at velocity V during some time Tc according to clock K. Phase 3: Rocket fires its engines in the opposite direction of K during a time Ta according to clock K until it is at rest with respect to clock K. The constant proper acceleration has the value −a, in other words the rocket is decelerating. Phase 4: Rocket keeps firing its engines in the opposite direction of K, during the same time Ta according to clock K, until K' regains the same speed V with respect to K, but now towards K (with velocity −V). Phase 5: Rocket keeps coasting towards K at speed V during the same time Tc according to clock K. Phase 6: Rocket again fires its engines in the direction of K, so it decelerates with a constant proper acceleration a during a time Ta, still according to clock K, until both clocks reunite. Knowing that the clock K remains inertial (stationary), the total accumulated proper time Δτ of clock K' will be given by the integral function of coordinate time Δt where v(t) is the coordinate velocity of clock K' as a function of t according to clock K, and, e.g. during phase 1, given by This integral can be calculated for the 6 phases: Phase 1 Phase 2 Phase 3 Phase 4 Phase 5 Phase 6 where a is the proper acceleration, felt by clock K' during the acceleration phase(s) and where the following relations hold between V, a and Ta: So the traveling clock K' will show an elapsed time of which can be expressed as whereas the stationary clock K shows an elapsed time of which is, for every possible value of a, Ta, Tc and V, larger than the reading of clock K': Difference in elapsed times: how to calculate it from the ship In the standard proper time formula Δτ represents the time of the non-inertial (travelling) observer K' as a function of the elapsed time Δt of the inertial (stay-at-home) observer K for whom observer K' has velocity v(t) at time t. To calculate the elapsed time Δt of the inertial observer K as a function of the elapsed time Δτ of the non-inertial observer K', where only quantities measured by K' are accessible, the following formula can be used: where a(τ) is the proper acceleration of the non-inertial observer K' as measured by himself (for instance with