Uncertainty in the atmospheric density is a crucial error source for the propagation of satellites in low earth orbit (LEO). As a result, establishing accurate thermospheric neutral density models are important to predict the motion of these satellites. Unfortunately, since density data in the altitude range between 140 km and 200 km are sparse, predicting the neutral density to estimate atmospheric drag effects on the motion of satellites operating in this altitude region may cause relatively large errors. Previous study found that the Jacchia-Bowman model (JB2006) is the most reliable thermospheric empirical neutral density model above 200 km and the Naval Research Laboratory's Mass Spectrometer Incoherent Scatter (NRLMSISE-00) model, whose core formulation is based on incoherent scatter radar data, and can be considered a more reliable neutral density model below approximately 140 km. We have developed a bridging technique to blend the two models between these two regions. A simple two-body model with atmospheric drag was used to compare effects of various atmospheric density models. These tests are conducted by propagating the positions of satellites orbiting between 140 and 200 km, with various ballistic coefficients, using the JB2006, the NRLMSISE-00, and the bridging technique we have developed.