 Solution

Use a year of $365.25$ days, so $t=9.46728\times 10^8\mathrm{s}$, and $k=\rho A=10^{-11}\mathrm{kg}{\mathrm{m}}^{-1}$. With $M_p=722\mathrm{kg}$ and $v_{\infty }\simeq 1.752\times 10^4\mathrm{m}{\mathrm{s}}^{-1}$, e givesThe corresponding cloud thickness is $x_f=(M_f-M_p)/k\simeq 1.50\times 10^{13}\mathrm{m}$. Checking $M_f{v}_f=M_p{v}_{\infty }$ verifies conservation of momentum; using the initial speed for all thirty years would overestimate the collected mass.