Two satellites S_{1} and S_{2} are revolving | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) From Kepler's third law,we have $T^{2} \propto R^{3}$.For satellites $S_{1}$ and $S_{2}$,we have $\left(\frac{T_{1}}{T_{2}}\right)^{2} = \left(\fr

Vedclass · Accepted Answer

$S_{1}$ is $3 \pi 	imes 10^{4} \,km \,h^{-1}$,when $S_{2}$ is closest to $S_{1}$

Vedclass · Answer

(D) From Kepler's third law,we have $T^{2} \propto R^{3}$.For satellites $S_{1}$ and $S_{2}$,we have $\left(\frac{T_{1}}{T_{2}}ight)^{2} = \left(\frac{R_{1}}{R_{2}}ight)^{3}$.Given $T_{1} = 3 \,h$,$T_{2} = 24 \,h$,and $R_{1} = 3 	imes 10^{4} \,km$.The radius of the orbit of satellite $S_{2}$ is $R_{2} = R_{1} \left(\frac{T_{2}}{T_{1}}ight)^{2/3} = 3 	imes 10^{4} 	imes \left(\frac{24}{3}ight)^{2/3} = 3 	imes 10^{4} 	imes (8)^{2/3} = 3 	imes 10^{4} 	imes 4 = 12 	imes 10^{4} \,km$.Since the satellites revolve in opposite senses,when they are closest to each other,their velocity vectors are in opposite directions relative to the planet,meaning their relative speed is the sum of their orbital speeds.The orbital speeds are $v_{1} = \frac{2 \pi R_{1}}{T_{1}} = \frac{2 \pi 	imes 3 	imes 10^{4}}{3} = 2 \pi 	imes 10^{4} \,km \,h^{-1}$ and $v_{2} = \frac{2 \pi R_{2}}{T_{2}} = \frac{2 \pi 	imes 12 	imes 10^{4}}{24} = \pi 	imes 10^{4} \,km \,h^{-1}$.The relative speed of $S_{2}$ as observed from $S_{1}$ is $v_{rel} = v_{1} + v_{2} = 2 \pi 	imes 10^{4} + \pi 	imes 10^{4} = 3 \pi 	imes 10^{4} \,km \,h^{-1}$.

Similar Questions

Two planets,$A$ and $B$,orbit around a star such that the time period of $A$ is $8$ times the time period of $B$. The ratio of the orbital velocities of planets $A$ and $B$ is:

Even though the gravitational force of the Earth acts on the Moon towards its center,why does the Moon not fall onto the Earth?

Two satellites $P$ and $Q$ go round a planet in circular orbits having radii $3R$ and $R$ respectively. If the speed of satellite $P$ is $2V$,what will be the speed of satellite $Q$?

Two stars of masses $m$ and $2m$ at a distance $d$ rotate about their common centre of mass in free space. The period of revolution is

$A$ planet revolves around the sun in an elliptical orbit. When it is closest to the sun,its distance from the sun is $d_1$ and its velocity is $v_1$. When it is farthest from the sun,its distance from the sun is $d_2$ and its velocity is $v_2$. Find the value of $v_2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module