First from a one-dimensional MHD model we derive estimates for position and shape of the bow shock applicable for arbitrary magnetosonic Mach numbers >1 in the solar wind. This generalization is important in the case of the Giotto encounter with P/Grigg-Skjellerup with the unusual interplanetary magnetic field (IMF) of 18 nT. We compare three-dimensional model calculations with observations from six cometary missions and derive new corrected estimates for the gas production of P/Grigg-Skjellerup, which turn out to be substantially lower than those hitherto proposed assuming a large magnetosonic Mach number in the solar wind. Furthermore, we use global MHD models for this comet to determine from the measured magnetic field the position of the Giotto trajectory with respect to the comet. As a measure of the goodness of fit we use the mean square of the difference of the observed and the model field. We fit segments of the measured data of three different lengths centered near closest approach and for three different values of the unperturbed IMF. For all parameters considered, we find a unique best approximating trajectory which depends only little on the parameters. In any case, our best fitting trajectory pass through the comet at the side of the nucleus nearly straightly eastward (within ¿15¿) at a distance of 400 km. It has closest approach at about 1518:59 space craft event time (SCET). ¿ American Geophysical Union 1993