Centre of mass vs. centre of gravity

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The discussion highlights the relationship between the center of mass and the center of gravity for a symmetrical solid body, particularly in varying gravitational fields. It notes that for a uniform density body, the center of mass coincides with the geometric center. When moving from a weaker gravitational field, like Earth, to a stronger one, such as Jupiter, the center of gravity is effectively lowered, making the body harder to tip over. The conversation raises the question of whether a formula exists to calculate the center of gravity in different gravitational fields. Overall, the center of gravity and center of mass are assumed to coincide on Earth for practical purposes.
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consider a symmetrical solid body. we say its centre of mass is at its geometric centre. that is, for uniform density we've taken mass to vary exactly as volume. now when the same body is taken from a place of gravitational field A to gravitational field B. say from the Earth to jupiter, this body (consider it to be a cone) would be harder to tip over were it standing on its base. that is because , for a body to tip over, the vertical line through the centre of gravity should pass outside the base. the geometry of the body unchanged, we say its centre of gravity is lowered in this stronger field. is there a formula by which we can calculate the centre of gravity in particular fields in relation to those in others?. I am assuming we take centre of gravity and centre of mass to coincide on Earth for convinience's sake.
 
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