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## Main Question or Discussion Point

I have several questions about the Newtonian equation for Gravity Gm1m2/r^2. First, I want to point out this equation is only valid for point masses or when the two objects are sufficiently far apart.This is because the r squared term on bottom means that the relationship between force and distance is exponential rather than linear. The curve flattens out as the objects become further away, which is why at sufficient distances this approximation is valid. The basic premise of Newton was that all matter attracts all other matter, using the center of gravity was just a simplification in order to create an equation. This is why his equation was unable to determine the orbit of Mercury for instance.

Examples are why tidal forces would pull you apart when entering a black hole or why if you were in a hollow sphere you would NOT be pulled towards the center of it.

My question is one, was Newton aware of this limitation?

Two, did Newton or other people since then try to create a more accurate equation for certain situations such as an equation for determining the force of gravity between a point mass and a uniform sphere of radius r that is distance d away? (integrating the force over the volume rather than using the center of mass).

Examples are why tidal forces would pull you apart when entering a black hole or why if you were in a hollow sphere you would NOT be pulled towards the center of it.

My question is one, was Newton aware of this limitation?

Two, did Newton or other people since then try to create a more accurate equation for certain situations such as an equation for determining the force of gravity between a point mass and a uniform sphere of radius r that is distance d away? (integrating the force over the volume rather than using the center of mass).