  First we argue that many BV and homotopy BV structures, including both
familiar and new examples, arise from a common underlying construction. The
input of this construction is a cyclic operad along with a cyclically invariant
Maurer-Cartan element in an associated Lie algebra. Using this result we
introduce and study the operad of cyclically invariant operations, with
instances arising in cyclic cohomology and $S^1$ equivariant homology. We
compute the homology of the cyclically invariant operations; the result being
the homology operad of $\mathcal{M}_{0,n+1}$, the uncompactified moduli spaces
of punctured Riemann spheres, which we call the gravity operad after Getzler.
Motivated by the line of inquiry of Deligne's conjecture we construct `cyclic
brace operations' inducing the gravity relations up-to-homotopy on the cochain
level. Motivated by string topology, we show such a gravity-BV pair is related
by a long exact sequence. Examples and implications are discussed in course.
