a
\({T}_{1}=1\) \(hour\)

\(\Rightarrow \omega_{1}=2 \pi {rad} / {hour}\)

\({T}_{2}=8\) \(hours\)

\(\Rightarrow \omega_{2}=\frac{\pi}{4} {rad} /\) \(hour\)

\({R}_{1}=2 \times 10^{3} {km}\)

As \({T}^{2} \propto {R}^{3}\)

\(\Rightarrow\left(\frac{{R}_{2}}{{R}_{1}}\right)^{3}=\left(\frac{{T}_{2}}{{T}_{1}}\right)^{2}\)

\(\Rightarrow \frac{{R}_{2}}{{R}_{1}}=\left(\frac{8}{1}\right)^{2 / 3}=4 \Rightarrow {R}_{2}=8 \times 10^{3} {km}\)

\({V}_{1}=\omega_{1} {R}_{1}=4 \pi \times 10^{3} {km} / {h}\)

\({V}_{2}=\omega_{2} {R}_{2}=2 \pi \times 10^{3} {km} / {h}\)

Relative \(\omega=\frac{{V}_{1}-{V}_{2}}{{R}_{2}-{R}_{1}}=\frac{2 \pi \times 10^{3}}{6 \times 10^{3}}\)

\(=\frac{\pi}{3} {rad} /\) \(hour\)

\({x}=3\)