Solution (source code)

= Solution

Doubt was reasonable if it concerned the physical cause or unlimited extrapolation of <Newton's law of universal gravitation>; wholesale dismissal of the quantitative evidence was harder to justify. Early eighteenth-century investigators had to distinguish the success of an inverse-square <force law> in explaining observations from the claim that every material body directly attracts every other one without a mediating mechanism.

The strongest case for <Isaac Newton>'s framework was its unification of phenomena previously treated separately. <Kepler's third law> and nearly <elliptic orbits> could be connected to an inverse-square central <force>. Comparing terrestrial <gravity> with the <centripetal acceleration> of the Moon supported continuity between falling bodies and celestial <motion>. The <Philosophiae Naturalis Principia Mathematica by Isaac Newton> also developed treatments of interacting bodies, <tides> and the Earth's figure. These were substantive tests and organized a research programme capable of producing further quantitative comparisons.<Philosophiae Naturalis Principia Mathematica by Isaac Newton>[Book III, propositions on planetary forces, lunar gravity and universal attraction]{ref}

There were nevertheless rational reservations. A law proportional to $m_1m_2/r^2$ inferred from accessible bodies and distances did not logically establish unrestricted universality. Individual celestial predictions involved uncertain observations and approximations to difficult many-body <classical mechanics>. The Moon's motion and the Earth's shape were demanding tests whose successful treatment was not complete at the beginning of the century. A dissenter could question auxiliary assumptions, numerical accuracy or the inference from special cases without denying every success.

A deeper objection concerned explanation. In traditions requiring contact mechanisms, unexplained attraction across empty space appeared to reintroduce an occult quality. <René Descartes>'s vortices supplied a mechanical alternative, though they faced their own serious dynamical difficulties. <Newton> himself separated a mathematically established pattern from a claimed cause of <gravity>; the 1713 <General Scholium by Isaac Newton> declined to invent an unsupported physical mechanism. Treating every criticism of action at a distance as a failure to understand evidence would therefore misrepresent the available positions.<General Scholium by Isaac Newton>[1713 discussion of gravitational cause and the evidential status of hypotheses]{ref}

Later confirmations cannot be counted as evidence already possessed by an early-eighteenth-century critic. Subsequent geodetic measurements, improved lunar theory and successful comet predictions helped shift the balance, but their timing matters. Nor did retaining a mechanical alternative remain equally reasonable after every failed prediction: responsible doubt required comparative assessment and willingness to revise it. The balanced conclusion is that selective, explicit scepticism about universality or cause was defensible, while the breadth of <Newtonian mechanics>' quantitative achievements already imposed a substantial explanatory burden on rival accounts.