted to each other with a force that is directly proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between them.

Let's look at the quantities that are included in this law. So, the law of universal gravitation itself looks like this:

There is one more value here - $G$, gravitational constant. Its physical meaning lies in the fact that it shows the force with which two bodies with a mass of $1$ kg, each $1$ kg, located at a distance of $1$ m interact. This value is very small, it is only $10^ in order of magnitude. (-11).$

$G=6.67\cdot 10^(-11) \frac(H\cdot m^2)(kg^2)$

Its value tells about the ratio in which they are located, with what force the bodies that are nearby interact, and even if they are close enough (for example, two standing people), they will absolutely not feel this interaction, since the order of force is $10^( -11)$ will not give a significant sensation. The action of the gravitational force begins to affect only when the mass of the bodies is large.

Limits of applicability of the law of universal gravitation

In the form in which we use the law of universal gravitation, it is not always true, but only in some cases:

• if the dimensions of the bodies are negligible compared to the distance between them;

Figure 2.

• if both bodies are homogeneous and have a spherical shape - in this case, even if the distances between the bodies are still not so great, the law of universal gravitation is applicable if the bodies have a spherical shape and then the distances are defined as the distances between the centers of the bodies under consideration;

Figure 3

• if one of the interacting bodies is a ball, the dimensions of which are much larger than the dimensions of the second body (of any shape) located on the surface of this ball or near it, this is the case of the movement of satellites in their orbits around the Earth.

Figure 4

Example 1

An artificial satellite moves in a circular orbit around the Earth at a speed of $1$ km/s at an altitude of 350,000 km. We need to determine the mass of the Earth.

Given: $v=1$ km/s, $R=350000$ km.

Find: $M_(3) $-?

Since the satellite is moving around the Earth, it has a centripetal acceleration equal to:

$F=G\frac(mM_(3) )(R^(2) ) =ma$. (2)

Taking into account (1) from (2), we write the expression for finding the mass of the Earth:

$M_(3) =\frac(v^(2) R)(G) =5.24\cdot 10^(24) $kg

Answer: $M_(3) =5.24\cdot 10^(24) $ kg.

The most important phenomenon constantly studied by physicists is motion. 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 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 recorded 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 fairly obvious from a simpler expression for the 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, since 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.

Second space velocity

We write the law of conservation of energy:

,

where on the right side of the equality is the work of gravity: A = Fs.

From here we get that the second cosmic velocity is equal to:

Thus, the second space velocity is times greater than the first:

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.