I copy Brian Koberlein’s explanations in Google+ on the history of Kepler’s law.
Kepler’s first two rules, that the orbit of a planet is an ellipse, and that a line drawn from the Sun to a planet sweeps out area at a constant rate were proposed in 1609. While these rules allowed for a more accurate description of observed planetary motion, they weren’t perfect. For one thing, the planets don’t actually move in exact ellipses, nor is Kepler’s “constant area” rule exact.
In 1619 Kepler added a third rule, relating the square of a planet’s orbital period to the cube of its semi-major axis (a measure of its distance from the Sun). But by the late 1600s there were several proposed models for planetary motion that were similarly accurate to Kepler’s model. Kepler’s first two rules were favored by many astronomers, largely due to Kepler’s prediction of Mercury’s 1631 transit of the Sun.
But there were two major difficulties with Kepler’s approach.
The first difficulty concerned the elliptical nature of planetary orbits. Kepler proposed that all planet have elliptical orbits. Observationally this was far from proven. While it was generally agreed that ellipses were an accurate approximation of the oval orbits of Mercury and Mars, it wasn’t clear that they were true ellipses (they aren’t).
The second difficulty had to deal with the orbit of the Moon. Kepler’s model was that of a fundamental relationship between planetary motion. In 1643 it was found that the four known moons of Jupiter (now known as the Galilean moons) followed Kepler’s rules. This would imply that the orbit of the Moon should likewise follow them. But the Moon’s motion doesn’t obey Kepler’s rules with nearly the accuracy of planetary motion. Some of the other proposed models made more accurate lunar predictions.
The upshot of all this is that Kepler’s laws were not universally accepted before Newton began his work on universal gravity in the late 1600s. It was only after Newton showed the rules to be exact for two (and only two) bodies moving under mutual gravitational attraction that Kepler’s model was preferred over the alternatives.
(Image from Wikipedia.)