The molar mass of the earth is How much does the earth weigh? Law of gravity

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Find out exactly what is the mass of the earth is the third planet in the solar system. Description of the calculation formula, equation with components and the final result of the mass of the planet.

Reaches a 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 form - 5,973,600,000,000,000,000,000,000,000 kg. Wow!

How to find out the mass of the Earth?

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

Physics tells us that any body with mass attracts. If you put two billiard balls side by side, 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 to 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 = 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 attracted 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 to the formula, you get 6 x 10 24 kg.

It is important to note that it is correct to use the word "mass" in the question, and not "weight", because the latter concept is the force that is needed to calculate the gravitational field. You can take the 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's is constant.

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

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

First determined weight of planet earth in 1798 the famous English scientist Cavendish(1731–1811). He took advantage of Newton's law of gravitation and for the first time used a device, simple in concept, called a torsion balance to weigh the Earth. Henry Cavendish - the first to determine the weight of the planet Earth using a torsion balance. The principle of these balances is the basis of the modern gravitational variometer. This device has exceptionally high sensitivity and is widely used in geo-prospecting.

Dimensions of the planet Earth

The Earth is a relatively large world (celestial) body. Dimensions of the planet Earth are:

polar radius- 6 thousand 357 kilometers,
equatorial radius a little over 6 thousand 378 kilometers,
polar diameter 12 thousand 714 kilometers,
equatorial diameter 12 thousand 757 kilometers,
meridian length, i.e., a circle drawn through both poles, 40 thousand 4 kilometers;
equator length 40 thousand 75 kilometers;
surface of the entire globe about 510 million square kilometers;
of them sushi about 148 million kilometers,
seas and oceans about 362 million square kilometers;
volume of the entire Earth is 1 billion 83 billion cubic kilometers,
density Earth is 5.5 times the density of water,
weight of planet earth about 6 thousand trillion tons, more precisely 5,989,000,000,000,000,000,000 tons.

If it were possible to immerse the entire mass of the Earth into wagons, loading 50 tons each, then we would get a train set that is 8 billion times longer than the distance from the Earth to the Sun. That's how big and heavy our Earth is!

Density of planet Earth

Medium density of planet earth 4 times the average density of the Sun and 5.5 times denser than water. Individual metals found in the bowels of the Earth have an even greater density. For example, platinum is 21 times denser than water. However, the density of platinum is not so great, if we take into account that among the world bodies there are those whose density seems to us absolutely incredible.

Density of other planets

Density the satellite of Sirius is 40 thousand times the density of water. If you fill a matchbox with the substance of this star and put it on a scale pan, then in order to bring the scales into balance, 15 people must be placed on another scale pan. Even more astonishing density is the small star discovered by the astronomer Kiner. The substance of this star is 10 thousand times denser than platinum. A matchbox filled with this substance will weigh about 50 tons! Try putting this box in your pocket! However, it should be pointed out that among the stars there are also those whose average density is 100 times less than the density of the air surrounding us. That's how different the density of stars is.

Law of gravity

When it became known that our planet is limited in space from all sides, the question was involuntarily raised, on what, after all, does it "hold" in the abyss of space. What force keeps it in its orbit? This question remained open for a long time. For several centuries, no one could solve it. Finally, the brilliant mathematician, mechanic, physicist and astronomer, the great (1643–1727) discovered law of gravity. Newton proved that all bodies located in the space of the Universe are mutually attracted to each other, (more:). The force of attraction of any two bodies is the greater, the smaller the distance between them and the greater their mass. More precisely, Newton's law reads as follows: every material particle attracts another material particle with a force directly proportional to their masses and inversely proportional to the square of the distance between them.

Isaac Newton - discovered the law of universal gravitation. Consequently, in order to keep all the planets in their orbits, the central body of the system, around which all the planets move (including our Earth), must have a gigantic mass. Indeed, the mass of the Sun, the central body of the planetary system, is 750 times greater than the mass of all the planets and their satellites and more than 330,000 times greater than the mass of the Earth. The Sun holds the planets in their orbits by its gravity.. If there were no attraction of the planet to the Sun, then the planet P, moving, for example, in the direction of PC, would move in this direction rectilinearly and uniformly (according to the law of inertia). In the first second, it would move from point P to point K and, finally, it would leave the solar system. On the contrary, if the planet experienced only attraction to the Sun, then in the first second it would move from point P to point L. But since this world body is simultaneously attracted to the Sun and moves, it will move along the diagonal of the PA parallelogram built on these movements. Consequently, the planet at the end of the first second will not be at point K or at point L, but will move diagonally to point A. Arguing in a similar way, we will conclude that the planet will move to point B in the second second, in the third second - to point B, etc. It turns out that in the silence of the immeasurable abysses of world space, what force constantly carries away our Earth and other planets without the slightest pushes and tremors around the Sun. Many of you probably had the pleasure of twirling a rubber band in your hands with a pebble tied to its end as a child. When rotating, the rubber band is always in a state of tension, but as soon as you stop rotating it, immediately it contracts, and the pebble approaches the hand. In the event that the rubber band suddenly breaks out of the hands, the pebble with the rubber band will immediately fly away. Something similar would happen to the planets if the Sun suddenly stopped attracting them.

