Question

The period of a satellite in a circular orbit of radius $R$ is $T$. The period of another satellite in a circular orbit of radius $4R$ is

• A. $4T$
• B. $8T$
• C. $T/4$
• D. $T/8$

Answer 1

The correct option is B $8T$

$T=2\pi \sqrt{\frac{R^3}{G{M}_e}}$

When $R\prime =4R\prime$

$T\prime =2\pi \sqrt{\frac{(4R{)}^3}{G{M}_e}}=2\pi \sqrt{\frac{64R^3}{G{M}_e}}=8\left(2\pi \sqrt{\frac{R^3}{G{M}_e}}\right)=8T$