Precision orbit determination (POD) plays a vital role in the success of space-borne laser altimetry missions, such as ICESat (Ice, Cloud, and Land Elevation Satellite). Although current ICESat POD processing standards are achieving remarkable accuracy, new time-varying geopotential models derived from the GRACE (Gravity Recovery And Climate Experiment) mission were investigated as candidates to improve POD performance for the planned ICESat-2 mission. The objective of this research is to examine the effect of these time-varying geopotential models -- which include models of non-tidal atmospheric and ocean variability, seasonal variability caused by water mass motion, and secular variations caused by present-day ice-melt and glacial isostatic adjustment -- on ICESat POD. The quality of the POD solutions produced with the new geopotential models was quantified by examining the usual orbit quality tests -- DDHL (double-differenced high-low) and SLR (satellite laser ranging) observation residuals and orbit overlaps. Although the solutions produced in every test case indicated consistency and high accuracy of 1-2 cm, these metrics were rather insensitive to the small changes in the POD solutions induced by the new geopotential models, and were incapable of identifying any statistically significant improvements in the POD. However, examination of geographically correlated radial orbit perturbations showed that the radial orbit differences exhibited significant variability on the order of several millimeters, and were coherent with the temporal variability of the models implemented. Since radial orbit errors directly relate to the scientific quantities of interest in the ICESat mission -- the altimetry measurements and derived ice-sheet surface elevations -- this result is of obvious importance. The most notable effects included an annual radial orbit variation of up to 4 mm over the Amazon region induced by implementing the GRACE Annual model, and a secular variation of radial orbit differences over Greenland when the GRACE Trend model was applied. The effect of radial orbit error on ice-sheet altimetry was quantified by examining the mean geographically correlated radial orbit differences. Since the ice sheet elevation rates computed by ICESat scientists are on the order of tens of centimeters per year, it was concluded that, although the radial orbit perturbations are readily observable, with magnitudes on the order of a few millimeters they are too small to have a significant impact on the altimetry science. However, depending on the scientific objectives and radial orbit accuracy requirements set for ICESat-2, these effects may be important, and the use of time-varying geopotential models in ICESat-2 POD may be beneficial. / text