Since about a decade, it has been suggested that the solar diameter may vary in time. The amplitude of the observed variations does not exceed 0.7 '' over 15 years and has been probably less (0.3 '') during the last five years. Recently, new measurements of the solar oblateness made at the Pic du Midi Observatory (France) seem to confirm a possible oscillation with the solar cycle as previously conjectured by a Princeton group. Over a one year period (July 1993 - July 1994), the reported difference between the equatorial diameter and the polar one is 11.5 +/- 3.4 are ms, consistent with previous observations made in 1983 and 1984, giving support for a solar activity dependence. However, the question is not yet settled as very few solar observatories are able to undertake unambiguous and accurate measurements. In order to free the data from atmospheric disturbances, it is here suggested to conduct a space experiment with the following objectives: (i) to confirm (or invalidate) the temporal (equatorial) diameter variations; in the mean time trying to interprete past - or simultaneously - obtained data to understand effects of the atmosphere; (ii) to measure the solar oblateness and its time variations if any; (iii) to determine the true shape of the helioid and its possible changing sizes; (iv) to correlate the data with the solar irradiance variations and produce a forecasting model; (v) to study the response on the Earth climatic system. An innovative instrument of about 50 Kg could be built, based on the experience of our scanning heliometer. A 0.002 are s accuracy must be achieved, which seems to be within our grasp with up-to-date technologies. All cooperation is welcome.