Q157 / 200 · Manipal (MET) 2013 · Physics

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

  • A
    32 days
  • B
    18 days
  • Correct answer
    C
    8 days
  • D
    9 days

Solution

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 $\therefore \quad T^2 \propto R^3$ $\frac{T_s}{T_c}=\left(\frac{R_s}{R_c}\right)^{3 / 2}$ given $\quad R_s=4 R_c$ $\begin{aligned} & \qquad \frac{T_s}{T_c}=\left(\frac{4 R_c}{R_c}\right)^{3 / 2}=8 \\ & \text { for } T_c=1 \text { day } \\ & T_s=8 \text { days. }\end{aligned}$

Hence, the correct answer is option: 'C'.

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