Satellite operations in low Earth orbit will be extremely frequent in the near future, and consequently the optimization of trajectories between such orbits is becoming of extreme interest. Low-thrust electric propulsion will arguably be the preferred option for many missions, as it provides benefits in terms of propellant consumption. Low-thrust trajectories in low Earth orbit require several revolutions around the Earth and they are carried out in an environment where the two-body problem approximation is not suited to describe the motion of a satellite. The objective of this thesis is to illustrate a general methodology to take into account the effects of the oblateness of the Earth and aerodynamic drag, and obtain significant solutions to the minimum-time and minimum-propellant problems.