Two satellites S₁ and S₂ revolve round a planet in coplanar circular orbits in the same sense. Their periods of revolution are 1 hour and 8 hour respectively. The radius of the orbit of S₁ is 10⁴ km., the angular speed of S₂ as observed by an astronaut in S₁ is

$\frac{\pi}{3}$

$\omega=\left|\frac{v_2-v_1}{r_2-r_1}\right|$

$\Rightarrow \omega=\left|\frac{10^4 \pi}{3 \times 10^4}\right|$

$\Rightarrow \omega=\frac{\pi}{3}$ rads⁻¹