The gravitational constant is not a constant value. What does "gravitational constant" mean?

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When Newton discovered the law of universal gravitation, he did not know a single numerical value for the masses of celestial bodies, including the Earth. He also did not know the value of the constant G.

Meanwhile, the gravitational constant G has the same value for all bodies in the Universe and is one of the fundamental physical constants. How can one find its meaning?

From the law of universal gravitation it follows that G = Fr 2 /(m 1 m 2). This means that in order to find G, you need to measure the force of attraction F between bodies of known masses m 1 and m 2 and the distance r between them.

The first measurements of the gravitational constant were made in the middle of the 18th century. It was possible to estimate, albeit very roughly, the value of G at that time as a result of considering the attraction of a pendulum to a mountain, the mass of which was determined by geological methods.

Accurate measurements of the gravitational constant were first carried out in 1798 by the remarkable scientist Henry Cavendish, a wealthy English lord who was known as an eccentric and unsociable person. Using the so-called torsion balance (Fig. 101), Cavendish was able to measure the negligible force of attraction between small and large metal balls using the angle of twist of thread A. To do this, he had to use such sensitive equipment that even weak air currents could distort the measurements. Therefore, in order to exclude extraneous influences, Cavendish placed his equipment in a box, which he left in the room, and he himself carried out observations of the equipment using a telescope from another room.

Experiments have shown that

G ≈ 6.67 10 –11 N m 2 /kg 2.

The physical meaning of the gravitational constant is that it is numerically equal to the force with which two particles with a mass of 1 kg each, located at a distance of 1 m from each other, are attracted. This force, therefore, turns out to be extremely small - only 6.67 · 10 –11 N. Is this good or bad? Calculations show that if the gravitational constant in our Universe had a value, say, 100 times greater than that given above, this would lead to the fact that the lifetime of stars, including the Sun, would sharply decrease and intelligent life on Earth I wouldn't have time to show up. In other words, you and I wouldn’t exist now!

A small value of G means that the gravitational interaction between ordinary bodies, not to mention atoms and molecules, is very weak. Two people weighing 60 kg at a distance of 1 m from each other are attracted with a force equal to only 0.24 μN.

However, as the masses of bodies increase, the role of gravitational interaction increases. For example, the force of mutual attraction between the Earth and the Moon reaches 10 20 N, and the attraction of the Earth by the Sun is even 150 times stronger. Therefore, the movement of planets and stars is already completely determined by gravitational forces.

During his experiments, Cavendish also proved for the first time that not only planets, but also ordinary bodies surrounding us in everyday life are attracted according to the same law of gravity, which was discovered by Newton as a result of the analysis of astronomical data. This law is truly the law of universal gravitation.

“The law of gravity is universal. It extends over vast distances. And Newton, who was interested in the Solar System, could well have predicted what would come out of Cavendish’s experiment, for Cavendish’s scales, two attracting balls, are a small model of the Solar System. If we magnify it ten million million times, we get the solar system. Let's increase it another ten million million times - and here you have galaxies that attract each other according to the same law. When embroidering her pattern, Nature uses only the longest threads, and any, even the smallest, sample of it can open our eyes to the structure of the whole” (R. Feynman).

1. What is the physical meaning of the gravitational constant? 2. Who was the first to make accurate measurements of this constant? 3. What does the small value of the gravitational constant lead to? 4. Why, sitting next to a friend at a desk, do you not feel attracted to him?

As one of the fundamental quantities in physics, the gravitational constant was first mentioned in the 18th century. At the same time, the first attempts were made to measure its value, but due to the imperfection of instruments and insufficient knowledge in this area, this was only possible in the middle of the 19th century. Later, the obtained result was corrected several times (the last time this was done in 2013). However, it should be noted that there is a fundamental difference between the first (G = 6.67428(67) 10 −11 m³ s −2 kg −1 or N m² kg −2) and the last (G = 6.67384( 80) 10 −11 m³ s −2 kg −1 or N m² kg −2) values ​​do not exist.

