The pure mathematics underlying *Newton’s Law of Universal Gravitation* is straightforward.

Newton’s law of universal gravitationstates 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.

https://en.wikipedia.org/wiki/Newton’s_law_of_universal_gravitation

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 idealizationof 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 ofgravity, physicists often discussa point mass, meaning a point particlewith 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 distanceis the concept thatan 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.https://en.wikipedia.org/wiki/Action_at_a_distance

Under the special theory of relativity,

a particle(that has rest mass) with subluminal velocityneeds 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*.