Science is fraught with a huge number of various interesting facts. About one of them now I want to talk. We will talk about how much is the mass of the Earth and how it was possible to calculate it.

pioneers

At the very beginning, it is worth telling that for the first time the interesting figures about the mass of the Earth were obtained by Nevil Makelin from the Scottish town of Perthshire back in the distant 18th century, namely in 1774. As a result of his calculations, the Scottish scientist determined that the mass of the Earth is 5,879,000,000,000,000,000,000 tons. How to pronounce this number correctly? So, this is 5879 sextillion tons.

About modernity

It is definitely worth mentioning that these figures haunted scientists for a long time. Did Makelin calculate everything correctly, is it possible that his calculations turned out to be erroneous? So, modern physicists decided to double-check this and submitted their calculations for discussion. According to their calculations, the mass of the planet Earth is 5,976,000,000,000,000,000,000, i.e. 5976 sextillion tons. This is only some 97 sextillion tons more than previous results. However, not so much. In addition, the fact that the weight of the Earth is constantly increasing will be important. It's all the fault of cosmic dust (according to some, but not all scientists), which every minute settles on the surface of our planet, giving it extra weight.

About measurements

Many people may have a logical question: "But how can you measure the mass of the Earth, because you can't just take it and put it on a huge scale?" However, scientists were not afraid of difficulties and took as a basis the gravitational field, which causes objects to attract each other. All calculations were obtained experimentally. First, a small weight was suspended on a thread, the position of which in space was measured. Further, next to this load, scientists placed a rather weighty lead cube that weighed a ton (after all, everyone knows that the heavier the object, the stronger its gravitational field attracts surrounding objects). In the course of this experiment, the gravitational field of a huge lead cube pulled a small weight towards itself by only 0.00002 millimeters, but this was enough for scientists to calculate the mass of planet Earth, obtaining such desired numbers.

About extension

As mentioned above, the mass of the Earth is constantly increasing. However, it is worth saying that our planet is also expanding. After all, how can one explain the fact that all the continents can be put together without any problems, like one big puzzle? Maybe this means that they were all once connected, and then dispersed? It is worth mentioning that for the first time the theory of the expansion of the Earth was discussed back in 1889 by the scientist I.O. Yurkovsky. And, although there was no confirmation of this at that time, these thoughts did not disappear without a trace and from time to time visited the most diverse scientists around the world.

About formula

There is a fairly simple formula that relates the force of gravity on the Earth, its mass, and also the distance of its surface from the center. In the literal version, this will look like the ratio of the mass of the Earth and the square of the distance from its center to the surface.

If it can be proved that the force of gravity decreases with time, then it can be proved that the increase in the planet was due to an increase in its volume. The mass, however, remained unchanged.
However, if we prove that the force of gravity increases with time, then the following conclusion is logical: the whole point is the increase in the mass of the Earth.

About calculations

It is also worth mentioning that today the mass of the Earth can be calculated even by a schoolboy on his own at home. To do this, you just need to know the above formula: g \u003d φ (M / R 2). First of all, you need to extract mass from it. Thus, by simple configurations, we obtain the following relation: M = g R 2 / φ. At the same time, the radius of the earth is already known, it does not need to be calculated, it is 6300 km (in meters - 6.38x10 6). Numerical versions of g and φ were obtained long ago experimentally. So, thanks to fairly simple mathematical operations, you can get the desired figure, which is equal to 5976 sextillion tons.

Development of events

So does the mass of the Earth increase with time? Yes! And this has been proven by modern scientists. Over 50 years of observation in Washington, gravity has increased from 980,098 to 980,120 milligals. As for Central Asia, these indicators were as follows: on average, the force of gravity here increased by about 0.05-0.10 milligals per year. However, how much is it, a lot or a little? If you look at the received figures for years and even centuries, then this is very small. However, if we recalculate these indicators for millions of years? The scientists did it too. So, for a hundred million years on the surface of the Earth, gravity has increased by about 2.5 times. At the same time, the radius of our planet has doubled! The following fact will be interesting: even 600 million years ago, our planet was about 6-8 times smaller than its modern version. Has its mass changed? Scientists still do not have a definite answer to this question. Dust from outer space falls to Earth, that's for sure. But no one knows yet how much the planet loses in this case.

What happened?

However, how has the weight of our planet changed since its formation? Scientists managed to find out that the mass of the Earth at the first stages of its origin was 99 times less than its current version. To explain everything is simple: even before the moment when the atmosphere arose on Earth and it became habitable, our planet was constantly attacked by giant asteroids. Scientists believe that it was only thanks to such a “shelling” that the Earth lost unnecessary excess weight and thus became habitable. And all because these bombardments brought the core of the planet into a “working” state, turning on the global process within the planet itself.

