Low-thrust propulsion's main advantage is its efficient propellant usage. This holds for manoeuvres as well as for major orbital changes, both for LEO/MEO/GEO satellites and for interplanetary missions. In designing such missions, extensive numerical models as well as less demanding analytic first-order approximations can be used. A specific kind of the latter category of methods are called shape-based methods. TU Delft's Astrodynamic Toolbox (TUDAT) contains the framework for shape-based methods with spherical shaping and hodographic shaping already implemented for use by students and staff. Having more shape-based method available allows for a more versatile toolbox and combining several shapes with for example coasting would lead to more attractive and efficient transfers. This thesis provides the theory required for the implementation of both exponential sinusoids and the sixth order inverse polynomials with 3D capabilities. These methods have been successfully implemented, verified and validated into the TUDAT shape-based framework.
The four shape-based methods have been applied to an Earth-Tempel-1 transfer for start dates from 2020 to 2025 and time of flights of 100 to 8900 days. It is found that the following order can be established with respect to their lowest ΔV, based on both an unoptimised grid search and global optimisation: Inverse polynomial shaping (10.51 km/s), Spherical shaping (11.71 km/s), Exponential shaping (13.09 km/s), Hodographic shaping (26.22 km/s).
Optimising for ΔV and peak thrust acceleration with the Earth-Tempel-1 transfer including a coasting arc between two powered arcs for inverse polynomials and spherical shaping compared to the standard transfer, yields the following results: Trajectories with similar and lower ΔVs, similar and lower peak thrust for the same ΔV and similar and longer time of flights. In conclusion coasting arcs provide more flexibility in terms of start date, time of flight and peak acceleration thrust for a marginal increase or decrease in ΔV.

Lunar exploration initially started as a race between two superpowers to see who had the highest technical capabilities to send a human onto the Moon’s surface. Until recently, the frequency of Moon missions has been in decline, but in the last couple years there has been an increasing interest in returning. Scientific studies and observations will be performed and will give humanity a better understanding of the solar system and our place in it. As a result there will be a need for a direct communication line between the lunar surface and Earth, such that rovers can be controlled in real-time and immediately relay their data back, independent of their location on the Moon.