A huge circular arc of length 4 . 4   ly subtends an angle 4 s at the centre of the circle. How long it…

$\ell =4.4\mathrm{ly}=4.4\times 9.46\times {10}^{15}$

length of Arc. $=\ell =R\theta$

$4.4\times 9.46\times {10}^{15}=\mathrm{R}\theta$

$\theta =4 \mathrm{S}=4\times 4.843\times {10}^{-6}=1.94\times {10}^{-5}$ rad

$4.4\times 9.46\times {10}^{15}=\mathrm{R}\times 1.94\times {10}^{-5}$

$R=2.1455\times {10}^{21}$ meter

Speed $=8\mathrm{Au}=8\times 1.5\times {10}^{11} {\mathrm{ms}}^{-1}=12\times {10}^{11} {\mathrm{ms}}^{-1}$

$4$ revolution means distance $=4\times 2\pi R$ metre

time $=\frac{\text{ distance }}{\text{ speed }}=\frac{4\times 2\pi \mathrm{R}}{12\times {10}^{11}};$ time $=\frac{8\times 3.14\times 2.1455\times {10}^{21}}{12\times {10}^{11}}\Rightarrow 4.5\times {10}^{10}\sec$