# How do measure the mass of a planet?

Of the eight planets in the solar system, Mercury is closest to the Sun, followed by Venus and then Earth. That means the third planet of the solar system is our earth. Earth is the fifth largest planet in the solar system. Earth is the sixth planet in the solar system in terms of mass.

## What is the mass of the earth?

The mass of the earth is **5.972 x 10 ^ 24 kg** or about **6,000,000,000,000,000,000,000,000 kg**. Even though we understand such a large number, it is very difficult to estimate how much this mass is. Let’s see the mass of the earth converted into different units.

The mass of the earth

= 6,000,000,000,000,000,000,000,000 kg

Or, 6 trillion-trillion kilograms

= 6,000,000,000,000,000,000,000 metric tons

= 6,000,000,000,000,000 megatons

= 6,000,000,000,000 giga tons

## How has the mass of the earth been measured?

Naturally, innumerable questions and dilemmas arise among us about measuring the mass of the earth. We wonder how the mass of this huge planet was measured. Of course, it is no longer possible to use a beard scale to measure other objects. So how has the mass of the earth been determined?

The man credited with measuring the mass of the earth was Henry Cavendish (1731-1810). However, the one whose name is particularly noteworthy in this case is Sir Isaac Newton (1642-1727), one of the greatest physicists of all time.

Among the various laws of physics, we know from the universal law of gravitation that any two objects in the universe are attracted to each other. This force of attraction is proportional to the mass of the two objects and disproportionate to the square of the distance. The mathematical form of the formula is:

**F = Gm1m2 / d ^ 2**

Where, F is the force of attraction m1, m2 is the mass of the two objects and d is the distance between the two objects.

In 1798, Cavendish was able to determine the mass of the earth using this formula.

Cavendis tried to measure the force of attraction of the lead sphere with a torsion balancing instrument (pictured below). But this instrument was insufficient to measure small-gravity gravity between two small metal spheres. So Cavendish took a new step for the test.

He made a huge dumbbell, so that two lead spheres of two inches were attached to the two ends of a six-foot-long piece of wood. The dumbbell was hung along the center with a rope so that the dumbbell could rotate freely.

He then took another dumbbell with two 12-inch lead spheres attached to it, each weighing 350 pounds. He then placed this large dumbbell next to the small dumbbell as shown in the figure below. According to Newton’s law of gravitation, large spheres have a larger shape and mass, so they will attract two smaller spheres, creating a motion illusion in the smaller dumbbell.

Cavendis thus set up the instrument and observed it for hours.

Since he knew the mass of the spheres and the distance between them, he very carefully observed the movement of the spheres and mathematically determined the force of attraction of the large spheres over the smaller spheres. This time he determined the value of the gravitational constant G from Newton’s law of gravitation from the value of this attraction ball.

Now, if we find the weight of the two spheres through the formula F = mg, the gravitational force of the earth on the two spheres will come out. Since the density of the two spheres was known, he calculated the density of the earth from the comparison of the two balls.

In order to avoid errors, he performed the test by twisting the instruments in different ways and took subtle lessons in each case. After identifying each of the potentially complex errors, Cavendis corrected them and finally reported his findings in a 57-page study entitled “Experiments for Determining the Density of the Earth” at the Royal Society in June 1998. He states that the density of the earth is 5.48 times the density of water (the current value is 5.52).

Understand, if the density of an object is known, it is also possible to find its mass. Fortunately the radius of the earth was determined long before this event. So it was possible to find the mass of the earth easily by using the formula “density = mass / volume” to find the volume from the radius.

Another method was used to find out the mass of the earth. However, Newton’s formula was also used in this case. In Newton’s time, people learned to determine Chad’s distance from Earth using geometry. And how long it took Chad to orbit the earth could be known only through the lunar month. With the help of this information, Newton’s Me = (4 π ^ 2 d ^ 3 / G T ^ 2) formula was used to find the same mass of the earth.

In this way, without the hassle of weighing anything, it is only possible to determine mathematically the mass of a planet or star, just as the mass of the earth was determined.

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