  A moderately massive early Sun has been proposed to resolve the so-called
faint early Sun paradox. We calculate the time-evolution of the solar mass that
would be required by this hypothesis, using a simple parametrized
energy-balance model for Earth's climate. Our calculations show that the solar
mass loss rate would need to have been 2-3 orders of magnitude higher than
present for a time on the order of ~2 Gy. Such a mass loss history is
significantly at variance (both in timescale and in the magnitude of the mass
loss rates) with that inferred from astronomical observations of mass loss in
younger solar analogues. While suggestive, the astronomical data cannot
completely rule out the possibility that the Sun had the required mass loss
history; therefore, we also examine the effects of the hypothetical historical
solar mass loss on orbital dynamics in the solar system, with a view to
identifying additional tests of the hypothesis. Planetary and satellite orbits
provide a few tests, but these are weak or non-unique.
