Answer:
[tex]T_B=(\frac{T}{\sqrt{8}})[/tex]
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
[tex]\frac{T_A^2}{T_B^2}=\frac{R_A^3}{R_B^3}[/tex]
[tex]T_B^2=T_A^2 \frac{R_A^3}{R_B^3}[/tex]
[tex]T_B^2=T_A^2 (\frac{R_A}{R_B})^3[/tex]
[tex]T_B^2=T^2 (\frac{R}{2R})^3[/tex]
[tex]T_B^2=T^2 (\frac{1}{R})^3[/tex]
[tex]T_B^2=(\frac{T^2}{8})[/tex]
Therefore the following expressions is correct for the number of hours it takes Planet B to complete one revolution around the star
[tex]T_B=(\frac{T}{\sqrt{8}})[/tex]
The number of hours that it takes for planet B to complete one revolution around the star is : ( A ) ( [tex]\frac{T}{\sqrt{8} }[/tex] )
Given data :
Distance of Planet A from massive star = 2R
Time taken by Planet A to orbit the massive star = Tₐ
Distance of Planet B from massive star = R
Time taken by Planet B to orbit the massive star = T[tex]_{b}[/tex]
To determine the proper expression exhibiting the correct number of hours it will take for Planet B to complete a revolution
we will apply Kepler's law of periods
[tex]\frac{T^{2} _{a} }{T_{b} ^{2} } = \frac{R_{a} ^{3} }{R_{b} ^{3} }[/tex]
∴ [tex]T_{b} ^{2} = T_{a} ^{2} ( \frac{R_{a} }{R_{b} } )^{3}[/tex]
[tex]T_{b} ^{2} = T^2 ( 1/R)^3[/tex]
Hence T[tex]_{b}[/tex] = ( [tex]\frac{T}{\sqrt{8} }[/tex] )
There we can conclude that The number of hours that it takes for planet B to complete one revolution around the star is : ( A ) ( [tex]\frac{T}{\sqrt{8} }[/tex] )
Learn more about kepler law of periods : https://brainly.com/question/929044
