  We present a focused parameter study of solar wind - magnetosphere
interaction for the young Sun and Earth, $~3.5$ Ga ago, that relies on
magnetohydrodynamic (MHD) simulations for both the solar wind and the
magnetosphere. By simulating the quiescent young Sun and its wind we are able
to propagate the MHD simulations up to Earth's magnetosphere and obtain a
physically realistic solar forcing of it. We assess how sensitive the young
solar wind is to changes in the coronal base density, sunspot placement and
magnetic field strength, dipole magnetic field strength and the Sun's rotation
period. From this analysis we obtain a range of plausible solar wind conditions
the paleomagnetosphere may have been subject to. Scaling relationships from the
literature suggest that a young Sun would have had a mass flux different from
the present Sun. We evaluate how the mass flux changes with the aforementioned
factors and determine the importance of this and several other key solar and
magnetospheric variables with respect to their impact on the
paleomagnetosphere. We vary the solar wind speed, density, interplanetary
magnetic field strength and orientation as well as Earth's dipole magnetic
field strength and tilt in a number of steady-state scenarios that are
representative of young Sun-Earth interaction. This study is done as a first
step of a more comprehensive effort towards understanding the implications of
Sun-Earth interaction for planetary atmospheric evolution.

Solar and Stellar Astrophysics