Three enemy spacecraft have been causing trouble in the asteroid belt. they always travel in a line, evenly spaced apart, attempting to chase down local spacecraft to steal their goods. the local asteroid colonists have decided to set a trap to capture these three spacecraft. they'll get them to chase one of their fastest ships into an asteroid with a large hole in it and, once the three enemy ships are inside, close two giant trapdoors on each side of the asteroid to catch them. these spacecraft all travel close to the speed of light so the locals will have to take relativity into account. intelligence about the enemy spacecraft reveals that, in their reference frame, they always travel 90 m behind their teammate, each spacecraft is 10 m in length, and their maximum velocity is 90% the speed of light (relative to the asteroids). the asteroid tunnel is only 215 m in length. in this problem we will analyze whether the locals will be able to capture the enemy spacecraft after taking into account relativity.
one of the local students had been studying relativity and began to question the plan. how would this all appear to the enemy spacecraft as they flew through the asteroid? specifically, if the spacecraft were in an inertial frame (i. e., one with no acceleration) how long would the asteroid tunnel appear to be in their rest frame?