Question

Q.4) Two satellites A and B revolve around a planet in coplanar circular orbit in the same direction with period of revolutions 1 hour and 8 hours respectively. The radius of satellite A is 10⁴ km then find the angular speed of 'B' with respect to A ?

Answer 1

$$\begin{gathered} Dearstudent \\ {T}^2=k{R}^{3}bykepler\text{'}slaw \\ \frac{{r_2}^3}{{r_1}^3}=\left(\frac{{T_2}^2}{{T_1}^2}\right)(r_1={10}^4;T_1=1hr;T_2=hr) \\ {r}_2=r_1\times \sqrt[3]{\left(\frac{{T_2}^2}{{T_1}^2}\right)}=4\times {10}^{4}km \\ {v}_1=\frac{2\pi R_1}{T_1} \\ {v}_1=\frac{2\pi {10}^4}{1}=2\pi \times {10}^{4}km/h \\ {v}_2=\frac{2\pi R_2}{T_2} \\ {v}_2=\frac{2\pi \times 4\times {10}^4}{8}=\pi \times {10}^{4}km/h \\ relativeangularvelocity=\frac{\left|v_1-v_2\right|}{\left|r_1-r_2\right|}=\frac{\left|2\pi \times {10}^4-\pi \times {10}^4\right|}{\left|4\times {10}^4-{10}^4\right|}=\frac{\pi }{3}rad/hr \\ Regards \end{gathered}$$