Past exam of the physics 1 paper of the University of Oxford / 2013 / 10 / c / ii / Solution

Launch and arrival occur on the capsule's own worldline, so its clock measures the proper time. In the ship frame its Lorentz factor is ${\gamma }_{c/s}=(1-0.9^2{)}^{-1/2}$; thereforeThis uses the station-frame distance convention stated in i. With a one-light-day distance in the ship frame instead, it becomes $\Delta {\tau }_c=\sqrt{0.19}/1.75\mathrm{day}\simeq 0.249080\mathrm{day}$. The uncertainty is a distance-frame convention in the wording, not a missing figure or an unanswered mathematical part.