  Let M be a smooth manifold and V a Euclidean space. Let Ebar(M,V) be the
homotopy fiber of the map from Emb(M,V) to Imm(M,V). This paper is about the
rational homology of Ebar(M,V). We study it by applying embedding calculus and
orthogonal calculus to the bi-functor (M,V) |--> HQ /\Ebar(M,V)_+. Our main
theorem states that if the dimension of V is more than twice the embedding
dimension of M, the Taylor tower in the sense of orthogonal calculus
(henceforward called ``the orthogonal tower'') of this functor splits as a
product of its layers. Equivalently, the rational homology spectral sequence
associated with the tower collapses at E^1. In the case of knot embeddings,
this spectral sequence coincides with the Vassiliev spectral sequence. The main
ingredients in the proof are embedding calculus and Kontsevich's theorem on the
formality of the little balls operad.
  We write explicit formulas for the layers in the orthogonal tower of the
functor HQ /\Ebar(M,V)_+. The formulas show, in particular, that the (rational)
homotopy type of the layers of the orthogonal tower is determined by the
(rational) homology type of M. This, together with our rational splitting
theorem, implies that under the above assumption on codimension, the rational
homology groups of Ebar(M,V) are determined by the rational homology type of M.
