How Newton Knew he Was Correct:

Step 1: Assume that M1 is a small mass in a circular orbit about a much larger mass M2 . We can write down the Force law on M1 using Newton's formulations: Step 2: Combining terms yields: Step 3: In an orbit governed by a central force, the centripetal acceleration, a is given by: Step 4: For a circular orbit, the circular velocity, Vc is the total distance traveled (the circumference of the circle) divided by the orbital period, P or Vc = 2p R/P which then yields: in which the harmonic law of Kepler is now apparent as the R3/P2 term.

Measurements of R and P for any lesser body ( M₁ ) in orbit about a larger body ( M₂ ) now gives directly a physical quantity, mass. So this is magic, we can actually weigh planets without every going there!

The genius of Newton was his ability to use calculus and coordinate transformations to reveal the underlying physics.

After the Death of Newton, the scientific revolution continued to accelerate with more and more sophisticated experiments being done and methods of inquiry developed.

With the development of Calculus, statistical methods could now also be developed.

The roots of most modern scientific disciplines can therefore be found in this period. Morover, philosophy at this time was moving hand in hand with the Scientific Revolution:

Most notable during this period was Immanuel Kant (1724-1804):

He made a very influential synthesis of rationalism and empiricism. Empiricists, such as Locke and Hume, argued that all our knowledge comes from experience, or from reflection on experience. Rationalists argued that empirical knowledge is uncertain and only reason can lead us to truth.

Who is likely to be most correct here?

Moveover, Kant argues the following:

In man (as the only rational creature on earth), those natural capacities which are directed towards the use of his reason are such that they could be fully developed only in the species, but not in the individual.

Do we believe this?

Finally, what about this one?

Reason, in a creature, is a faculty which enables that creature to extend far beyond the limits of natural instinct the rules and intentions it follows in using its various powers, and the range of its projects is unbounded. But reason does not itself work instinctively, for it requires trial, practice and instruction to enable it to progress gradually from one stage of insight to the next.

What the hell does that mean?

In terms of astronomy, the most key figure in this period is William Herschel.

Herschel was able to construct the largest telescope of the period and therefore had the most precise scientific instrument available. With this instrument he:

Discovered the Planet Uranus

Made a Map of the Galaxy

Discovered and Measured Double Stars

Most importantly: Herschel breaks with the science of astronomy as one of determining positions of objects only and instead embarks on a much broader research program called The Construction of the Heavens

Most Important: Herschel made careful observations of double stars and found they obeyed Kepler's laws Why is this important?

Much of this period was also laying the groundwork for modern day chemistry:

See This Timeline of Science

A particularly important piece of work during this time is that of Jakob Bernoulli (1713 and beyond) who basically provided the mathematical basis for the field of statistics that would, two centuries later, begin to allow science to handle large numbers of samples.

The concept that nature "regresses to its average behavior over time" comes out of the work of Bernoulli in the form of the standard bell curve distribution.