Differential aging from acceleration: An explicit formula

We consider a clock paradox where an observer leaves an inertial frame, is accelerated, and after an arbitrary trip returns. We discuss a simple equation that gives an explicit relation in 1 + 1 dimensions between the time elapsed in the inertial frame and the acceleration measured by the accelerating observer during the trip. A non-closed trip with respect to an inertial frame appears closed with respect to another suitable inertial frame. We use this observation to define the differential aging as a function of proper time. The reconstruction problem of special relativity is discussed and it is shown that its solution would allow the construction of an inertial clock.