  As a star spins-down during the main sequence, its wind properties are
affected. In this work, we investigate how the Earth's magnetosphere has
responded to the change in the solar wind. Earth's magnetosphere is simulated
using 3D magnetohydrodynamic models that incorporate the evolving local
properties of the solar wind. The solar wind, on the other hand, is modelled in
1.5D for a range of rotation rates Omega from 50 to 0.8 times the present-day
solar rotation (Omega_sun). Our solar wind model uses empirical values for
magnetic field strengths, base temperature and density, which are derived from
observations of solar-like stars. We find that for rotation rates ~10
Omega_sun, Earth's magnetosphere was substantially smaller than it is today,
exhibiting a strong bow shock. As the sun spins down, the magnetopause standoff
distance varies with Omega^{-0.27} for higher rotation rates (early ages, > 1.4
Omega_sun), and with Omega^{-2.04} for lower rotation rates (older ages, < 1.4
Omega_sun). This break is a result of the empirical properties adopted for the
solar wind evolution. We also see a linear relationship between magnetopause
distance and the thickness of the shock on the subsolar line for the majority
of the evolution (< 10 Omega_sun). It is possible that a young fast rotating
Sun would have had rotation rates as high as 30 to 50 Omega_sun. In these
speculative scenarios, at 30 Omega_sun, a weak shock would have been formed,
but for 50 Omega_sun, we find that no bow shock could be present around Earth's
magnetosphere. This implies that with the Sun continuing to spin down, a strong
shock would have developed around our planet, and remained for most of the
duration of the solar main sequence.

Earth and Planetary Astrophysics;Solar and Stellar Astrophysics;Space Physics