A way of measuring the mass of the globe. Earth mass in numbers

Earth is a unique planet in the solar system. It is not the smallest, but not the largest either: it takes the fifth place in size. Among the terrestrial planets, it is the largest in mass, diameter, density. The planet is located in outer space, and finding out how much the Earth weighs is difficult. It cannot be put on a scale and weighed, therefore, it is said about its weight, summing up the mass of all the substances of which it consists. This figure is roughly 5.9 sextillion tons. To understand what this number is, you can simply write it down mathematically: 5,900,000,000,000,000,000,000. This number of zeros somehow dazzles the eyes.

History of attempts to determine the size of the planet

Scientists of all ages and peoples have tried to find an answer to the question of how much the Earth weighs. In ancient times, people assumed that the planet was a flat plate held by whales and a turtle. In some nations, elephants were used instead of whales. In any case, different peoples of the world represented the planet as flat and having its own edge.

During the Middle Ages, ideas about shape and weight changed. The first to talk about the spherical form was J. Bruno, however, for his convictions, he was executed by the Inquisition. Another contribution to science, which shows the radius and mass of the Earth, was made by the traveler Magellan. It was he who suggested that the planet is round.

First discoveries

The earth is a physical body that has certain properties, among which there is weight. This discovery allowed the start of a variety of studies. According to physical theory, weight is the force of the body on the support. Considering that the Earth has no support, we can conclude that it has no weight, but there is mass, and it is large.

Earth weight

For the first time, Eratosthenes, an ancient Greek scientist, tried to determine the size of the planet. In different cities of Greece, he took measurements of the shadow, and then compared the data obtained. Thus he tried to calculate the volume of the planet. After him, the Italian G. Galilei tried to carry out the calculations. It was he who discovered the law of free gravitation. The relay race to determine how much the Earth weighs was taken by I. Newton. Through attempts to make measurements, he discovered the law of gravity.

For the first time, the Scottish scientist N. Makelin managed to determine how much the Earth weighs. According to his calculations, the mass of the planet is 5.9 sextillion tons. Now this figure has increased. The differences in weight are due to the deposition of cosmic dust on the planet's surface. Roughly thirty tons of dust remain on the planet every year, making it heavier.

Earth mass

To find out exactly how much the Earth weighs, you need to know the composition and weight of the substances that make up the planet.

1. Mantle. The mass of this shell is approximately 4.05 X 10 24 kg.
2. Nucleus. This shell weighs less than the mantle - only 1.94 X 10 24 kg.
3. The earth's crust. This part is very thin and weighs only 0.027 X 10 24 kg.
4. Hydrosphere and atmosphere. These casings weigh 0.0015 X 10 24 and 0.0000051 X 10 24 kg, respectively.

Adding all this data, we get the weight of the Earth. However, according to different sources, the mass of the planet is different. So how much does planet Earth weigh in tons, and how much do other planets weigh? The weight of the planet is 5.972 X 10 21 tons. The radius is 6370 kilometers.

Based on the principle of gravity, the weight of the Earth can be easily determined. For this, a thread is taken, and a small load is suspended from it. Its location is precisely determined. A ton of lead is placed nearby. An attraction arises between the two bodies, due to which the load is deflected to the side by a small distance. However, even a deviation of 0.00003 mm makes it possible to calculate the mass of the planet. To do this, it is enough to measure the force of attraction in relation to the weight and the force of attraction of a small load to a large one. The data obtained make it possible to calculate the mass of the Earth.

Mass of the Earth and other planets

The Earth is the largest planet of the terrestrial group. In relation to it, the mass of Mars is about 0.1 Earth's weight, and Venus is 0.8. is about 0.05 of the earth. Gas giants are many times larger than Earth. If we compare Jupiter and our planet, then the giant is 317 times larger, and Saturn is 95 times heavier, Uranus is 14. There are planets that weigh 500 times or more than the Earth. These are huge gaseous bodies located outside our solar system.

