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From: blackhead on 9 Nov 2009 17:01
On 8 Nov, 13:25, DSeppala <dsepp...(a)austin.rr.com> wrote:
> The following seems contradictory.
> There are  two identical rockets separated a distance L as measured on
> the x-axis in an inertial reference frame.  Let the two rockets be on
> parallel lines to the x-axis.  An observer in a frame moving at V
> relative to the x-axis turns on the thrusters of both rockets
> simultaneously as measured in his frame. As viewed in this frame the
> tip of each rocket remains a distance L away from the tip of the other
> rocket even as the rockets accelerate. This occurs because  both
> rockets undergo identical simultaneous accelerations, so as one rocket
> changes position the other does the identical motion at a different
> location in space as measured in this frame.
>     How do people on board the rockets view things? In the inertial
> reference frame the rockets were initially in, the turning on of the
> thrusters of each of the two rockets were not simultaneous events.
> The thrusters of one rocket were turned on before the thrusters of the
> other rocket. Let's say you are in the rocket where the thruster was
> turned on first, and you start accelerating toward the other rocket at
> some constant acceleration rate.  After T seconds as measured  in your
> accelerating rocket, the thrusters of the other rocket are turned on
> so that both of you are now accelerating in the same direction.  

>You
> note that at this time you had a closing velocity of V (you and the
> other rocket were approaching each other).

If you perform the LTs for the simultaneous events from the
simultaneous frame to either rocket frame, you'll find that the rocket
in front is always turned on first and there is no closing velocity.


>  You know the other rocket
> is identical to yours, and you are still accelerating at the same
> constant rate.  If the closing rate continues  at least at V or
> greater, after some point in time the tip of your rocket will pass the
> tip of the other rocket.  But we've already established that as
> measured in the inertial reference frame where turning on the
> thrusters were simultaneous events, the tips of the two rockets never
> are at the same point in space at the same time, and hence can never
> pass each other.  It seems to me at some point in time the rocket that
> started accelerating first must pass the other rocket.
>    Thanks for explaining this from the point of view of someone in the
> first rocket.
> David Seppala
> Bastrop Texas

Have a go at using the LTs for transforming the simultaneous events to
the frame of either rocket.
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