Question

A satellite moves around the earth in a circular orbit of radius $R$ making one revolution per day. A second satellite moving in a circular orbit moves around the earth once in $8$ days. The radius of the orbit of the second satellite is

• A. $8R$
• B. $4R$
• C. $2R$
• D. $R$

Answer 1

Answer: (B)

Given that, $T_{1} = 1$ day and $T_{2} =$ 8 days
∴ $\frac{T_{2}}{T_{1}} = \left(\right. \frac{r_{2}}{r_{1}} \left.\right)^{3 / 2}$ $\Rightarrow $ $\frac{r_{2}}{r_{1}} = \left(\right. \frac{T_{2}}{T_{1}} \left.\right)^{2 / 3} = \left(\right. \frac{8}{1} \left.\right)^{2 / 3} = 4$ $\Rightarrow $ $r_{2} = 4 r_{1} = 4 R$