  Because of the dynamic nature of the interstellar medium, the Sun should have
encountered a variety of different interstellar environments in its lifetime.
As the solar wind interacts with the surrounding interstellar medium to form a
heliosphere, different heliosphere shapes, sizes, and particle contents result
from the different environments. Some of the large possible interstellar
parameter space (density, velocity, temperature) is explored here with the help
of global heliosphere models, and the features in the resulting heliospheres
are compared and discussed. The heliospheric size, expressed as distance of the
nose of the heliopause to the Sun, is set by the solar wind - interstellar
pressure balance, even for extreme cases. Other heliospheric boundary locations
and neutral particle results correlate with the interstellar parameters as
well. If the H0 clouds identified in the Millennium Arecibo survey are typical
of clouds encountered by the Sun, then the Sun spends ~99.4% of the time in
warm low density ISM, where the typical upwind heliosphere radii are up to two
orders of magnitude larger than at present.
