Final answer:
Halley's Comet moves in an elliptical orbit around the Sun. Using the principle of conservation of angular momentum, we can find its speed when it is farthest from the Sun.
Step-by-step explanation:
Halley's comet moves in an elliptical orbit around the Sun. The comet's closest approach to the Sun is 0.36 AU, while its greatest distance is 46 AU. To find its speed when it is farthest from the Sun, we can use the principle of conservation of angular momentum.
The angular momentum of a comet remains constant throughout its orbit if there are no external forces acting on it. Since the comet's mass does not change and its angular momentum is conserved, we can use the formula for angular momentum.
The formula is given by: $mvr = m_{1}v_{1}r_{1}$
where $m$ is the mass of the comet, $v$ is its speed, and $r$ is the distance from the Sun.
At its closest approach, the comet's speed and distance are given as $v_{1} = 45\ m/s$ and $r_{1} = 0.36\ AU$. We can substitute these values into the formula to find $v_{2}$, the speed of the comet when it is farthest from the Sun.
Using the conservation of angular momentum formula, we have: $mvr = m_{1}v_{1}r_{1}$
$vr = v_{1}r_{1}$
$v = \frac{v_{1}r_{1}}{r}$
Substituting the known values, we find: $v = \frac{45\ m/s\ \cdot\ 0.36\ AU}{46\ AU}$.