On average, the Earth weighs about 5,976 sextillion tons. This number contains 21 decimal places - if you visualize such a figure, then the number of zeros will charge your eyes! At the same time, determining the mass of the Earth is not as easy as, say, the weight of a watermelon. After all, it is impossible to take and weigh the whole planet on the scales! So how much does the Earth weigh? Many centuries passed before scientists found the answer to this question.

Understanding the parameters of the Earth - a little history

At the dawn of humanity, there were their own concepts of the size, shape and mass of the Earth. In the view of ancient people, the model of the Earth resembled a hemisphere ("flat plate"), placed on three whales and a huge turtle, standing at the very base of this pyramid of the universe. Alternatively, elephants could act instead of whales. Be that as it may, in ancient times there was a common opinion - the Earth was flat and had its own edge.

During the Middle Ages, ideas about the shape and weight of the Earth underwent the first progressive changes. The discoverer of the spherical shape of the Earth was Giordano Bruno, who was sent to the fire of the Inquisition for his beliefs. Another significant contribution to earth science was made by the around-the-world traveler Magellan, who in practice confirmed the theory that the earth is round.

How much does our Earth weigh - the first discoveries

So, the Earth is a physical body and has certain properties, the main of which is weight. This discovery of medieval scholars gave rise to a number of scientific discoveries and research. How much does the Earth weigh? According to the laws of physics, weight is the force that a body exerts on a support. However, the Earth has no physical support. It turns out that the Earth has no weight either. But there is a lot, and what a lot!

How much does the Earth weigh in kg?

For the first time, the ancient Greek scientist Erastosthenes tried to determine the size of the Earth. Measuring the shadow with a stick in different cities of Greece and comparing the results, Eratosthenes obtained a formula for calculating the volume of the Earth.

It is interesting!

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Then there was the famous Italian physicist, mechanic and astronomer Galileo Galilei, who discovered the law of free fall in the 17th century. Isaac Newton took the baton of great discoveries, thanks to whom the world learned about the law of gravity. So, according to this law, the force of attraction of two bodies is directly proportional to their mass and inversely proportional to the square of the distance between them.

Now all that remains is to use the formulas and calculate how much the Earth weighs. For the first time, the mass of the Earth was determined by the Scottish doctor N. Makelin in 1774. According to the results of calculations, the mass of the planet was 5.879 sextillion tons. However, at present this figure has slightly increased - up to 5.976 sextillion tons.

The earth weighs about 5,976 sextillion tons.

However, these discrepancies are in no way evidence of inaccuracies in the calculations of the medieval scientist. On the contrary, these measurements are striking in their accuracy, and the discrepancy between the indicators is explained by the constant increase in the mass of our Earth due to the settling of cosmic dust. Every year the Earth gets heavier by about 30,000 tons!

By the way, based on the principle of gravity, the weight of the Earth can be measured quite simply. We hang a small weight on the thread and measure its exact position. We have a ton of lead nearby. The mutual attraction between the two bodies will cause the small weight to tilt slightly to the side - less than 0.00002 mm. This is a very small value, but it can be used to calculate the mass of the Earth. It is enough to measure the force of gravity in relation to the weight and the force of attraction of a small weight to lead. Based on the resulting relative difference, the Earth's mass can be calculated.

Earth mass distribution

It is known that our planet is heterogeneous in composition. So, here is the approximate distribution of the total mass of the Earth (in decreasing order):

• The mantle is a shell consisting of iron, calcium and magnesium silicates. Its mass is 4.043 x 10 24 kg
• The core, which includes iron and nickel - about 1.93 x 10 24 kg
• The earth's crust, which is the habitat of humanity - 0.026 x 10 24 kg
• Hydrosphere - it accounts for about 0.0014 x 10 24 kg
• Atmosphere occupies approximately 0.0000051 x 10 24 kg

How much does the Earth weigh - compared to other planets?

Our Earth is the largest among the planets Terrestrial group... For example, the mass of Mars is about 0.108 Earth's weight, Venus's is 0.815, and Mercury's is 0.055.

