  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.
