  The use of quantum field theory to understand astrophysical phenomena is not
new. However, for the most part, the methods used are those that have been
developed decades ago. The intervening years have seen some remarkable
developments in computational quantum field theoretic tools. In particle
physics, this technology has facilitated calculations that, even ten years ago
would have seemed laughably difficult. It is remarkable, then, that most of
these new techniques have remained firmly within the domain of high energy
physics. We would like to change this. As alluded to in the title, this is the
first in a series of papers aimed at showcasing the use of modern on-shell
methods in the context of astrophysics and cosmology. In this first article, we
use the old problem of the bending of light by a compact object as an anchor to
pedagogically develop these new computational tools. Once developed, we then
illustrate their power and utility with an application to the scattering of
gravitational waves.
