Halley’s Question

In the fall of 1684, Edmond Halley, an accomplished astronomer, traveled to
Cambridge with a question for Newton. Halley had concluded that the gravitational
force between the Sun and the planets followed an inverse-square law—
that is, the connection between this “centripetal force” (as Newton later called
it) and the distance r between the centers of the planet and the Sun is
1
centripetal force . r2
(Read “proportional to” for the symbol .) The force decreases by 1⁄22 1⁄4 if r
doubles, by 1⁄32 1⁄9 if r triples, and so forth. Halley’s visit and his question were
later described by a Newton disciple, Abraham DeMoivre:
In 1684 Dr Halley came to visit [Newton] at Cambridge, after they had some
time together, the Dr asked him what he thought the curve would be that would
be described by the Planets supposing the force of attraction towards the Sun
to be reciprocal to the square of their distance from it. Sr Isaac replied immediately
that it would be an [ellipse], the Doctor struck with joy & amazement
asked him how he knew it, why saith he I have calculated it, whereupon Dr
Halley asked him for his calculation without farther delay, Sr Isaac looked
among his papers but could not find it, but he promised him to renew it, & then
send it to him.
A few months later Halley received the promised paper, a short, but remarkable,
treatise, with the title De motu corporum in gyrum (On the Motion of Bodies
in Orbit). It not only answered Halley’s question, but also sketched a new system
of celestial mechanics, a theoretical basis for Kepler’s three laws of planetary
motion.