How many newtons does Earth weigh?

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t-nez | High School Teacher | (Level 3) Associate Educator

Posted on

The earth's weight can only be specified in the context of its attraction to another body. 

The weight of an object on the surface of the earth is its mass times 9.8 m/s2, its acceleration toward the earth due to gravity. The force that an object exerts on the earth equals the force that the earth exerts on the object, according to Newton's second law. This force is F=ma. Since the earth's mass is much, much larger than the mass of an object on its surface, it's acceleration toward the object is extremely small compared to 9.8 m/s, and is unnoticeable. 

The body that attracts the earth with the greatest force is the sun, due to the sun's very large mass and its promiximity compared to other similarly sized bodies.

Since the earth isn't on the sun's surface it's not quite correct to refer to its attraction to the sun as weight, but there's a force of gravitational attraction that can be calculated knowing the masses of the sun and the earth:

`F = (GM_1M_2)/(d^2)`

Where G is the universal gravitational constant 6.67 x 10^(-11) m^3/g-s^2, M1 and M2 are the masses of the two bodies, and d is the distance between them. The acceleration due to gravity that acts on objects on earth is derived from this equation. 

In summary, the earth's weight would depend on the mass of the body on whose surface it is theortetically exerting force. 

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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

Posted on

Hello!

Body's weight, by the definition, is a force exerted by this body on a base where it resides.

For example, when a book lies on a table, which stands near Earth's surface, its weight acts downward and has the magnitude of `mg,` where `m` is the book's mass and `g` is the gravity acceleration near Earth's surface. On the Moon's surface it will be about 6 times less, in a rocket in a deep space flying by inertia (with the engines turned off) it will be zero.

 

What is a base for Earth? No such a base. Therefore NO force and NO weight (not even zero).

If, imagine, Earth would lie on the Jupiter, its weight would be approximately the mass of Earth multiplied by the Jupiter's gravity acceleration.

So the answer: now Earth has no weight. It may have different weight in some imaginary situations.

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