The historical method of precise orbit determination is a dynamic approach. However, with the improvement of GPS tracking data and associated tracking networks, two newer methods have been developed: reduced-dynamic and kinematic. In addition to orbit determination, alternative methods of gravity field recovery have been developed using kinematic orbits which do not rely on any force modeling. However, one significant drawback of kinematic orbits is that they lack any velocity or acceleration information. These have to be derived numerically. Based on the results of this thesis, the Savitzky-Golay filter, without using a remove-restore procedure, is recommended for deriving kinematic velocities of the GRACE mission. In addition, the numerical differentiation methods are tested to see how well accurately they represent the satellite's acceleration for all three orbit types. Finally, with the kinematic orbits properly reconstructed, the results can also be compared to dynamic and reduced-dynamic orbits through K-Band Ranging residuals. / text