The resolution may require some entirely new insight, such as Newton realizing that he needed to invent Calculus to solve the problems he faced three centuries ago. A possible area to investigate more precisely and thoroughly, is the behavior of the Trojan asteroids. One of the few exceptions is the behavior of those Trojan asteroids. They orbit the Sun in meta-stable orbits which have effectively the same radius as Jupiter's orbit, but they permanently remain 60 degrees ahead of or behind that planet as they orbit the Sun. There are several large Trojan asteroids in each of these two groups.
Several questions come to mind.
Much more research is necessary in these areas, and they might contribute toward a more complete theory for Gravitation. When I was calculating the precise orbits of the four Galilean satellites during 1996, I came up with results that there would be several mutual eclipses during the Summer of 1997. A couple of these involved Io eclipsing the Sun's light from getting to Europa. As it happens, Io has a larger diameter than Europa, so the eclipse would be a total eclipse. An event like that early that Summer was when Jupiter was not very near opposition, from our viewpoint on Earth.