A new technique is developed where the potential difference between a conductive spacecraft at floating potential and an electric field probe, negatively biased in relation to the spacecraft, with a current of 50 nA, is used to determine electron densities in the range 1--70 cm-3. The density can be obtained with an acceptable accuracy without any knowledge of the electron energy, provided the latter does not exceed 100 eV. This technique has been applied to the Phobos 2 spacecraft data to determine characteristic densities in the solar wind near Mars, in the foot of the bow shock, in the planetosheath, and at the top of the ionosphere. In the latter region, measurements have also been made using a Langmuir probe on board the spacecraft. A magnetic barrier, with a low plasma density, is observed between the planetosheath and the top of the ionosphere. Pronounced electron density increases are observed on the flanks and in the tail, some correlated and some anticorrelated with variations in the magnetic field strength. ¿American Geophysical Union 1991