F=GMm/r2=mv2/r, v=2pir/t
equating the two values for F and remembering to include the equation for v, GMm/r^2 = m(2pir/t^2)^2/r. Rearranging to find t^2, t^2 = 4pi^2r^3/GM where 4pi^2/GM equals the constant k. Therefore for the purpose of the question, k = 2.97x10^-19s^-2m^-3.