When using this coefficient for practical calculations, it should be understood that the constant is such in global universal concepts (if you do not make reservations about the physics of elementary particles and other little-studied sciences). This means that the gravitational constant of the Earth, Moon or Mars will not differ from each other.

This quantity is a basic constant in classical mechanics. Therefore, the gravitational constant is involved in a variety of calculations. In particular, without information about the more or less exact value of this parameter, scientists would not be able to calculate such an important coefficient in the space industry as the acceleration of free fall (which will be different for each planet or other cosmic body).

However, Newton, who spoke in general terms, knew the gravitational constant only in theory. That is, he was able to formulate one of the most important physical postulates without having information about the quantity on which it is essentially based.

Unlike other fundamental constants, physics can only say with a certain degree of accuracy what the gravitational constant is equal to. Its value is periodically obtained again, and each time it is different from the previous one. Most scientists believe that this fact is not due to its changes, but to more banal reasons. Firstly, these are measurement methods (various experiments are carried out to calculate this constant), and secondly, the accuracy of instruments, which gradually increases, the data is refined, and a new result is obtained.

Taking into account the fact that the gravitational constant is a quantity measured by 10 to the -11 power (which is an extremely small value for classical mechanics), the constant refinement of the coefficient is not surprising. Moreover, the symbol is subject to correction starting from 14 decimal places.

However, there is another theory in modern wave physics, which was put forward by Fred Hoyle and J. Narlikar back in the 70s of the last century. According to their assumptions, the gravitational constant decreases over time, which affects many other indicators that are considered constants. Thus, the American astronomer van Flandern noted the phenomenon of slight acceleration of the Moon and other celestial bodies. Guided by this theory, it should be assumed that there were no global errors in the early calculations, and the difference in the results obtained is explained by changes in the value of the constant itself. The same theory speaks about the inconstancy of some other quantities, such as

After studying a physics course, students are left with all sorts of constants and their meanings in their heads. The topic of gravity and mechanics is no exception. Most often, they cannot answer the question of what value the gravitational constant has. But they will always answer unequivocally that it is present in the law of universal gravitation.

From the history of the gravitational constant

It is interesting that Newton's works do not contain such a value. It appeared in physics much later. To be more specific, only at the beginning of the nineteenth century. But that doesn't mean it didn't exist. Scientists just haven’t defined it and haven’t found out its exact meaning. By the way, about the meaning. The gravitational constant is constantly being refined because it is a decimal fraction with a large number of digits after the decimal point, preceded by a zero.

It is precisely the fact that this quantity takes such a small value that explains the fact that the effect of gravitational forces is imperceptible on small bodies. It’s just that because of this multiplier, the force of attraction turns out to be negligibly small.

For the first time, the value that the gravitational constant takes was established experimentally by physicist G. Cavendish. And this happened in 1788.

His experiments used a thin rod. It was suspended on a thin copper wire and was about 2 meters long. Two identical lead balls with a diameter of 5 cm were attached to the ends of this rod. Large lead balls were installed next to them. Their diameter was already 20 cm.

When the large and small balls came together, the rod rotated. This spoke of their attraction. Based on the known masses and distances, as well as the measured twisting force, it was possible to determine quite accurately what the gravitational constant is equal to.

It all started with the free fall of bodies

If you place bodies of different masses into a void, they will fall at the same time. Provided they fall from the same height and start at the same point in time. It was possible to calculate the acceleration with which all bodies fall to the Earth. It turned out to be approximately 9.8 m/s 2 .

Scientists have found that the force with which everything is attracted to the Earth is always present. Moreover, this does not depend on the height to which the body moves. One meter, a kilometer or hundreds of kilometers. No matter how far away the body is, it will be attracted to the Earth. Another question is how will its value depend on distance?

It was this question that the English physicist I. Newton found the answer to.

Decrease in the force of attraction of bodies as they move away

To begin with, he put forward the assumption that gravity is decreasing. And its value is inversely related to the distance squared. Moreover, this distance must be counted from the center of the planet. And carried out theoretical calculations.

