Hi, Imagine a rocket accelerating in flat space. Let's say for the sake of argument it measures its acceleration by using an onboard accelerometer as (a). (E1)What would a momentarily comoving inertial observer measure the acceleration of the rocket to be using his own local rulers and clocks as the rocket passes him? (E2)What would an observer on the rocket measure the acceleration of a mass released from a somewhere near the nose of the rocket falling over a short distance? This measurement should be the same as the apparent acceleration (as in change of velocity per unit time) of the inertial observer in (E1) as measured by the observer in the rocket. This should also be similar to the average acceleration of a ball tossed up into the air by an observer onboard the rocket as measured by that same observer. Using the equivalence principle, is the acceleration calculated by placing a mass on some weighing scales in a gravitational field exactly the same (in relativistic terms) as the acceleration measured by timing the fall time over a short distance so that the change in gravitational radius and velocity is infinitesimal? Which of the above practical measurements is closest to the formal definition of proper acceleration?