What is the relationship between center of mass and center of gravity?

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The center of mass and center of gravity can differ in location, particularly in non-uniform gravitational fields. The center of gravity is influenced by the gravitational field, which varies with distance from a massive object like Earth. In such fields, the center of gravity is typically slightly below the center of mass due to stronger gravitational pull on the lower half of the object. As the distance from the gravitating body increases, this difference diminishes because the gravitational field weakens. For most practical applications near Earth's surface, the two centers are often treated as equivalent due to the uniformity of Earth's gravity.
texasratt
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Can anyone give me an object where the center of mass and the center of gravity are in different locations?
 
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The center of gravity is not an intrinsic property of an object. It depends on the gravitational field the object is in. In the gravitational field of a spherical object (like, say, the Earth), and object's center of gravity will always be slightly below its center of mass; but, the farther it is from the center of the gravitating body, the smaller this difference.
 
why is it below and why does this get smaller with distance?
 
texasratt said:
why is it below and why does this get smaller with distance?
Because the gravitational field is not uniform: It's stronger the closer you are to the spherical object, so the lower half is pulled more strongly than the upper half. Since the field falls off inversely with the square of the distance, the farther away you are the less it matters.

Note that for ordinary-sized objects near the Earth's surface, Earth's gravity can be considered uniform for practical purposes. That's why many introductory texts treat "center of gravity" as synonymous with "center of mass".
 
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