Question

In figure A, a stationary spacecraft of mass $M$ is passed by asteroid A of mass $m$, asteroid N of the same mass $m$, and asteroid of mass $2m$. The asteroids move along the indicated straight paths at the same speed; the perpendicular distances between the spacecraft on the paths are given as multiples of $R$. Figures B gives the gravitational potential energy U(t) of the spacecraft-asteroid system during the passage of each asteroid treating time $t=0$ as the moment when seperation in minimum. Which asteroid corresponds to which plot of $U\left(t\right)$?

• A. $A-1,B-2,C-3$
• B. $B-1,A-3,C-2$
• C. $B-1,A-2,C-3$
• D. None

Answer 1

The correct option is C $B-1,A-2,C-3$

Let us take a look at the minimum potential energies of the spacecraft and asteroids individually.

For asteroid A, ${PE}_{min}=-\frac{GMm}{R}$

For asteroid B, ${PE}_{min}=-\frac{GMm}{2R}$

For asteroid C, ${PE}_{min}=-\frac{2GMm}{R}$

Thus, we must have: $C-3,A-2$ and $B-1$.