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 speed of S₂ relative to S₁ when they are closet (in kmh^-1) is

10⁴ π

Since T² ∝ r³

$\Rightarrow \frac{r_1^3}{r_2^3}=\frac{T_1^2}{T_2^2}=\frac{1}{64}$

$\Rightarrow \frac{r_1}{r_2}=\frac{1}{4}$

$\Rightarrow r_2=4 \times 10^4$ km

$v_1=\frac{2 \pi r_1}{T_1}$  and  $v_2=\frac{2 \pi r_2}{T_2}$

$\Rightarrow v_1=\frac{2 \pi \times 10^4}{1}$  and  $v_2=\frac{2 \pi \times 4 \times 10^4}{8}$ (in kmph)

⇒ v₁ = 2π × 10⁴ kmh⁻¹ and v₂ = π × 10⁴ kmh⁻¹

So, speed of S₂ with respect to S₁ is π × 10⁴ kmh⁻¹.