Question

An earth satelites S has orbit radius which $4$ times that of communication satellite C. The period of revolution of S will be.

• A. $32$ days
• B. $18$ days
• C. $8$ days
• D. $9$ days

Answer 1

Answer: (C)

$8$ days

Larger the distance of planet from the sun, larger will be its period of revolution around the sun.
Kepler's third low planetary motion the square of the period of revolution of any planet around the sun is directly proportional to the cube of the semi-major axis of its elliptical orbit.
$\therefore T^2\propto R^3$
$\frac{T_s}{T_c}={\left(\frac{R_s}{R_c}\right)}^{3/2}$
given $R_s=4R_c$
$\frac{T_s}{T_c}{\left(\frac{4R_c}{R_c}\right)}^{3/2}=8$
for $T_c=1$day
$T_s=8$ days.