But the gas giant planets are many times larger than the Earth and just as much heavier. Compared to Jupiter, our planet is 317.8 times lighter - however, this "giant" is far from any other "inhabitant" Solar system... For comparison: Saturn is 95.1 times heavier than Earth, Neptune is 17.2 times, Uranus is 14.5 times.

Now we know how much the Earth weighs, as well as the ratio of its mass to the weight of other planets in the solar system.

To measure the globe, you need to know the value of its radius or the length of its great circumference, for example, by measuring the distance traveled in a round-the-world trip along the equator or meridians. But such travels were expensive and in ancient times were technically unfeasible.

In the III century BC. e. the Greek scientist Eratosthenes invented a surprisingly simple way of measuring the Earth, which is still used today. If it is already known that the Earth is a sphere, then it is not necessary to measure the entire length of its circumference. It is enough to measure the length of only a small arc of a circle and determine how much of it is from the entire circle, that is, what part of 360 degrees is the angle between the radii drawn through the ends of the arc. The direction along the radius on a spherical, non-rotating planet coincides with the direction of gravity and is determined by the direction of the plumb line in space in relation to the stars, for example, the North Star. Thus, to calculate the radius of the Earth, you need to measure the distance between any points on level ground along the meridian and measure the angle between the directions of the plumb lines at these points.

Eratosthenes measured the angles between the direction to the Sun and the directions of the plumb lines in Alexandria and Siena. Dividing the distance between these cities by the angle between the plumb lines in radians, he determined the radius of the Earth at 6000-7000 kilometers. Measurements by Arab scientists in the 7th century AD e. clarified the value of the Earth's radius to 6400 kilometers.

Distances that are inaccessible for direct measurement in geodesy and astronomy are calculated based on the property of a triangle: from a known side and two adjacent angles, all sides of a triangle can be calculated.

When linear and angular measurements were made in many places on the earth's surface, it turned out that the radius of curvature of the surface is not the same everywhere. The earth is not an exact ball, but due to rotation it is flattened from the poles. On average, our planet can be thought of as an ellipsoid of revolution with an equatorial radius of 6378 kilometers and a polar radius of 6357 kilometers.

In addition to the described geodetic method for studying the shape of the Earth, gravimetric and astronomical methods are currently used. Due to the flattening of the Earth, the equator has excess mass compared to the pole. Therefore, the force of gravity is directed not exactly to the center of the Earth, but somewhat to the equator. The magnitude of this force at the equator is less than at the pole, due to the greater distance to the center. Consequently, the shape of the Earth can be studied by the magnitude and direction of the force of attraction at different points on the earth's surface, that is, by the gravimetric method.

Gravimetric and astronomical methods, in addition to the shape of the Earth, also measure its mass. According to Newton's law of gravity, the force of attraction of any two bodies is proportional to the product of their masses and inversely proportional to the square of the distance. After measuring the gravitational force of two test balls in a laboratory on a torsion balance, the scientists calculated a proportionality coefficient called the gravitational constant.

The acceleration with which bodies fall to the Earth at the poles is caused only by universal gravity. Therefore, multiplying the acceleration of gravity by the square of the Earth's radius and dividing by the gravitational constant, we immediately find the mass of the Earth, equal to 6,000,000,000,000 billion tons. If you measure the acceleration not at the pole, but at an arbitrary latitude and make more accurate calculations, then you need to take into account the centrifugal force arising from the rotation of the Earth. The current value of the mass of the Earth is estimated at 5,976,000,000,000 billion tons.

Nowadays, gravimetric and astronomical measurements of the force of gravity on the surface and above the Earth continue in order to clarify the mass of the planet.

Knowing the size, shape, mass and gravitational field of the Earth helps calculate the trajectories of satellites and rockets.

A negative result for the value of the comet's closest distance from the Sun indicates the inconsistency of the initial data of the problem. In other words, a comet with such a short orbital period - 2 years - could not have moved as far from the Sun as indicated in the novel by Jules Verne.

How was the Earth weighed?

