Q.Two satellites A and B are revolving around a planet. Their periods of revolution are 1 hour and 8 hours respectively. The radius of orbit of satellite B is $4\times10^4$ km. Find the radius of orbit of satellite A.

[!TLDR] Using Kepler's third law $(T_A/T_B)^2=(r_A/r_B)^3$ with $T_A=1$h, $T_B=8$h gives $r_A/r_B=1/4$, so $r_A …

By Kepler's third law (law of periods, also derivable for satellites from $T^2=4\pi^2r^3/GM$), $T^2\propto r^3$ for satellites orbiting the same planet, so $\left(\dfrac{T_A}{T_B}\right)^2=\left(\dfrac{r_A}{r_B}\right)^3.$ Given $T_A=1$ hour and $T_B=8$ hours: $$\left(\dfrac{1}{8}\right)^2=\dfrac{1}{64}=\left(\dfrac{r_A}{r_B}\right)^3\quad\Longrightarrow\quad\dfrac{r_A}{r_B}=\left(\dfrac{1}{64}\right)^ …

Apply Kepler's third law in ratio form between the two satellites orbiting the same planet, using their giv …

Taking the cube root incorrectly, or forgetting to cube-root (1/64) fully to get exactly …