Henry Cavendish Method

It is worth saying that the mass of the Earth was of interest to many different scientists. One of them is Henry Cavendish, who tried to get these figures by measuring the gravitational constant using a device such as a torsion balance. What conclusion did he come to in the end? So, the results will be very interesting. The scientist said that the mass of the planet Earth is zero, since it is in a state of free fall, and the gravity that acts on it from other space objects is mutually balanced and does not at all lead to a change in the position of the Earth on the trajectory of its "fall".

Comparison: Sun

Everyone knows that our planet is part of the solar system, in the center of which is the star Sun. It is also worth mentioning that this is the largest body in this system, around which all the planets revolve. The following fact will be very informative: the mass of the Sun is approximately 99.866% of the mass of the entire solar system! I also want to know how much this star is larger than our home planet? You can find out with simple calculations. If the mass of the Sun is 2 trillion quadrillion tons, and the mass of the Earth, as mentioned above, is almost 6 sextillions, then the difference will be quite impressive. The center of our system - the Sun - is larger than the planet Earth by about 333,000 times!

Comparison: Moon

It is also worth considering some other figures. Interestingly, how many times the mass of our planet is greater than the mass of the Moon, our constant satellite? This figure is 81.3. This value was adopted as a constant in 1964 by the International Astronomical Union. It is imperative to clarify that this fact was once again confirmed in 1966.

Planet Earth is the third largest planet in the solar system. It is also the largest in terms of mass, diameter and density among the terrestrial planets (this includes Venus, Mercury, Earth and Mars). However, the Earth, for example, is 14 times smaller in mass than another gas planet - Uranus.

Few today know what is the mass of our huge and immense planet, while scientists have long calculated it. It is equal to 5.98 10 24 kilograms.

In our article, we will describe in detail what the mass of the Earth is and how it is calculated.

Gravity, mass and weight

Gravity, mass and weight are one of the basic physical quantities, however, many people confuse these concepts. It is necessary to clarify the meaning of each of them.

Gravity is a force that acts on any body located near the surface of the earth or relative to another body. In other words, gravity is the force with which bodies are attracted to the surface of the Earth;
Weight is the physical force or amount with which a body acts on a support. Suppose if a body is at rest on the surface of the earth, then weight is nothing but the force with which this body acts on the surface. The basic unit of measurement is newtons;
Body mass is a measure that measures the ability of any material body to gravitational interaction. It is measured in grams, kilograms, centners, tons. Gravitational attraction or interaction, in turn, underlies the universal gravitation discovered by I. Newton.

Mass of the Earth

Measuring the mass of the Earth is a long historical process, to which the minds of many of the greatest scientists have applied. The dimensions of our planet were first discovered by Eratosthenes around 240 BC. e.

For many centuries, Ptolemy's geocentric system dominated physics and astronomy, according to which the Earth was located at the center of the solar system. Only after the discovery by N. Copernicus, I. Kepler, G. Galileo and others did a detailed study of the parameters of the planet Earth begin. The basic laws of dynamics were discovered - the laws of I. Newton, which laid the foundation for measuring the mass of the Earth.

The mass of the Earth was first measured in the 18th century by the British chemist G. Cavendish. For his experiment, he used a torsion balance setup with lead balls tied at the ends. Alternately bringing two large lead balls to these balls, the scientist determined how many times the force of attraction of a small ball to a large one differs from the force of attraction of the Earth. The mass of the Earth, according to the calculations, turned out to be 6·10 21 kilograms. Such a number is very close to the value of the mass of the Earth, accepted already in our time, it is approximately 5.98·10 24 kilograms.

The formula for calculating the Earth according to the basic laws of dynamics is as follows:

M = q r 2 /G, where:

q - gravitational acceleration or gravitational acceleration, given to the body by gravity. It is measured in meters per second and depends primarily on the latitude and time of day on the surface of planet Earth. In physics, the number 9.8 is taken as gravitational acceleration;

On average, the Earth weighs about 5.976 sextillion tons. This number contains 21 decimal places - if you visually imagine 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 simple 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 bit of history

At the dawn of mankind, there were their own concepts about 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, instead of whales, elephants could act. Be that as it may, in ancient times there was a consensus - the Earth was flat and had its edge.

In 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 stake of the Inquisition for his beliefs. Another significant contribution to the science of the Earth was made by 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 scientists gave rise to a number of scientific discoveries and studies. How much does the Earth weigh? According to the laws of physics, weight is the force exerted by a body on a support. However, the Earth is not supported in the physical sense. It turns out that the Earth has no weight. But the mass is, and even what!

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. By measuring the shadow in different cities of Greece with a stick 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. The baton of great discoveries was taken over by Isaac Newton, thanks to whom the world learned about the law of gravity. So, according to this law, the force of attraction between two bodies is directly proportional to their mass and inversely proportional to the square of the distance between them.

Now it remains only 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 increased slightly - 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 a 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 becomes heavier by about 30,000 tons!

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

Earth mass distribution

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

The mantle is a shell consisting of silicates of iron, calcium and magnesium. 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 mankind - 0.026 x 10 24 kg
Hydrosphere - it accounts for about 0.0014 x 10 24 kg
The atmosphere occupies approximately 0.0000051 x 1024 kg

How much does the Earth weigh compared to other planets?

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

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