Short answers, pulled from the story.
Newton's law of universal gravitation was first published on the 5th of July 1687, in his work Philosophiae Naturalis Principia Mathematica. The book combined Newton's laws of motion with mathematical analysis to explain Kepler's observations of planetary motion.
G is the Newtonian constant of gravitation, a fixed value that appears in the formula relating gravitational force to the masses of two objects and the square of the distance between their centers. Its value was first accurately determined from the results of the Cavendish experiment conducted by Henry Cavendish in 1798.
Henry Cavendish, a British scientist, conducted the first laboratory test of Newton's gravitational theory between masses in 1798. The experiment took place 111 years after the publication of Newton's Principia and approximately 71 years after Newton's death.
The law was called the "first great unification" because it unified the previously separate phenomena of gravity on Earth with known astronomical behaviors, showing both were governed by the same force. This was the first time terrestrial and celestial mechanics had been brought under a single physical law.
Newton's law fails in situations involving very strong gravitational fields, very high velocities, or the need for extreme accuracy. Observed discrepancies include a 43 arcsecond per century error in Mercury's orbital precession and a predicted light deflection by gravity that is only half the value astronomers actually observe; both are corrected by Einstein's general relativity.
In the General Scholium of the Principia's second edition in 1713, Newton used the Latin phrase Hypotheses non fingo, translated as "I feign no hypotheses," to state that he could describe how gravity behaves without being able to explain why it exists or how it acts across empty space. He was deeply uncomfortable with the idea of action at a distance but refused to speculate beyond what the phenomena showed.