  We study the gravitational behaviour of a spherically symmetric radiating
star when the fluid particles are in geodesic motion. We transform the
governing equation into a simpler form which allows for a general analytic
treatment. We find that Bernoulli, Riccati and confluent hypergeometric
equations are possible. These admit solutions in terms of elementary functions
and special functions. Particular models contain the Minkowski spacetime and
the Friedmann dust spacetime as limiting cases. Our infinite family of
solutions contains specific models found previously. For a particular metric we
briefly investigate the physical features, derive the temperature profiles and
plot the behaviour of the casual and acasual temperatures.