Then this scientist used astronomers’ data on the movement of the Earth’s natural satellite, the Moon. Newton calculated the acceleration with which it revolves around the planet, and obtained the same results. This testified to the veracity of his reasoning and made it possible to formulate the law of universal gravitation. The gravitational constant was not yet in his formula. At this stage it was important to identify the dependency. Which is what was done. The force of gravity decreases in inverse proportion to the squared distance from the center of the planet.

Towards the law of universal gravitation

Newton continued his thoughts. Since the Earth attracts the Moon, it itself must be attracted to the Sun. Moreover, the force of such attraction must also obey the law described by him. And then Newton extended it to all bodies of the universe. Therefore, the name of the law includes the word “worldwide”.

The forces of universal gravity of bodies are defined as proportionally depending on the product of masses and inverse to the square of the distance. Later, when the coefficient was determined, the formula of the law took on the following form:

• F t = G (m 1 * x m 2) : r 2.

It introduces the following notations:

The formula for the gravitational constant follows from this law:

• G = (F t X r 2) : (m 1 x m 2).

The value of the gravitational constant

Now it's time for specific numbers. Since scientists are constantly refining this value, different numbers have been officially adopted in different years. For example, according to data for 2008, the gravitational constant is 6.6742 x 10 -11 Nˑm 2 /kg 2. Three years passed and the constant was recalculated. Now the gravitational constant is 6.6738 x 10 -11 Nˑm 2 /kg 2. But for schoolchildren, when solving problems, it is permissible to round it up to this value: 6.67 x 10 -11 Nˑm 2 /kg 2.

What is the physical meaning of this number?

If you substitute specific numbers into the formula given for the law of universal gravitation, you will get an interesting result. In the particular case, when the masses of the bodies are equal to 1 kilogram, and they are located at a distance of 1 meter, the gravitational force turns out to be equal to the very number that is known for the gravitational constant.

That is, the meaning of the gravitational constant is that it shows with what force such bodies will be attracted at a distance of one meter. The number shows how small this force is. After all, it is ten billion less than one. It's impossible to even notice it. Even if the bodies are magnified a hundred times, the result will not change significantly. It will still remain much less than one. Therefore, it becomes clear why the force of attraction is noticeable only in those situations if at least one body has a huge mass. For example, a planet or a star.

How is the gravitational constant related to the acceleration of gravity?

If you compare two formulas, one of which is for the force of gravity, and the other for the law of gravity of the Earth, you can see a simple pattern. The gravitational constant, the mass of the Earth and the square of the distance from the center of the planet form a coefficient that is equal to the acceleration of gravity. If we write this down as a formula, we get the following:

• g = (G x M) : r 2 .

Moreover, it uses the following notation:

By the way, the gravitational constant can also be found from this formula:

• G = (g x r 2) : M.

If you need to find out the acceleration of gravity at a certain height above the surface of the planet, then the following formula will be useful:

• g = (G x M) : (r + n) 2, where n is the height above the Earth’s surface.

Problems that require knowledge of the gravitational constant

Task one

Condition. What is the acceleration of gravity on one of the planets of the solar system, for example, on Mars? It is known that its mass is 6.23 10 23 kg, and the radius of the planet is 3.38 10 6 m.

Solution. You need to use the formula that was written down for the Earth. Just substitute the values ​​given in the problem into it. It turns out that the acceleration of gravity will be equal to the product of 6.67 x 10 -11 and 6.23 x 10 23, which then needs to be divided by the square of 3.38 x 10 6. The numerator gives the value 41.55 x 10 12. And the denominator will be 11.42 x 10 12. The powers will cancel, so to answer you just need to find out the quotient of two numbers.

Answer: 3.64 m/s 2 .

Task two

Condition. What needs to be done with bodies to reduce their force of attraction by 100 times?

Solution. Since the mass of bodies cannot be changed, the force will decrease due to their distance from each other. A hundred is obtained by squaring 10. This means that the distance between them should become 10 times greater.

Answer: move them away to a distance 10 times greater than the original one.