KLT of radio signals from relativistic spaceships in uniform and decelerated motion

Abstract

It is well known that in special relativity two time variables exist: the coordinate time t, which is the time measured in the fixed reference frame, and the proper time τ, which is the time shown by a clock rigidly connected to the moving body. They are related by

$$ \tau (t) = \int_0^t {\sqrt {1 - \frac{{v^2 (s)}} {{c^2 }}} ds} $$

(11.1)

where v(t) is the body velocity and c is the speed of light (see [1, p. 44]).