How much does Earth the weigh?

Answer 1

It has a mass of about 6 x 1021 tonnes (6 x 1024 kg) but it has no actual weight because it is in freefall in its orbit around the Sun. In any event, its weight would depend on the strength of the gravitational force to which it was subjected.

The measurement of weight on Earth is derived from the gravitational attraction that the Earth has for objects near it. Any two masses have a gravitational attraction for one another. If you put two Bowling balls near each other, they will attract one another gravitationally. The attraction is extremely slight, but could be measured. From that measurement, you could determine the mass of the two objects. The same is true for two Golf balls, but the attraction is even slighter because the amount of gravitational force depends on mass of the objects.

Newton showed that, for spherical objects, you can make the simplifying assumption that all of the object's mass is concentrated at the center of the sphere. The following equation expresses the gravitational attraction that two spherical objects have on one another:F = G * M1 * M2 / R2

• R is the distance separating the two objects.
• G is a constant that is 6.67259x10-11m3/s2 kg.
• M1 and M2 are the two masses that are attracting each other.
• F is the force of attraction between them.

Assume that Earth is one of the masses (M1) and a 1-kg sphere is the other (M2). The force between them is 9.8 kg*m/s2 -- we can calculate this force by dropping the 1-kg sphere and measuring the acceleration that the Earth's gravitational field applies to it (9.8 m/s2).

The radius of the Earth is 6,400,000 meters (6,999,125 yards). If you plug all of these values in and solve for M1, you find that the mass of the Earth is 6,000,000,000,000,000,000,000,000 kilograms (6 x 1024 kilograms / 1.3 x 1025 pounds).

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It is "more proper" to ask about mass rather than weight because weight is a force that requires a gravitational field to determine. You can take a bowling ball and weigh it on the Earth and on the moon. The weight on the moon will be one-sixth that on the Earth, but the amount of mass is the same in both places. To weighthe Earth, we would need to know in which object's gravitational field we want to calculate the weight. The mass of the Earth, on the other hand, is a constant.
In pounds the estimated weight of the Earth is 1.3 x 1025

You would have to do the math to convert to the appropriate tonnage.

Earth's mass is 5.9736 X 10^24 kilograms.

5.9736 kilograms = 0.00658476685 short tons.

So the earth 'weighs':

6,584,766,850,000,000,000,000 short tons, or:

5,973,600,000,000,000,000,000 metric tons, or:

5,879,256,110,000,000,000,000 long tons.

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Remember that weight is a measure that depends on the gravity of the place where you are measuring the object. Strange as it sounds, earth is weightless as it travels in its orbit, because it is not in a gravitational frame of reference where its weight can be measured. See link. If we could weigh the earth on the earth, which is a rather odd mental picture, the above weight is what you would get.

Mass is a measure of a thing that does not depend on gravity, and so it is more useful and meaningful.

See link for different ways that the term 'ton' is used.

Answer 2

The measurement of the planet's weight is derived from the gravitational attraction that the Earth has for objects near it.

It turns out that any two masses have a gravitational attraction for one another. If you put two bowling balls near each other, they will attract one another gravitationally. The attraction is extremely slight, but if your instruments are sensitive enough you can measure the gravitational attraction that two bowling balls have on one another. From that measurement, you could determine the mass of the two objects. The same is true for two golf balls, but the attraction is even slighter because the amount of gravitational force depends on mass of the objects.

Newton showed that, for spherical objects, you can make the simplifying assumption that all of the object's mass is concentrated at the center of the sphere. The following equation expresses the gravitational attraction that two spherical objects have on one another: F = G * M1 * M2 / R2

• R is the distance separating the two objects.
• G is a constant that is 6.67259x10-11m3/s2 kg.
• M1 and M2 are the two masses that are attracting each other.
• F is the force of attraction between them.

Assume that Earth is one of the masses (M1) and a 1-kg sphere is the other (M2). The force between them is 9.8 kg*m/s2 -- we can calculate this force by dropping the 1-kg sphere and measuring the acceleration that the Earth's gravitational field applies to it (9.8 m/s2).

The radius of the Earth is 6,400,000 meters (6,999,125 yards). If you plug all of these values in and solve for M1, you find that the mass of the Earth is 6,000,000,000,000,000,000,000,000 kilograms (6 x 1024 kilograms / 1.3 x 1025 pounds).

It is "more proper" to ask about mass rather than weight because weight is a force that requires a gravitational field to determine. You can take a bowling ball and weigh it on the Earth and on the moon. The weight on the moon will be one-sixth that on the Earth, but the amount of mass is the same in both places. To weighthe Earth, we would need to know in which object's gravitational field we want to calculate the weight. The mass of the Earth, on the other hand, is a constant.

The concept of the Earth's weight does not serve us well. To have weight the Earth would have to be sitting on a surface attracting it at one gravity. Instead we must refer to the mass of the Earth. The mass of the Earth is 6 000 000 000 000 000 000 000 000 kilograms (6x1024 kilograms or 1.3x1025 pounds)

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