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 $\left(1.01\right)R$. The period of the second satellite is larger than that of the first one by approximately

• A. $0.5$%
• B. $1$%
• C. $1.5$%
• D. $3.0$%

Answer 1

The correct option is C $1.5$%

In the problem, orbital radius is increased by $1$%
Time period of satellite T $\propto r^{3/2}$
Hence
$\Delta T=\frac{3}{2}\Delta R$
Percentage change in time period
= $\frac{3}{2}$ (% change in orbital radius)
= $\frac{3}{2}$($1$%)=$1.5$%

Why this question? Note: For a functional relation, $y=f\left(x\right)$, for a small change $\Delta x$, the change $\Delta y=f^{\prime }\left(x\right)\Delta x$.