The Inverse Square Law and Distributed Attraction
Gravitational Causality is Distibuted
It’s essential to understand that gravity doesn’t act from a single point within an object. Instead, every single particle (atom, molecule) within one object is related to every single particle ( or its energy) within the other object.
Inverse Square’s Effect: The inverse square law means that the attraction between any two pairs of particles is stronger when they are closer and weaker when they are farther apart.
Why This Matters for Center of Attraction
Even in a perfectly spherical object with uniform density, the center of attraction is not precisely at the geometric center (which is also the center of mass). Here’s why:
Nearer Side Attraction: Consider two spheres attracting each other. Particles on the near side of each sphere are, on average, closer to the particles of the other sphere than particles on the far side.
Stronger Net Attraction: Due to the inverse square law, the gravitational forces between the closer particles are stronger than those between the farther particles.
Shifted Center of Attraction: This difference in force means that the vector sum of all the individual gravitational forces is not directed precisely toward the geometric center of either sphere. Instead, the net attraction is slightly skewed toward the nearer side.
The Shell Theorem and Its Limitations
Shell Theorem: The shell theorem does state that for a spherically symmetric object, the gravitational force it exerts on an object outside of it is the same as if all its mass were concentrated at its center.
Where It Applies: The shell theorem is crucial for simplifying calculations of the gravitational force between two objects.
Where It Doesn’t Fully Apply: However, the shell theorem doesn’t fully describe the internal distribution of the attractive forces within the objects themselves. It simplifies the external effect, not the internal cause. It doesn’t mean that the source of the attraction is solely the center.
In Summary
The center of attraction is determined by the vector sum of all the individual particle-particle attractions.
The inverse square law causes the nearer parts of objects to attract each other more strongly.
Even for uniform spheres, this results in the center of attraction being slightly closer than the center of mass.
This is a subtle but important distinction that highlights the complexity of gravitational interactions.