The pure mathematics underlying Newton’s Law of Universal Gravitation is straightforward.
Newton’s law of universal gravitation states that any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
However, the applied mathematics associated with Newton’s Law of Universal Gravitation is a conceptual nightmare.
Firstly, nobody can find an idealised point particle [a mass without structure or volume] in the real world.
A point particle (ideal particle or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics.
Its defining feature is that it lacks spatial extension: being zero-dimensional, it does not take up space.
In the theory of gravity, physicists often discuss a point mass, meaning a point particle with a nonzero mass and no other properties or structure.
Secondly, nobody knows how gravity is mediated in the real world and the applied mathematician is required to employ a magical action at a distance that has no underlying mechanics.
In physics, action at a distance is the concept that an object can be moved, changed, or otherwise affected without being physically touched (as in mechanical contact) by another object.
In other words: Nobody knows whether gravity is a pulling or pushing vector.
Thirdly, the applied mathematician has to grapple with a mechanics-less gravity vector that propagates instantaneously [regardless of distance] whilst confining all other real world objects to less than the speed of light [unless the object has unquantifiable infinite energy].
Newton’s theory of gravity offered no prospect of identifying any mediator of gravitational interaction.
His theory assumed that gravitation acts instantaneously, regardless of distance.
Under the special theory of relativity, a particle (that has rest mass) with subluminal velocity needs infinite energy to accelerate to the speed of light, although special relativity does not forbid the existence of particles that travel faster than light at all times (tachyons).
Needless to say, the applied mathematician have had a field day with this conceptual nightmare.
Presented with any problem the applied mathematicians can determine the gravity of the situation [whilst totally ignoring the impossible conceptual realities of their situation].
In isolation many of these gravity solutions appear [superficially] plausible provided the mathematical advocate applies sufficient spin [aka mumbo jumbo], omits the confounding details and avoids mentioning the underlying conceptual nightmare.
The technique of devising individual solutions [aka divide and conquer] has slowly evolved into the Universal Newton where the sum of the parts reveals a nightmare of inconsistencies and contradictions.
Such is the magic of Settled Science.