The maximum and minimum distances of a comet from the Sun are $8 \times 10^{12} \, \text{m}$ and $1.6 \times 10^{12} \, \text{m}$. If its velocity when nearest to the Sun is $60 \, \text{m/s}$, what will be its velocity in m/s when it is farthest?
Show Hint
The velocity of a comet is inversely proportional to the distance from the Sun when it follows an elliptical orbit.
The velocity of a comet follows the law of conservation of angular momentum:
\[
m v_1 r_1 = m v_2 r_2
\]
where:
$m$ is the mass of the comet,
$v_1$ and $v_2$ are the velocities at the nearest and farthest points, and
$r_1$ and $r_2$ are the corresponding distances.
Using the given values:
\[
v_2 = \frac{v_1 r_1}{r_2} = \frac{60 \times 8 \times 10^{12}}{1.6 \times 10^{12}} = 12 \, \text{m/s}
\]