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Atmospheric drag stands out as the predominant non-gravitational force acting on satellites in Low Earth Orbit (LEO), with altitudes below 2000 km. This drag exhibits a strong dependence on the thermospheric mass density (TMD), a parameter of vital significance in the realms of orbit determination, prediction, collision avoidance, and re-entry forecasting. A multitude of empirical TMD models have been developed, incorporating contemporary data sources, including TMD measurements obtained through onboard accelerometers on LEO satellites. This paper delves into three different TMD modelling techniques, specifically, Fourier series, spherical harmonics, and artificial neural networks (ANNs), during periods of geomagnetic quiescence. The TMD data utilised for modelling and evaluation are derived from three distinct LEO satellites: GOCE (at an altitude of approximately 250 km), CHAMP (around 400 km), and GRACE (around 500 km), spanning the years 2002 to 2013. The consistent utilisation of these TMD data sets allows for a clear performance assessment of the different modelling approaches. Subsequent research will shift its focus to TMD modelling during geomagnetic disturbances, while the present work can serve as a foundation for disentangling TMD variations stemming from geomagnetic activity. Furthermore, this study undertakes precise TMD modelling during geomagnetic quiescence using data obtained from the GRACE (at an altitude of approximately 500 km), CHAMP (around 400 km), and GOCE (roughly 250 km) satellites, covering the period from 2002 to 2013. It employs three distinct methods, namely Fourier analysis, spherical harmonics (SH) analysis, and the artificial neural network (ANN) technique, which are subsequently compared to identify the most suitable methodology for TMD modelling. Additionally, various combinations of time and coordinate representations are scrutinised within the context of TMD modelling. Our results show that the precision of low-order Fourier-based models can be enhanced by up to 10 % through the utilisation of geocentric solar magnetic coordinates. Both the Fourier- and SH-based models exhibit limitations in approximating the vertical gradient of TMD. Conversely, the ANN-based model possesses the capacity to capture vertical TMD variability without manifesting sensitivity to variations in time and coordinate inputs. [ABSTRACT FROM AUTHOR]