Question

A space expedition discovers a planetary system consisting of a massive star and several spherical planets. The planets all have the same uniform mass density. The orbit of each planet is circular. In the observed planetary system, Planet A orbits the central star at the distance of 2R and takes T hours to complete one revolution around the star. Planet B orbits the central star at the distance of R. Which of the following expressions is correct for the number of hours it takes Planet B to complete one revolution around the star?
a. 1/√8T
b. 1/2T
c. 1/√4T
d. 2T
e. √8T

Answer 1

Answer:

$T_B=(\frac{T}{\sqrt{8}})$

Explanation:

Distance of Planet A from Central star 2R

Time of Resolution T_A=T

Distance of Planet B from orbit star R

Generally the equation for Kepler's law of periods is given by

   $\frac{T_A^2}{T_B^2}=\frac{R_A^3}{R_B^3}$

   $T_B^2=T_A^2 \frac{R_A^3}{R_B^3}$

  $T_B^2=T_A^2 (\frac{R_A}{R_B})^3$

  $T_B^2=T^2 (\frac{R}{2R})^3$

  $T_B^2=T^2 (\frac{1}{R})^3$

  $T_B^2=(\frac{T^2}{8})$

Therefore the following expressions is correct for the number of hours it takes Planet B to complete one revolution around the star

  $T_B=(\frac{T}{\sqrt{8}})$