There is an anecdotal story about a naive person who was most surprised in astronomy by the fact that scientists learned what the stars are called. Seriously speaking, the most amazing achievement of astronomers should probably seem to be what they did. weigh and the Earth on which we live, and the distant heavenly bodies. Indeed: in what way, on what scales could the Earth and the sky be weighed?

Figure: 87. On what scales could the Earth be weighed?

Let's start by weighing the Earth. First of all, let us be aware of what should be understood by the words "the weight of the globe." We call the weight of the body the pressure that it exerts on its support, or the tension that it exerts on the weight point. Neither one nor the other is applicable to the globe: the Earth rests on nothing, is not suspended from anything. Hence, in this sense, the globe has no weight. What have scientists determined by "weighing" the Earth? They determined its mass. In fact, when we ask to weigh 1 kg of sugar for us in the shop, we are not at all interested in the force with which this sugar presses on the support or pulls the weight gain. In sugar, we are interested in something else: we only think about how many glasses of tea you can drink with it, in other words, we are interested in the amount of the substance contained in it.

But there is only one way to measure the amount of matter: to find with what force the body is attracted by the Earth. We assume that equal amounts of matter correspond to equal masses, and we judge the mass of a body only by the force of its attraction, since attraction is proportional to the mass.

Moving on to the weight of the Earth, we say that its "weight" will be determined if its mass becomes known; So, the problem of determining the weight of the Earth must be understood as the problem of calculating its mass.

Figure: 88. One way to determine the mass of the Earth: Yolly scales

Let us describe one of the ways to solve it (Yolly's way, 1871). In fig. 88 you see a very sensitive pan scale in which two light cups are suspended from each end of the rocker: an upper and a lower one. The distance from the top to the bottom is 20–25 cm. On the lower right cup we put a spherical weight with a mass m v For balance, put a weight on the upper left cup t t These weights are not equal, since, being at different heights, they are attracted by the Earth with different strengths. If you put a large lead ball with mass under the lower right cup M,then the balance of the weights will be violated, since the mass m l will be attracted by the mass of the lead ball Mwith force F v proportional to the product of these masses and inversely proportional to the square of the distance d,separating their centers:

where to -the so-called constant of gravitation.

To restore the disturbed balance, put on the upper left pan of the balance a small weight with a mass p.The force with which he presses on the scale is equal to his weight, that is, equal to the force of attraction of this weight by the mass of the entire Earth. That power Fequals

Ignoring the negligible effect that the presence of a lead ball has on the weights lying on the upper left cup, we can write the equilibrium condition as follows:

In this ratio, all quantities, except for the mass of the Earth

Can be measured. From here we define

In the experiments mentioned, M \u003d5775.2 kg, R \u003d6366 km, d \u003d56.86 cm, m 1 = 5.00 kg and n \u003d589 mg.

As a result, the mass of the Earth turns out to be 6.15 x 10 27 g.

The modern definition of the mass of the Earth, based on a large number of measurements, gives

5.974 x 10 27 g, i.e. about 6 thousand trillion tons. Possible error in determining this value is not more than 0.1%.

So, astronomers have determined the mass of the globe. We have every right to say that they weighed the Earth, because every time we weigh a body on a lever balance, we, in essence, determine not in it, not the force with which it is attracted by the Earth, but the mass: we establish only that the body weight is equal to the weight of the weights.

What are the bowels of the Earth made of?

It is appropriate to note here a mistake that one has to meet in popular books and articles. In an effort to simplify the presentation, the authors present the matter of weighing the Earth as follows: scientists measured the average weight of 1 cm 3 of our planet (i.e., its specific gravity) and, having calculated geometrically its volume, determined the weight of the Earth by multiplying its specific gravity by volume. The indicated path, however, is impracticable: it is impossible to directly measure the specific gravity of the Earth, since only its relatively thin outer shell is available to us and nothing is known about what substances the rest, a much larger part of its volume consists of.

