Planets \(\mathrm{A}\) and \(\mathrm{B}\) are 10 light years apart in the reference frame of planet A. (One light year is the distance light travels in one year.) A deep-space probe is launched from \(\mathrm{A}\), and \(5 \mathrm{y}\) later (in reference frame A) a similar probe is launched from B. Does a reference frame exist in which these two events 

\((a)\) are simultaneous and 

\((b)\) occur at the same position?

(c) Compute, if possible, the proper time interval between the events?

(d) How do your answers to parts \(a-c\) change if the planets are (in reference frame A) 5 light years apart and the time interval between launch from \(A\) and launch from \(B\) is \(10 \mathrm{y}\) ?