A resultant gravitational force due to the current estimates of the virial mass of the Milky Way galaxy, dominated by dark matter, is estimated near the Sun and is described in two different analytical models yielding consistent results. One is a two step Hernquist model, the other is a Navarro–Frenk–White model. The effect of this force is estimated on trajectories for spacecraft sufficiently far from the Sun. The difficulty of detecting this force is studied. It is concluded that its effect should be considered for certain spacecraft missions. Its effect on the Pioneer and New Horizons spacecrafts is discussed. A future mission is discussed that may be able to detect this force. Implications of this force are discussed with its impact for problems in planetary astronomy and astrophysics.

It is shown that a class of approximate resonance solutions in the three-body problem under the Newtonian gravitational force are equivalent to quantized solutions of a modified Schrödinger equation for a wide range of masses that transition between energy states. In the macroscopic scale, the resonance solutions are shown to transition from one resonance type to another through weak capture at one of the bodies, while in the Schrödinger equation, one obtains quantized wave solutions transitioning between different energies. The resonance transition dynamics provides a classical model of a particle moving between different energy states in the Schrödinger equation. This methodology provides a connection between celestial and quantum mechanics.

It is shown that a class of approximate resonance solutions in the three-body problem under the Newtonian gravitational force are equivalent to quantized solutions of a modified Schr\"odinger equation for a wide range of masses that transition between energy states. In the macroscopic scale, the resonance solutions are shown to transition from one resonance type to another through weak capture at one of the bodies, while in the Schr\"odinger equation, one obtains quantized wave solutions transitioning between different energies. The resonance transition dynamics provides a classical model of a particle moving between different energy states in the Schr\"odinger equation. This methodology provides a connection between celestial and quantum mechanics.