  Exotic spin-dependent interactions mediated by new light particles led to
solutions to several important questions in modern physics. Such interactions
involving a scalar coupling $g_S^N$ at one vertex and a pseudo-scalar coupling
$g_P^n$ at the polarized neutron vertex can be induced by the exchange of
spin-0 bosons, or a vector/axial-vector coupling $g_V^N$/$g_A^N$ at one vertex
and an axial-vector coupling $g_A^n$ at the polarized neutron vertex can be
induced by the exchange of spin-1 bosons. If such new interactions exist, the
Sun and the Moon can induce sidereal variations of effective fields along the
direction perpendicular to the Earth's rotation axis. We derived new
experimental upper limits on such exotic spin-dependent interactions at
astronomical interaction ranges by analyzing existing data from laboratory
measurements on the Lorentz and CPT violation. We set the most stringent
experimental limits on $g_S^Ng_P^n$ ranging from $\sim 2\times 10^{10}$m to
$\sim 10^{14}$m. Previously, the best limit on $g_S^Ng_P^n$ at this range is
from astrophysics. The result is the first time laboratory limits surpass the
astrophysical ones on the scalar-pseudoscalar type interaction, to our best
knowledge. We report new constraints on vector-axial-vector and
axial-axial-vector type interaction at the range of astronomical scales. The
new limits on vector-axial-vector are improved by as much as $\sim$12 orders of
magnitude. We also apply the analysis to the Hari-Dass interactions and obtain
corresponding new constraints on the interactions. We discuss the possibilities
of using the beam method to further search the interaction involving other
particles, such as electrons, muons, etc., based on the same idea.
