  In this paper we focus on the Earth matter effects for the solar parameter
determination by a medium baseline reactor experiment such as JUNO. We derive
perturbative expansions for the mixing angles $\theta_{12}$ and $\theta_{13}$
as well as the $\Delta m^2_{21}$ and $\Delta m^2_{31}$ in terms of the matter
potential relevant for JUNO. These expansions, up to second order in the matter
potential, while simple, allow one to calculate the electron antineutrino
survival probability to a precision much better than needed for the JUNO
experiment. We use these perturbative expansions to semi-analytically explain
and confirm the shift caused by the matter effects on the solar neutrino mixing
parameters $\theta_{12}$ and $\Delta m^2_{21}$ which were previously obtained
by a purely numerical $\chi^2$ analysis. Since these shifts do not satisfy the
naive expectations and are significant given the precision that can be achieved
by the JUNO experiment, a totally independent cross check using a completely
different method is of particular importance. We find that these matter effect
shifts do not depend on any of the details of the detector characteristics
apart from the baseline and earth mass density between reactor(s) and detector,
but do depend on the normalized product of reactor neutrino spectrum times the
inverse-beta decay cross-section. The results of this manuscript suggests an
alternative analysis method for measuring $\sin^2 \theta_{12}$ and $\Delta
m^2_{21}$ in JUNO which would be a useful cross check of the standard analysis
and for the understanding of the Wolfenstein matter effect. The explanation of
these shifts together with a quantitative understanding, using a
semi-analytical method, is the principal purpose of this paper.
