Kepler’s laws were a beautifully simple explanation of what the planets did, but they did not address why they moved as they did. Did the sun exert a force that pulled a planet toward the center of its orbit, or, as suggested by Descartes, were the planets circulating in a whirlpool of some unknown liquid? Kepler, working in the Aristotelian tradition, hypothesized not just an inward force exerted by the sun on the planet, but also a second force in the direction of motion to keep the planet from slowing down. Some speculated that the sun attracted the planets magnetically.
Once Newton had formulated his laws of motion and taught them to some of his friends, they began trying to connect them to Kepler’s laws. It was clear now that an inward force would be needed to bend the planets’ paths. This force was presumably an attraction between the sun and each planet (although the sun does accelerate in response to the attractions of the planets, its mass is so great that the effect had never been detected by the prenewtonian astronomers). Since the outer planets were moving slowly along more gently curving paths than the inner planets, their accelerations were apparently less. This could be explained if the sun’s force was determined by distance, becoming weaker for the farther planets. Physicists were also familiar with the noncontact forces of electricity and magnetism, and knew that they fell off rapidly with distance, so this made sense.
F=ma=mv2/r.
Now although this equation has the magnitude, vv, of the velocity vector in it, what Newton expected was that there would be a more fundamental underlying equation for the force of the sun on a planet, and that that equation would involve the distance, rr, from the sun to the object, but not the object’s speed, vv—motion doesn’t make objects lighter or heavier.