A satellite is launched in a circular orbit of radius R around earth while a second satellite is launched into a orbit of radius 1.02 R . The Percentage difference in the time period of the two satellite is

Options

A. 0.7
B. 1 .0
C. 1.5
D. 3

Answer

D

Explanation

From kepler's law , `T^2alphaR^3`
`((T_1)/(T_1))`= `((R_1)/(R_2))^3`
`(T_1)/(T_2)=((R_1)/(R_2))3/2=((R)/1.02)3/2= (50/51)3/2` = 0.97
`Rightarrow(T_1)/(T_2) = 0.97`
`Rightarrow T_1= 0.97x`
`Rightarrow` difference, `T_2- T_1 = 0.97x = 0.03x`
% difference = `(0.03x)/(x)xx 100= 3%`