  The Rayleigh equation 3/2 R'+RR"+p/rho=0 with initial conditions R(0)=Rmax,
R'(0)=0 models the collapse of an empty spherical bubble of radius R(T) in an
ideal, infinite liquid with far-field pressure p and density rho. The solution
for r=R/Rmax as a function of time t=T/Tcollapse, where R(Tcollapse)=0, is
independent of Rmax, p, and rho. While no closed-form expression for r(t) is
known we find that s(t)=(1-t^2)^(2/5) approximates r(t) with an error below 1%.
A systematic development in orders of t^2 further yields the
0.001%-approximation r*(t)=s(t)[1-a Li(2.21,t^2)], where a=-0.01832099 is a
constant and Li is the polylogarithm. The usefulness of these approximations is
demonstrated by comparison to high-precision cavitation data obtained in
microgravity.