We already know that it was just the opposite: the determination of the mass of the earth preceded the determination of its average density. It turned out to be 5.5 g per 1 cm 3 - much more than the average density of the rocks that make up the earth's crust. This indicates that very heavy substances lie in the depths of the globe. According to their supposed specific gravity (as well as for other reasons), they used to think that the core of our planet consists of iron, strongly compacted by the pressure of the overlying masses. It is now believed that, in general, the central regions of the Earth do not differ in composition from the crust, but their density is greater due to the tremendous pressure.

Weight of the sun and moon

Oddly enough, the weight of the distant sun turns out to be incomparably easier to determine than the weight of the moon much closer to us. (It goes without saying that we use the word "weight" in relation to these luminaries in the same conventional sense as for the Earth: we are talking about determining mass.)

The mass of the Sun is found by the following reasoning. Experience has shown that 1 g attracts 1 g at a distance of I cm with a force equal to 1 / 15,000,000 mg. Mutual attraction f two bodies with masses Mand ton distance Dexpressed according to the law of universal gravitation as follows:

If a M -mass of the Sun (in grams), t -the mass of the earth, D -the distance between them is equal to 150,000,000 km, then their mutual attraction in milligrams is equal to (1/15,000,000) x (15,000,000,000,000 2) mg On the other hand, this force of attraction is the centripetal force that holds our planet in its orbit and which, according to the rules of mechanics, is (also in milligrams) mV 2 / D, where t -the mass of the Earth (in grams), V -its circular velocity equal to 30 km / s \u003d 3,000,000 cm / s, a D -distance from the Earth to the Sun. Hence,

The unknown is determined from this equation M(expressed, as said, in grams):

M \u003d 2x10 33 r \u003d 2x10 27 t.

Dividing this mass by the mass of the globe, i.e., calculating

we get 1/3 million.

Another way to determine the mass of the Sun is based on the use of Kepler's third law. The third law is derived from the law of universal gravitation in the following form:

- the mass of the Sun, T -the stellar period of the planet's revolution, and -the average distance of a planet from the Sun is the mass of the planet. Applying this law to the Earth and the Moon, we get

Substituting known from observations

and neglecting in the first approximation in the numerator the mass of the Earth, which is small in comparison with the mass of the Sun, and in the denominator, the mass of the Moon, which is small in comparison with the mass of the Earth, we obtain

Knowing the mass of the Earth, we get the mass of the Sun.

So, the Sun is a third of a million times heavier than the Earth. It is not difficult to calculate the average density of the solar ball: for this you only need to divide its mass by volume. It turns out that the density of the Sun is about four times less than the density of the Earth.

As for the mass of the moon, then, as one astronomer put it, "although it is closer to us than all other celestial bodies, it is more difficult to weigh it than Neptune, the most distant (then) planet." The moon does not have a satellite that would help calculate its mass, as we have now calculated the mass of the sun. Scientists had to resort to other, more complex methods, of which we will mention only one. It consists in comparing the height of the tide produced by the sun and the tide generated by the moon.

The height of the tide depends on the mass and distance of the body that generates it, and since the mass and distance of the Sun are known, the distance of the Moon is also known, the mass of the Moon is determined from the comparison of the height of the tides. We will come back to this calculation when we talk about tides. Here we will report only the final result: the mass of the Moon is 1/81 of the mass of the Earth (Fig. 89).

Knowing the diameter of the moon, we calculate its volume; it turns out to be 49 times smaller than the volume of the Earth. Therefore, the average density of our satellite is 49/81 \u003d 0.6 of the Earth's density.

Figure: 89. The Earth "weighs" 81 times more than the Moon

This means that the Moon, on average, consists of a looser substance than the Earth, but denser than the Sun. Further we will see (see the plate on page 199) that the average density of the Moon is higher than the average density of most planets.

Weight and density of planets and stars

The way in which the Sun was "weighed" is applicable to the weighing of any planet that has at least one satellite.

