  We restate the notion of orthogonal calculus in terms of model categories.
This provides a cleaner set of results and makes the role of O(n)-equivariance
clearer. Thus we develop model structures for the category of n-polynomial and
n-homogeneous functors, along with Quillen pairs relating them. We then
classify n-homogeneous functors, via a zig-zag of Quillen equivalences, in
terms of spectra with an O(n)-action. This improves upon the classification of
Weiss. As an application, we develop a variant of orthogonal calculus by
replacing topological spaces with orthogonal spectra.
