= Solution
\b[The Newtonian achievement combined a dynamical framework, a universal gravitational interaction and a distinctive standard of physical explanation.] It was problematic partly because its mathematical successes exceeded what it supplied as a physical mechanism. Calling it a system should not conceal the difference between <Isaac Newton>'s own writings, their later development and simplified versions promoted by his followers.
The <Philosophiae Naturalis Principia Mathematica by Isaac Newton> began with definitions and the <Newton's laws of motion>. <Inertia> distinguished persistence in uniform rectilinear <motion> from changes requiring impressed <force>. <Newton's second law> related such changes to impressed <force>; <Newton's third law> required reciprocal interactions. The account also distinguished absolute and relative quantities, raising questions about the meaning of true <motion>. In modern notation, a central part of the programme is expressed by
$$
\frac{\mathrm d\mathbf p}{\mathrm dt}=\mathbf F,
\qquad
F_{\mathrm{grav}}=\frac{Gm_1m_2}{r^2}.
$$
Here <momentum>, <force>, masses and separation have their modern notation, and $G$ is the <gravitational constant>; the display is not a quotation of <Isaac Newton>'s symbols. Combining <Newton's laws of motion> with <Newton's law of universal gravitation> made it possible to explain a wide range of terrestrial and celestial phenomena together.<The Mathematical Principles of Natural Philosophy by Isaac Newton (1846 edition)>[Definitions, scholium on time and space, Laws of Motion, and Book III propositions 1–8]{ref}
The quantitative content matters. For an ideal circular orbit of a small body around a much larger mass $M$, <centripetal acceleration> gives, in modern notation,
$$
\frac{v^2}{r}=\frac{GM}{r^2},
\qquad
T^2=\frac{4\pi^2}{GM}r^3.
$$
This restricted illustration recovers the period–radius relation in <Kepler's third law>. It is not a reconstruction of the full original proof for an elliptical orbit. More generally the same interaction could account for the Moon's departure from a straight path, the paths of comets and mutual perturbations. Universal attraction made celestial irregularities potential consequences of a common law rather than reasons to assign a separate nature to each class of object.
The associated Newtonian programme extended beyond <gravity>. In <optics>, experiments on <refraction> supported the heterogeneous composition of white light: a <prism> could separate constituents with different refrangibilities rather than manufacture colours from a previously homogeneous ray. This challenged accounts that treated colour primarily as a modification introduced by the medium. It belongs to the broader Newtonian programme, although the 1704 <Opticks by Isaac Newton> must not be conflated with the content or publication date of the 1687 <Philosophiae Naturalis Principia Mathematica by Isaac Newton>.<Opticks by Isaac Newton>[book I, part I, propositions on different refrangibility and the composition of light; linked fourth edition, 1730, retains the 1704 advertisement]{ref}
The greatest conceptual difficulty concerned <action at a distance>. For a defender of a contact mechanism, the mutual attraction of bodies through empty space appeared to reintroduce an occult quality instead of explaining an interaction. <Cartesian vortices> offered at least a material picture of how bodies might be carried around, whereas an inverse-square <force law> did not specify what transmitted the influence. <Isaac Newton> could point to the difficulties of reconciling such vortices with planetary periods and the varied paths of comets, but defeating that particular mechanism did not itself furnish an alternative mechanical cause.<General Scholium by Isaac Newton>[opening paragraphs: orbital periods, comets and the vortex hypothesis]{ref}
It is particularly important that <Isaac Newton> did not simply identify unmediated attraction as an essential property of matter. In his letter to <Richard Bentley> of 25 February 1692/3, he rejected that attribution and left open whether the relevant agent was material or immaterial. In the <General Scholium by Isaac Newton>, he distinguished establishing how <gravity> acts from assigning a cause not warranted by the phenomena.<Letter to Richard Bentley of 25 February 1693 by Isaac Newton>[Trinity College manuscript, folios 7r–7v: innate gravity and the unspecified agent]{ref}<General Scholium by Isaac Newton>[closing gravitational discussion: mathematical law and the cause of gravity]{ref}
Other difficulties followed from the standard of demonstration itself. The demanding geometry made the work hard to master; approximations and mutual interactions meant that apparent agreement had to be earned through calculation, not assumed from a slogan about universal attraction. Absolute <motion> and divine government also raised philosophical questions that a successful orbital calculation could not settle. Initial resistance thus included reasonable disputes about mechanism, evidence and explanatory adequacy. The system's later authority came from its capacity to sustain successful investigation despite those unresolved foundations, not from having answered every foundational question at publication.
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