When leaving the Solar system: Dark matter makes a difference

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.