As you ascend, the gravitational pull of the Earth on objects decreases, making them lighter. If you were to exit the Earth’s atmosphere, the weight of an object would be zero. Conversely, one might assume that the deeper you go into the Earth’s core, the heavier the object becomes. However, this assumption is entirely misleading!
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| When an object is placed deep within the Earth, it is acted upon by forces from many directions, yet only the gravitational pull from the Earth’s core on the object remains significant. (Illustration: nobelprize) |
The Earth attracts external objects as if its entire mass were concentrated at its center. According to the law of gravitation: the gravitational force decreases inversely with the square of the distance; as you ascend, the gravitational pull of the Earth on objects weakens.
If you raise a 1 kg weight to a height of 6,400 km, which is twice the Earth’s radius away from the center, the gravitational force will decrease by a factor of 2 squared, or 4 times. Consequently, the weight hanging from a spring scale will only register 250 grams instead of the full 1 kg. If you take the weight 12,800 km away from the surface, which is three times the distance from the center of the Earth, the gravitational pull decreases by 9 times, and the 1 kg weight will only weigh 111 grams….
From this calculation, one might assume that when you take the weight deep into the Earth, that is, moving it closer to the center, the gravitational attraction should increase, making the weight heavier. However, in reality, an object does not increase in weight when taken deep into the Earth’s core; rather, it becomes lighter.
The reason for this is that the object is no longer subjected to gravitational pull from one direction; instead, it experiences forces from multiple sides in the Earth (below, left, right…). As a result, the forces from the sides and above cancel each other out, leaving only the gravitational pull of the sphere with a radius equal to the distance from the Earth’s center to the location of the object. Therefore, the deeper you go into the Earth, the more rapidly the weight of the object decreases. At the Earth’s core, the object becomes weightless.
Thus, on the surface of the Earth, the object will indeed weigh more (*).
* This scenario holds true if the Earth were completely uniform in density. However, in reality, the density of the Earth increases as you approach the core: thus, initially, gravitational force does increase to some extent when going deep into the Earth, before it starts to decrease. |
