What is the mass of Earth? How was the weight of our planet calculated?

The mass of the Earth was determined with fair accuracy as early as the 17th century. However, it was only possible to precisely determine it for the first time on the basis of Cavendish’s experiment. What was it about?

What is the mass of the Earth?

The actual mass of the Earth can be difficult to visualize. Its latest estimates put this value at a colossal 5.9722⋅10²⁴ kg with a standard deviation of 6⋅10²⁰ kg. If the exponential notation does not tell you exactly how much the Earth weighs, it can also be written in full length as: 5,972,200,000,000,000,000,000,000,000 kg. That’s almost 6 quadrillion kilograms, or almost 6 trillion tons.

On an astronomical scale, such a result is nothing special – Jupiter is 318 times greater than Earth, and the Sun as much as 333,000 times. Still, this enormous weight is hard to compare with anything we know from everyday life. For example, the entire human population would have to be increased a hundred quadrillion times to come close to such a mass. No wonder – the average radius of the Earth is 6371 km, and its average density is 5513 kg / m³, which is the highest result in the Solar System.

Calculations of how much planet Earth weighs was initially based on attempts to determine density without access to precise measurement methods. There were also difficulties with imprecise estimates of the actual size of the planet. Sir Isaak Newton theorized that the earth’s density is about 5-6 times that of water. In his calculations, however, he used the size of the planet about 30% smaller than its real size. Nevertheless, the law of universal gravitation determined by him became the basis for more precise calculations.

Who was the first to calculate the mass of the Earth?

Henry Cavendish (1731-1810) was a British chemist and physicist – his achievements include determining the composition of air, water and nitric acid, as well as the release of hydrogen and carbon dioxide. He also conducted research on electricity (before Coulomb and Ohm), but they were not published during his lifetime. In an experiment carried out in the years 1797-1798, he managed to determine the precise value of the gravity constant in Newton’s formulas.

Cavendish’s experiment used a device called a twist scale. It consisted of a horizontally placed wooden beam 6 feet long. Suspended from its ends were small lead balls, two inches in diameter. This whole arrangement was hanging on a wire. Two larger spheres were placed nine inches from the small spheres, twelve inches in diameter and weighing more than 150 kg. The force of attraction between the pairs of lead sinkers caused the arm to rotate, on which the smaller ones hung.

Knowing the twist angle and the moment of force necessary to cause it, it was possible to determine the strength of the interaction of pairs of spheres. However, the instrument was extremely sensitive to external factors that made measurements difficult, such as wind, mass of nearby bodies or vibrations of the ground. The weight of the twists was therefore sealed and placed inside the shed. Cavendish made his observations through two small holes in the walls. For this purpose, he used a telescope, the vernier of which allowed for precise measurement of angles.

The study was complicated by the fact that the system remained in continuous, albeit insignificant, oscillation. Its duration was about 20 minutes and the amplitude was only 4 mm. The force responsible for torsion of the system was set at 1.74⋅10^-7 N, which translates into the density of the Earth – 5448 kg / m³ – which is an underestimation of only 1% in relation to the currently measured values. The same difference exists between the current gravity constant and that calculated using Cavendish’s earth density.

Although Cavendish’s experiment is repeated on a regular basis, it is not the only method of determining Earth’s density. The fact that the planet, like all other objects in the solar system, orbits the sun is used more often. Knowing its mass, orbital radius and orbital period, you can calculate how much the Earth weighs. It also works the other way around. Thanks to laser techniques for measuring distance to satellites (SLR) and the moon (LLR), based on the parameters of the orbit and the mass of an object orbiting the planet, its weight can also be determined.

Is the Earth gaining or losing mass?

Humans have little influence on how much the Earth weighs. The mass of the planet remains virtually unchanged, regardless of how much mineral resources have been mined in one place and used for construction elsewhere, or how much fossil fuels have been used by transport or energy. With a few exceptions, such as the sending of space probes, everything that humanity uses of Earth’s resources is still there. The impact of changing the distribution of these masses – for example, extending the day after the activation of the Three Gorges Dam – is a separate issue.

There are two main factors that determine whether the Earth is gaining or losing weight. Every year, about 45,000 tons of materials from space – mainly dust and meteorites – fall into the planet’s atmosphere. At the same time, the lightest elements are escaping into space – about 1,600 tons of helium and 95,000 tons of hydrogen per year. In total, the Earth loses 54,000 tons of weight each year. However, such a small change is in no way felt by its inhabitants. The effect on orbital motion also remains too small to be measured.

From the earliest times, scientists and ordinary people have been fascinated by the Earth. How much does it weigh and does this weight change? Thanks to Cavendish’s experiment, drawing on Newton’s law of universal gravitation, the answer to the first question is known – almost 6 trillion tons. The second issue has also been resolved relatively precisely. It is known that the Earth loses 54,000 tons of weight each year. There are also more and more precise methods of determining the weight of our planet, using the latest technology.

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