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 $2 m$ . 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 $U (t)$ ?

Question

Verified by Toppr

Answer 1

Let us take a look at the minimum potential energies of the spacecraft and asteroids individually.
For asteroid A, $P E_{m i n} = - \frac{G M m}{R}$

For asteroid B, $P E_{m i n} = - \frac{G M m}{2 R}$

For asteroid C, $P E_{m i n} = - \frac{2 G M m}{R}$

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

Answer 2

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

For asteroid A,

P E_{m i n} = - \frac{G M m}{R}

For asteroid B,

P E_{m i n} = - \frac{G M m}{2 R}

For asteroid C,

P E_{m i n} = - \frac{2 G M m}{R}

Thus, we must have:

C - 3, A - 2

and

B - 1

.