  While the constant radial acceleration problem is known to be integrable and
has received some recent attention in an orbital mechanics context, a closed
form explicit solution, relating the state variables to a time parameter, has
eluded all researchers so far. It is here shown how such a solution exists and
is elegantly expressed in terms of the Weierstrass elliptic and related
functions. Previously known facts can be derived from the new explicit solution
and new insights are revealed.
