current and past mass loss are related by a power law:

$$\frac{\dot{m}v_{sw}}{\dot{m}_0v_{sw0}}=\left(\frac{t}{t_0}\right)^{-2.33}$$

where $\dot{m}_{0}$, $v_{sw0}$ are the present-day mass loss and solar wind velocity, respectively. As we will discuss later, this relationship should be applied to the Sun only for solar ages greater than $\sim$ 700 million years. This relationship suggests that the solar mass loss at 3.45 Ga was 2.4 x $10^{-13}$ M$_{\odot}$/yr, where M$_{\odot}$ is the current solar mass. This mass loss can be used to further derive a model (Model A of @Tarduno2010) of wind velocity and density change with time, which comprise solar wind pressure. Hence, we can now solve equation 1 to obtain estimates of magnetopause standoff distance as a function of dipole moment (Figure 5).

The paleointensity estimates for 3.4-3.45 Ga from the Kaapvaal Craton dacites suggest standoff distances of $\sim$5 Earth radii (R$_{e}$). One can also estimate mass loss from rotation and X-ray emission. Stellar evolution models predict the Sun at 3.45 Ga would appear to be a G6V star having a rotational period of $\sim$12 days [@Mamajek2008]. Mass loss rates among solar-type stars can be related to X-ray emission ($f_{X}$) and rotation as: $$\dot{m}=\dot{M_{\odot}}\left(\frac{\rm{R}}{\rm{R}_{\odot}}\right)^{2}\left(\frac{f_{X}}{f_{X_{\odot}}}\right)^{1.34\pm0.18}$$\
where R is solar radius, R$_{\odot}$ is the 