12) A space station wants to record the passage of an asteroid, which moves in uniform linear motion relative to it. Unfortunately, the station's radar is damaged and does not provide reliable distance measurements, while it accurately measures the angle at which the asteroid is seen. Several measurements are taken at regular time intervals. What is the minimum number of measurements needed to reconstruct the asteroid's trajectory?

$\begin{array}{llll}\text { (A) } 2 & \text { (B) } 3 & \text { (C) } 4 & \text { (D) a finite number greater than } 4\end{array}$

(E) no number of measurements is sufficient.
12) The answer is $\mathbf{( E )}$. Given a trajectory $r$ for the asteroid, any trajectory homothetic to it with respect to the station provides the same observations, so it cannot be determined uniquely, unless the asteroid collides with the station, an event to be absolutely avoided!