Answer
(a) $d = 9.4\times 10^{10}~km$
(b) The separation distance is $~~120~~$ times the distance of Jupiter from the sun.
Work Step by Step
We can write an equation for the resolution:
$\theta_{min} = \frac{1.22~\lambda}{D}$
$\theta_{min} = \frac{(1.22)~(650\times 10^{-9}~m)}{2.4~m}$
$\theta_{min} = 3.304\times 10^{-7}~rad$
We can find the separation distance $d$:
$\theta = \frac{d}{L}$
$d = L~\theta$
$d = (30,000)(9.46\times 10^{12}~km)(3.304\times 10^{-7}~rad)$
$d = 9.4\times 10^{10}~km$
(b) We can express this distance as a multiple of the distance of Jupiter from the sun:
$d = \frac{9.4\times 10^{10}~km}{7.8\times 10^8~km} = 120$
The separation distance is $~~120~~$ times the distance of Jupiter from the sun.
