Derive law of gravitation
Answers
Answer:
You don’t. Laws are not derived, they are formulated to explain experimental observations. Astronomers had made very careful observations of planetary positions, which lead Copernicus to propose the heliocentric theory. The observations were also explainable using Ptolmey’s geocentric theory, but it required too many ad hoc assumptions to succeed. Kepler analyzed the extremely accurate observations of Tycho Brahe and came out with his three laws, again on the basis of observation. Galileo, using the phases of Venus, showed that Copernicus/Kepler were right and Ptolmey was wrong. Newton was aware of all this and he wanted a simple explanation for all that was already known about gravity and he came out with the law. It was accepted not because it was derived from something else but because its predictions agreed with experiment.
Of course, it is possible today to derive the law from alternate formalisms, e.g. a Poisson equation for the gravitational potential or from an action formalism. But these are just equivalent formulations: deriving one from the other is tantamount to showing equivalence.
