This work is concerned with the final approach phase and vertical land
ing on a spherical asteroid with a power limited, electrically propell
ed spacecraft. With gravitational effects taken into account, a new so
lution to the fuel optimal vertical landing on an asteroid was obtaine
d. In this particular solution the spacecraft commanded acceleration i
s colinear with the vehicle velocity, and the spacecraft trajectories
are restricted to a plane. Based on qualitative methods of analysis, t
he guidance strategy and the resulting trajectories were studied. It i
s shown that these fuel optimal trajectories effectively assure a vert
ical soft landing on the asteroid. Results of numerical simulations fo
r the vertical landing starting from an elliptic orbit are presented.