In order to obtain accurate measurements of electrostatic noise spectra on board the ISEE 1 satellite near interplanetary shock waves, we perform a detailed theoretical and numerical study of an antenna consisting of a pair of spherical probes. We compute the quasi-thermal electrostatic noise observed theoretically on the antenna by assuming that the solar wind plasma can be properly represented by the sum of two Maxwellian distributions (core and halo). We study the dependence of the electrostatic spectra of the antenna length and on the different plasma parameters, particularly on the density and temperature ratio of the core and of the halo. We show that by also taking into account the instrumental noise and the shot noise on the antenna, a calibration factor can be precisely determined for the antenna that we consider. We display some results obtained from measurements of electrostatic noise spectra behind interplanetary shock waves. Finally, we discuss the real meaning of a specific halo temperature, and we show that, in a first approximation, our theoretical results are only slightly modified when we consider types of distributions other than Maxwellians. ¿American Geophysical Union 1990