Knowing the average speed v of the satellite in orbit and its average distance Dfrom the planet, we equate the centripetal force holding the satellite in its orbit, mv 2 / D, to the force of mutual attraction of the satellite and the planet, i.e. kmM / D 2, where to -force of attraction 1 g to 1 g at a distance of 1 cm, m -the mass of the satellite, M -planet mass:

This formula is easy to calculate the mass Mplanets.

Kepler's third law applies to this case as well:

And here, neglecting the small terms in brackets, we get the ratio of the mass of the Sun to the mass of the planet

Knowing the mass of the Sun, one can easily determine the mass of the planet.

A similar calculation is applicable to binary stars with the only difference that here, as a result of the calculation, not the masses of individual stars of a given pair are obtained, but the magnitude of their masses.

It is much more difficult to determine the mass of the satellites of the planets, as well as the mass of those planets that do not have satellites at all.

For example, the masses of Mercury and Venus were found by taking into account the disturbing influence that they have on each other, on the Earth, as well as on the motion of some comets.

For asteroids, the mass of which is so insignificant that they do not exert any noticeable disturbing effect on one another, the problem of determining the mass, generally speaking, is insoluble. Known only - and then guessingly - the upper limit of the total mass of all these tiny planets.

By the mass and volume of the planets, their average density is easily calculated. The results are summarized in the following table:

We see that our Earth and Venus are the densest of all the planets in our system. The low average densities of large planets are explained by the fact that the solid core of each large planet is covered with an enormous layer of the atmosphere, which has a low mass, but greatly increases the apparent volume of the planet.

Weight on the moon and on planets

People who are poorly read in astronomy often express amazement that scientists, without visiting the moon and planets, confidently speak about the force of gravity on their surface. Meanwhile, it is not at all difficult to calculate how many kilograms a weight transferred to other worlds should weigh. To do this, you just need to know the radius and mass of a celestial body.

Let's define, for example, the tension of gravity on the Moon. The mass of the Moon, as we know, is 81 times less than the mass of the Earth. If the Earth had such a small mass, then the tension of gravity on its surface would be 81 times weaker than it is now. But according to Newton's law, the ball attracts as if all its mass is concentrated in the center. The center of the Earth is spaced from its surface at the distance of the Earth's radius, the center of the Moon is at the distance of the lunar radius. But the lunar radius is 27/100 of the Earth's, and from a decrease in the distance by 100/27 times, the force of attraction increases by (100/27) 2 times. This means that ultimately the stress of gravity on the surface of the Moon is

So, a 1 kg weight transferred to the surface

The moon would have weighed only 1/6 kg there, but, of course, the decrease in weight could only be detected with the help of spring scales (Fig. 90), and not lever ones.

Figure: 90. How much would a person weigh on different planets. The weight of a person on Pluto is not 18 kg, but only 3.6 kg (according to modern data)

It is curious that if water existed on the moon, a swimmer would feel in a lunar reservoir just like on Earth. Its weight would decrease six times, but the weight of the water displaced by it would also decrease by the same amount; the ratio between them would be the same as on Earth, and the swimmer would submerge in the water of the moon exactly as much as he submerges with us.

However, efforts to rise above water would give a more noticeable result on the moon: since the swimmer's body weight has decreased, it can be lifted with less muscle tension.

Below is a table of the magnitude of gravity on different planets compared to the earth.

As can be seen from the tablet, our Earth in terms of gravity is in fifth place in the solar system after Jupiter, Neptune, Saturn and Uranus.

Record severity

The force of gravity on the surface of those "white dwarfs" such as Sirius reaches the greatest magnitude. IN,which we talked about in chapter IV. It is easy to understand that the huge mass of these luminaries with a relatively small radius should cause a very significant tension of gravity on their surface. Let's make a calculation for that star of the constellation Cassiopeia, the mass of which is 2.8 times the mass of our Sun, and the radius is half the radius of the Earth. Recalling that the mass of the Sun is 330,000 times greater than that of the Earth, we establish that the force of gravity on the surface of the said star exceeds that of the Earth by

2,8 330 000 2 2 \u003d 3,700,000 times.

