The recent discovery of J0737-3039A & B-two pulsars in a highly relativistic
orbit around one another - offers an unprecedented opportunity to study the
elusive physics of pulsar radio emission. The system contains a rapidly
rotating pulsar with a spin period of 22.7 ms and a slow companion with a spin
period of 2.77 s, hereafter referred to as 'A' and 'B', respectively. A unique
property of the system is that the pulsed radio flux from B increases
systematically by almost two orders-of-magnitude during two short portions of
each orbit. Here, we describe a geometrical model of the system that
simultaneously explains the intensity variations of B and makes definitive and
testable predictions for the future evolution of the emission properties of
both stars. Our model assumes that B's pulsed radio flux increases when
illuminated by emission from A. This model provides constraints on the spin
axis orientation and emission geometry of A and predicts that its pulse profile
will evolve considerably over the next several years due to geodetic precession
until it disappears entirely in 15-20 years