Could a trajectory exist that gave an object kinetic energy relative to the Earth/Moon that somehow passes zero as the Earth moved across the other's path, tugging on it? And having it happen at a potential energy minimum (e.g., a flat place on the surface of the Earth or Moon)?
I had been wondering about this as a way to soft-land on the moon with minimal $\Delta\ v$. A recent question mentioned something similar as a way to soft-land on Earth, but didn't appear set up to cancel the relative kinetic energy. My question also doesn't specify a keplerian orbit for the "lander", just whether a trajectory could exist and what features might describe a trajectory satisfying this scenario.
A compelling answer would show quantitatively the potential energies being considered and the range of relative kinetic energies for which a solution, if any, exists. I presume the lander's relevant kinetic energies come from the E/M system moving in orbit around the sun, the moon around the Earth, and their rotations ranging from effectively zero at the poles to an absolute maximum at their equators. I'm also presuming that inclinations, tilts, topography, and (Earth's) atmosphere don't drastically effect the answer's validity unless of course "making it" actually relies on any of those. Since some responses so far suggest it might be possible only elsewhere in the solar system, an answer that lets other planet and maybe moon masses, radii and velocities be substituted would be extra useful, though not necessary.