1 cm 3 of water, weighing 1 g on Earth, would weigh almost 3 3/4 tons on the surface of this star! 1 cm 3 of the substance of the star itself (which is 36 million times denser than water) should have a monstrous weight in this wonderful world

3,700,000 36,000,000 \u003d 133,200,000,000,000

A thimble of matter weighing one hundred million tons is a curiosity, the existence of which in the universe has not yet been thought of by the most daring science fiction writers.

The heaviness in the depths of the planets

How would the weight of the body change if it were transferred into the interior of the planet, for example, to the bottom of a fantastic deep mine?

Many people mistakenly believe that at the bottom of such a shaft the body should become heavier: after all, it is closer to the center of the planet, that is, to the point to which all bodies are attracted. This consideration, however, is incorrect: the force of attraction to the center of the planet does not increase at depth, but, on the contrary, weakens. The reader can find a generally understandable explanation of this in my "Entertaining Physics". In order not to repeat what was said there, I will only note the following.

In mechanics, it is proved that bodies placed in a cavity of a homogeneous spherical shell are completely devoid of weight (Fig. 91). It follows from this that a body inside a solid homogeneous sphere is subject to the attraction of only that part of the substance that is enclosed in a ball with a radius equal to the distance of the body from the center (Fig. 92).

Figure: 91. The body inside the spherical shell has no weight

Figure: 92. What determines the weight of a body in the bowels of the planet?

Figure: 93. To calculate the change in body weight with approaching the center of the planet

Based on these provisions, it is not difficult to deduce the law according to which the body weight changes with approaching the center of the planet. Let us denote the radius of the planet (Fig. 93) through Rand the distance of the body from its center through r... The force of attraction of the body at this point should increase by (R / r) 2 times and simultaneously weaken by (R / r) 3 times (since the attracting part of the planet has decreased by the specified number of times). Ultimately, gravity must weaken in

This means that in the depths of the planets, the body weight should decrease as many times as the distance to abstract

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\u003e\u003e\u003e Earth mass

Find out for sure what is the mass of the earth - the third planet of the solar system. Description of the calculation formula, equation with components and the final result of the planet's mass.

Reaches the mark of 5.9736 x 10 24 kg. This is a large number, but in order for our brain to get into a state of shock, then in full - 5,973,600,000,000,000,000,000,000,000 kg. Wow!

How do you know the mass of the Earth?

But it’s more interesting to know how they were able to understand at all what mass of the Earth? It's all about the gravity that our planet exerts on nearby objects.

Physics tells us that any body with mass will attract. If you put two billiard balls next to each other, they will tend to the next one. This force is not noticeable to us, but the devices capture due to their sensitivity. This calculation will help you derive the mass of both.

Newton suggested that the mass of spherical objects is concentrated at their centers. Then you can use the equation:

F \u003d G (M1 * M2 / R 2).

• F is the force of gravity between them.
• G - constant \u003d 6.67259 × 10 -11 m 3 / kg s 2.
• -M1 and M2 are attracting masses.
• R is the distance between them.

Let's say that one of the masses is represented by the Earth, and the second will be a kilogram sphere. The force between them is 9.8 kg * m / s 2. The earth's radius is 6,400,000 m. If you add these values \u200b\u200bto the formula, you get 6 x 10 24 kg.

It is important to note that in the question it is correct to use the word "mass", and not "weight", because the last concept is the force that is needed to calculate the gravitational field. You can take a ball and weigh it on the Earth and the Moon, and the mark will change. But the mass is a stable number and the earth is constant.

It seems that this is a lot, but let's not forget that in our system there are objects even larger. For example, our star is 330,000 times the mass of the Earth, and Jupiter is 318 times. There are, of course, crumbs. So the Martian mass occupies only 11% of the earth's.

We were lucky because of the highest planetary density in the system - 5.52 g / cm 3. This value came from the metal core, around which a layer of rocky mantle is concentrated. Less dense planets such as giant Jupiter are hydrogen and other gases. Now you know what the mass of the earth is.