Extended Features:

  1. Proof of the corollary to the shell theorem:
      F_1_2 = F_1p_2 (by shell theorem) 
            = -F_2_1p (by 3rd law which is explicitly true for Newtonian gravity) 
            = -F_2p_1p (by shell theorem) = F_1p_2p (by 3rd law again),
      and so    F_1_2 = F_1p_2p    QED.  
    Of course, the interaction between the 2 masses can break their spherical symmetry and then neither shell theorem nor its corollary apply at least NOT exactly.

  2. The general relativity analogue of the shell theorem is Birkhoff's theorem.

    Birkhoff's theorem tells the same story. Any spherically symmetric object's gravity is exactly the same as if all its mass were concentrated at a point at its center for objects outside of its radius.

    For example, a 1 solar mass black hole and the Sun have the same gravitational field as long as you are ≥ 1 solar radius from their centers.

    To conclude, the powerful gravity and exotic effects of a black hole only occur when you are relatively close to its event horizon or at least closer than the radius of an non-black-hole of the same mass as the black hole.

    So black holes are NOT monsters of gravity swallowing eveything in the observable universe.

  3. By the by, progress is being made toward a theory of quantum gravity In 2021, gravity was measured to within ∼ 10 % accuracy/precision between gold spheres of mass 92 mg ≅ 10**(-4) kg and the possibility exists of measuring gravity for masses to ∼ 10**(-8) kg (Christian Rothleitner 2021, Nature; Westphal et al. 2021, Nature). Now 10**(-8) kg (corresponding to a length scale for typical density solids of 100 μm) is still much above the atomic scale (∼ 0.1--1 nm) (note atomic mass unit (AMU) = (1/12) C-12 = 1.660 539 066 60(50)*10**(-27) kg) and even the mesoscopic scale (∼ 100 nm -- 1 μm), but it is in the low end the macroscopic scale (>∼ 1 μm). If quantum gravity effects are larger than we currently think, then they may show up for masses to ∼ 10**(-8) kg. Maybe there are sophisticated procedures to measure gravity for even smaller masses. Time will tell.

    Actually, it has been shown that gravity of the size of Earth surface gravity (fiducial value 9.8 N/kg) probably quantizes atomic states like other forces (see Evidence for Quantized Gravitational States of the Neutron, Frank Rioux, 2020; Quantum effects of gravity, Thomas J. Bowles, 2002, Nature; and for the research article itself, Nesvizhevsky et al. 2002, Nature). However, this result, IF VALID, is just what we thoroughly expected and does NOT tell us more than confirming what we thought. So it's wonderful, if valid, but does NOT elucidate quantum gravity very much.

File: Gravity file: gravity_two_spheres_animation_1bb.html.