Considering present attempts to develop a gradiometer with an accuracy between 10−3 E and 10−4 E, two applications for such a device have been studied: (a) mapping the gravitational field of the Earth, and (b) estimating the geocentric distance of a satellite carrying the instrument. Given a certain power spectrum for the signal and 10−4 E (rms) of white measurement noise, the results of an error analysis indicate that a six-month mission in polar orbit at a height of 200 km, with samples taken every three seconds, should provide data for estimating the spherical harmonic potential coefficients up to degree and order 300 with less than 50% error, and improve the coefficients through degree 30 by up to four orders of magnitude compared to existing models. A simulation study based on numerical orbit integrations suggests that a simple adjustment of the initial conditions based on gradiometer data could produce orbits where the geocentric distance is accurate to 10 cm or better, provided the orbits are 2000 km high and some improvement in the gravity field up to degree 30 is first achieved. In this sense, the gravity-mapping capability of the gradiometer complements its use in orbit refinement. This idea can be of use in determining orbits for satellite altimetry. Furthermore, by tracking the gradiometer-carrying spacecraft when it passes nearly above a terrestrial station, the geocentric distance of this station can also be estimated to about one decimeter accuracy. This principle could be used in combination with VLBI and other modern methods to set up a world-wide 3-D network of high accuracy.