Question

A satellite is launched into a circular orbit of radius $R$ around the earth. A second satellite is launched into an orbit of radius $1.01R$. The period of second satellite is larger than the first one by approximately

• A. $0.5$%
• B. $1.0$%
• C. $1.5$%
• D. $3.0$%

Answer 1

Answer: (C)

$1.5$%

$T=2\pi \sqrt{\frac{(R+h{)}^3}{GM}}$
$T_1=2\pi \sqrt{\frac{R^3}{GM}},T_2=2\pi \sqrt{\frac{(1.01R{)}^3}{GM}}$
$\frac{T_2-T_1}{T_1}\times 100=1.5$%