The attraction of bodies to the Earth is one of the cases universal gravity. For us, the inhabitants of the Earth, this power is of great importance.

with which a body of mass m is attracted to the Earth is somewhat different from the force of gravity acting on this body, determined by the formula F heavy = gm (this is due to the fact that the Earth, due to its daily rotation, is not a strictly inertial frame of reference). But since the difference between the indicated forces is significantly less than each of them, these forces can be considered approximately equal.

This means that for any body of mass m located on the surface of the Earth or near it, we can write:

From the last formula it follows that the acceleration of free fall of bodies located on the surface of the Earth or near it depends on the mass of the Earth and its radius (i.e., the distance between the center of the Earth and the given body).

Rice. 33. The value of the acceleration due to gravity depends on the height of the body above the Earth and geographical latitude places

If a body is raised to a height h above the Earth, as shown in Figure 33, a, then the distance between this body and the center of the Earth will be R З + h then

The greater the height h, the smaller g and the less strength body gravity. This means that with an increase in the height of a body above the Earth’s surface, the force of gravity acting on it decreases due to a decrease in the acceleration of gravity. But this decrease is usually very small, since the height of the body above the Earth is most often negligible compared to the radius of the Earth. For example, if a climber weighing 80 kg climbed a mountain 3 km high, then the force of gravity acting on him would decrease by only 0.7 N (or 0.09%). Therefore, in many cases, when calculating the force of gravity of a body located at a small height above the Earth, the acceleration of gravity is considered equal to 9.8 m/s 2, neglecting its slight decrease.

The values ​​of the g coefficient (and therefore the values ​​of gravity) also depend on the geographic latitude of the place on the globe. It varies from 9.78 m/s 2 at the equator to 9.83 m/s 2 at the poles, i.e. at the poles it is slightly greater than at the equator. This is understandable: after all, the Earth does not have a strictly spherical shape. It is slightly flattened at the poles (Fig. 33, b), therefore the distance from the center of the Earth to the poles R n is less than to the equator R a . And according to the law of universal gravitation, the smaller the distance between bodies, the more power attraction between them.

By substituting into the formula for the acceleration of gravity instead of the mass and radius of the Earth, respectively, the mass and radius of any other planet or its satellite, you can determine the approximate value of the acceleration of gravity on the surface of any of these celestial bodies. For example, the acceleration of gravity on the Moon is calculated by the formula:

It turns out that the relationship

6 times less than

Therefore, both the acceleration of free fall and the force of attraction of bodies to the Moon are 6 times less than on Earth. For example, a person whose mass is 60 kg is attracted to the Earth with a force of 588 N, and to the Moon with a force of 98 N.

Questions

1. Is it true that the attraction of bodies towards the Earth is one of the examples of universal gravitation?
2. How does the force of gravity acting on a body change as it moves away from the Earth's surface?
3. What formula can be used to calculate the force of gravity acting on a body if it is at a low altitude above the Earth?
4. In what case will the force of gravity acting on the same body be greater: if this body is in equatorial region globe or at one of the poles? Why?
5. What do you know about the acceleration of gravity on the Moon?

Exercise 16

1. What is the force of gravity acting on a body weighing 2.5 kg; 600 g; 1.2 t; 50 t? (Take g = 10 m/s2.)
2. Approximately determine the force of gravity acting on a person weighing 64 kg. (Take g = 10 m/s 2 .) Is the globe attracted to this person? If so, what is this force approximately equal to?
3. The first Soviet artificial Earth satellite was launched on October 4, 1957. Determine the mass of this satellite if it is known that on Earth it was subject to a gravity force equal to 819.3 N.
4. The rocket flies at a distance of 5000 km from the Earth's surface. Is it possible to calculate the force of gravity acting on a space rocket, taking g = 9.8 m/s 2? (It is known that the radius of the Earth is approximately 6400 km.) Explain your answer.
5. A hawk can hover at the same height above the Earth for some time. Does this mean that gravity does not act on it? What will happen to the hawk if it folds its wings?
6. Starts from Earth space rocket. At what distance from the Earth's surface will the rocket's gravity be 4 times less than before launch; 9 times less than before the start?

This is interesting...

Discovery of the planets Neptune and Pluto

Using the law of universal gravitation and Newton's laws, the trajectories of planetary motion were determined solar system, and also calculated their coordinates at any time for many years in advance. To do this, first, according to the law of universal gravitation, the force of gravitational interaction between the Sun and a given planet was calculated. Newton's second law was then used to calculate the acceleration with which the planet moves around the Sun. And other quantities characterizing movement, including coordinates, were determined from acceleration.

At the same time, the influence of other planets of the solar system on the movement of this planet was also taken into account.

The correctness of the planetary orbits and their positions calculated in this way at any time was confirmed by the results of astronomical observations.

In 1781, the English astronomer William Herschel, through observations, discovered the seventh planet of the solar system, which was named Uranus.

Soon after this, it was calculated how the coordinates of Uranus would change over time and in what orbit it would move.

As a result of many years of observations of the movement of Uranus in the first half of the 19th century. Scientists have finally become convinced that the real orbit of Uranus does not coincide with the calculated one. It seemed that there was another planet behind Uranus, which attracted Uranus to itself and thereby influenced its movement.

Based on deviations in the movement of Uranus, first the English scientist John Adams, and somewhat later the French scientist Urbain Le Verrier, based on the law of universal gravitation, were able to calculate the location of this supposed planet.

Adams was the first to finish his work and turned to the director of one of the observatories with a request to organize a search for the planet, the coordinates of which he found using theoretical calculations. Le Verrier also addressed the same observatory with a similar request.

But for some reason, the search for the planet was postponed indefinitely.

