Two asteroid clusters at rest with respect to each other are \(3.00 \times 10^{9} \mathrm{~m}\) apart, and both measure \(6.00 \times 10^{8} \mathrm{~m}\) across in the reference frame of the clusters. A pilot in a spaceship moving at \(0.900 c_{0}\) relative to the cluster reference frame is trying to pass between the two clusters. To an observer who is stationary in the reference frame of the clusters, the ship just barely misses the corners of the clusters as shown in Figure P14.51. If a line were drawn between the centers of the two clusters, what would be the angle between that line and the ship's path in (a) the reference frame of the clusters and \((b)\) the reference frame of the ship?

Data from Figure P14.51

Transcribed Image Text:

6.00 10% m asteroid cluster 3.00 10 m hip=0.90c asteroid cluster 6.00 x 10 m