We formulate the problem of a gravitationally collapsing body in terms of a single set of coordinates that are employed both in the vacuum region outside the body and inside the body where there is a zero pressure perfect fluid. The spatial coordinateRis the usual Schwarzschild radial coordinate, while the time coordinatetis measured by radially falling geodesic clocks. It is possible to follow the collapse of the body entirely on a single (R,t) space–time diagram. We give analytical expressions for the metrics in the interior and exterior regions which join smoothly and naturally at the surface of the collapsing body. Other features such as apparent and event horizons are also described.