Question

A satellite is launched in a circular orbit of radius $R$ around the earth. A second satellite is launched into an orbit of radius $1.01\,R$ . The period of second satellite is longer than the first one (approximately) by

• A. 1.50%
• B. 0.50%
• C. 3%
• D. 1%

Answer 1

Answer: (A)

1.50%

Answer 2

From Keplers law,
${{T}^{2}}\propto {{R}^{3}}$
Or ${{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{2}}={{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{3}}={{\left( \frac{1.01R}{R} \right)}^{3}}={{(1+0.01)}^{3}}$
Or $\frac{{{T}_{2}}}{{{T}_{1}}}={{(1+0.01)}^{3/2}}=1+\left( \frac{3}{2}\times 0.001 \right)$
Or $\frac{{{T}_{2}}-{{T}_{1}}}{{{T}_{1}}}=\frac{1.5}{100}=1.5$