Question

A satellite is launched in a circular orbit of radius $R$ and another satellite is launched in circular orbit of radius $1.01R$. The time period of second satellite is different from that of the first satellite by

• A. $1.5\%increased$
• B. $1\%decreased$
• C. $1\%increased$
• D. $1.5\%decreased$

Answer 1

Answer: (A)

$1.5\%increased$

Time period $T=2\pi \sqrt{\frac{R^3}{GM}}$
if $R$ is changed to $R+\delta R\Rightarrow T$ becomes $T+\delta T$
$T+\delta T=2\pi \sqrt{\frac{(R+\delta R{)}^3}{GM}}$
dividing this by $T,1+\frac{\delta T}{T}={\left(\frac{R+\delta R}{R}\right)}^{1.5}$
Simplifying this, $\delta T=0.015T\Rightarrow 1.5\%$more than $T$.