Question

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

• A. $3.0\%$
• B. $1.5\%$
• C. $0.7\%$
• D. $1.0\%$

Answer 1

Answer: (B)

$1.5\%$

We know that relation between radius of orbit and time period of revolution is $T^2\propto R^3$
$\frac{T^{\prime }}{T}={\left(\frac{1.01}{1}\right)}^{3/2}={(1+\frac{1}{100})}^{3/2}$
$=1+\frac{3}{2}\times \frac{1}{100}=1+\frac{3}{200}$
$\frac{T^{\prime }}{T}-1=1+\frac{3}{200}-1$
$\frac{T^{\prime }-T}{T}=\frac{3}{200}\Rightarrow \frac{\Delta T}{T}=\frac{3}{200}$
$\frac{\Delta T}{T}\times 100=\frac{3\times 100}{200}$
$\%$ Change in $T=1.5\%$