This report explores the concept of Shape- based approximation of Low-thrust Constrained Space Trajectories Using Fourier Series. In addition to the results obtained by the method developers Ehsan Taheri and Ossama Abdelkhalik on the aforementioned subject, a penalty was added to the transfer cost of the optimised trajectory. Its effects on the least squared error on the equations of motion were analysed. The two cases of orbit raising (moving from a Low-Earth Orbit to a Geo-Synchronous Orbit) and an orbit changing (from Earth to Mars) were analysed. The plots and tabulation compares the results of these two cases and its effects and future scope on space trajectory design and analysis.