A satellite is launched into a circular orbit of radius ' R ' around the earth. A second satellite is…

A satellite is launched into a circular orbit of radius ' R ' around the earth. A second satellite is launched into an orbit of radius 1.03 R. The time period of revolution of the second satellite is larger than the first one approximately by
  1. $9 \%$
  2. $3 \%$
  3. $4.5 \%$
  4. $2.5 \%$

Solution


$T_1 \propto(R)^{3 / 2}$
and $T_2 \propto(1.03 R)^{3 / 2}$
$\Rightarrow \quad T_2=(1.03 R)^{3 / 2} \cdot T_1 \approx 1.045 T_1$
So $T_2$ will larger by $4.5 \%$ w.r.t. $T_1$.

Asked in: JEE Main 2025 (24 Jan Shift 1)

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