Then Le Verrier sent a letter indicating the exact coordinates of the planet, which, in his opinion, should have been located beyond Uranus, to a young employee of the Berlin Observatory, Johann Galle.

On September 23, 1846, Halle, having received this letter, immediately began observations and on the same night discovered a scientifically predicted planet, the coordinates of which differed by only half a degree from those indicated in the letter.

Five days later, Le Verrier received a congratulatory letter from the director of the Berlin Observatory, which said, in part: “Your name will henceforth be associated with the most outstanding conceivable proof of the validity of the law of universal gravitation.”

At Le Verrier's suggestion, the planet was named Neptune.

And only a few years later, the scientific world recognized the merit of John Adams in the discovery of Neptune.

With the help of calculations based, in particular, on the application of the law of universal gravitation, and targeted astronomical observations, on February 18, 1930, another planet of the solar system was discovered - Pluto, which is almost three times farther from the Sun than Neptune.

Wanting to emphasize that the discovery of these planets was made theoretically, that is, exclusively with the help of calculations based on the laws of physics, they say that the planets Neptune and Pluto were discovered “at the tip of a pen.”

Currently, Pluto is ranked among dwarf planets, since, having a mass 500 times less than that of the Earth and a diameter of 2/3 that of the Moon, it does not correspond to the definition of the concept of “planet”, which was given in August 2006 by the International Astronomical Union.

§ 16. Acceleration of free fall on Earth and others celestial bodies(end)

By substituting into the formula for the acceleration of gravity instead of the mass and radius of the Earth, respectively, the mass and radius of any other planet or its satellite, you can determine the approximate value of the acceleration of gravity on the surface of any of these celestial bodies. For example, the acceleration of gravity on the Moon is calculated by the formula:

It turns out that the ratio is 6 times less than Therefore, both the acceleration of gravity and the force of attraction of bodies to the Moon are 6 times less than on Earth. For example, a person whose mass is 60 kg is attracted to the Earth with a force of 588 N, and to the Moon with a force of 98 N.

Questions

1. Is it true that the attraction of bodies towards the Earth is one of the examples of universal gravitation?

2. How does the force of gravity acting on a body change as it moves away from the Earth’s surface?

3. What formula can be used to calculate the force of gravity acting on a body if it is at a low altitude above the Earth?

4. In what case will the force of gravity acting on the same body be greater: if this body is located in the equatorial region of the globe or at one of the poles? Why?

5. What do you know about the acceleration of gravity on the Moon?

Exercise 16

1. What is the force of gravity acting on a body weighing 2.5 kg; 600 g; 1.2 t; 50 t? (Take g - 10 m/s 2.)

2. Approximately determine the force of gravity acting on a person weighing 64 kg. (Take g = 10 m/s 2 .) Is the globe attracted to this person? If so, what is this force approximately equal to?

3. The first Soviet artificial Earth satellite was launched on October 4, 1957. Determine the mass of this satellite if it is known that on Earth it was subject to a gravity force equal to 819.3 N.

4. A rocket flies at a distance of 5000 km from the surface of the Earth. Is it possible to calculate the force of gravity acting on a space rocket, taking g = 9.8 m/s 2? (It is known that the radius of the Earth is approximately 6400 km.) Explain your answer.

5. A hawk can hover at the same height above the Earth for some time. Does this mean that gravity does not act on it? What will happen to the hawk if it folds its wings?

6*. A space rocket launches from Earth. At what distance from the Earth's surface will the rocket's gravity be 4 times less than before launch; 9 times less than before the start?

Answers: Exercise 16

2. It is attracted with the same magnitude force.

6*. h 1 = R 3 ; h 2 = 2R 3 .

. Questions.

1. Is it true that the attraction of bodies towards the Earth is one of the examples of universal gravitation?

The attraction of bodies towards the Earth is one of the cases of universal gravitation.

2. How does the force of gravity acting on a body change as it moves away from the Earth’s surface?

3. What formula can be used to calculate the force of gravity acting on a body if it is at a low altitude above the Earth?

According to the formula F heavy = mg, F is the force of gravity, m is the mass of the body, g is the acceleration of free fall.

4. In what case will the force of gravity acting on the same body be greater: if this body is located in the equatorial region of the globe or at one of the poles? Why?

Since the Earth is slightly flattened at the poles, the force of gravity there will be greater than at the equator (therefore, spaceports are closer to the equator).

5. What do you know about the acceleration of gravity on the Moon?

Exercises.

1. What is the force of gravity acting on a body weighing 2.5 kg; 600 g; 1.2 t; 50 t? (g = 10 m/s 2)

2. Determine approximately the force of gravity acting on a person weighing 64 kg (g = 10 m/s 2). Is it attracted Globe to this person? If so, what is this force approximately equal to?

3. The first Soviet artificial Earth satellite was launched on October 4, 1957. Determine the mass of this satellite if it is known that on Earth it was acted upon by a force of gravity equal to 819.3 N?

4. Is it possible to calculate the force of gravity acting on a space rocket using the formula F heavy = 9.8 m/s 2 * m, where m is the mass of the rocket, if this rocket flies at a distance of 5000 km from the Earth’s surface? (It is known that the radius of the Earth is approximately 6400 km). Explain your answer. If this formula is not suitable, then what formula would you suggest using in this case?

5. A hawk can hover at the same height above the Earth for some time. Does this mean that gravity does not act on it? What happens to a hawk if it folds its wings?

No, the hawk is affected by gravity, and if it folds its wings it will dive down and fall to the ground.

6. A space rocket launches from Earth. At what distance from the Earth's surface will the rocket's gravity be 4 times less than before launch? 9 times less than before the start?