How heavy is the Earth?

It took experts hundreds of years to estimate the mass of the Earth and to this day there is no consensus on the exact figure.

It is very difficult to calculate the exact mass of the Earth. Photo: Science Times — It is very difficult to calculate the exact mass of the Earth. Photo: *Science Times*

The Earth contains everything from solid rocks and minerals to millions of living organisms, and is covered by countless natural and man-made structures. Therefore, there is no exact answer to the question of how much the Earth weighs. The weight of the Earth depends on the force of gravity acting on it, meaning the Earth could weigh trillions of kilograms or nothing, according to Live Science .

According to NASA, the mass of the Earth is 5.9722×1024 kg, which is equivalent to about 13 quadrillion Egyptian pyramids of Khafre (each pyramid weighs 4.8 billion kg). The mass of the Earth fluctuates slightly due to cosmic dust and gases leaking from the atmosphere, but these small changes do not affect the planet for billions of years.

However, physicists around the world have not yet agreed on the above figure and the calculation process is not an easy task. Since it is impossible to put the whole Earth on the scale, scientists have to use triangulation to calculate its mass.

The first ingredient in measurement is Isaac Newton's law of universal gravitation, according to Stephan Schlamminger, a metrologist at the US National Institute of Standards and Technology. Anything with mass has a gravitational force, meaning any two objects will always have a force acting on them. According to Newton's law of universal gravitation, the gravitational force between two objects (F) can be determined by multiplying the respective masses of the objects (m₁ and m₂), dividing by the square of the distance between their centers (r²), and then multiplying by the gravitational constant (G), i.e. F = Gx((m₁xm₂)/r²).

Using this equation, scientists could theoretically measure the mass of the Earth by measuring the planet's gravitational pull on an object on its surface. But the problem was that no one had yet calculated an exact number for G. In 1797, physicist Henry Cavendish began the Cavendish experiment. Using an object called a torsion balance, made of two rotating rods with lead balls attached, Cavendish found the gravitational force between them by measuring the angle on the rod, which changed as the smaller ball was attracted to the larger ball.

Knowing the masses and distances between the spheres, Cavendish calculated G = 6.74×10−11 m3 kg–1 s–2. Today, the Data Committee of the International Council for Science determines G = 6.67430 x 10−11 m3 kg–1 s–2, just a little different from Cavendish's original figure. Scientists then used G to calculate the mass of the Earth, using the known masses of other objects, and came up with the figure we know today: 5.9722×10−24 kg.

However, Schlamminger emphasizes that while Newton’s equations and the torsion balance are important tools, their measurements are still susceptible to human error. In the centuries since Cavendish’s experiment, different scientists have measured G dozens of times, each time with slightly different results. Although tiny, the differences are enough to change the calculation of the Earth’s mass and to confound scientists trying to measure it.

An Khang (According to Live Science )

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