Two satellites revolve around a planet in cop | vedclass

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

Question

(A) Given:$T_1 = 1\, h$,$T_2 = 8\, h$$R_1 = 2 	imes 10^3\, km$Angular velocities are $\omega_1 = \frac{2\pi}{T_1} = 2\pi\, rad/h$ and $\omega_2 = \fr

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(A) Given:$T_1 = 1\, h$,$T_2 = 8\, h$$R_1 = 2 	imes 10^3\, km$Angular velocities are $\omega_1 = \frac{2\pi}{T_1} = 2\pi\, rad/h$ and $\omega_2 = \frac{2\pi}{T_2} = \frac{\pi}{4}\, rad/h$.Using Kepler's third law,$\frac{R_2^3}{R_1^3} = \frac{T_2^2}{T_1^2} \Rightarrow \frac{R_2}{R_1} = (\frac{8}{1})^{2/3} = 4$.So,$R_2 = 4 	imes R_1 = 8 	imes 10^3\, km$.The linear velocities are $v_1 = \omega_1 R_1 = 2\pi 	imes 2 	imes 10^3 = 4\pi 	imes 10^3\, km/h$ and $v_2 = \omega_2 R_2 = \frac{\pi}{4} 	imes 8 	imes 10^3 = 2\pi 	imes 10^3\, km/h$.When the satellites are closest,the relative angular velocity $\omega_{rel}$ as observed from the nearer satellite is given by $\omega_{rel} = \frac{v_1 - v_2}{R_2 - R_1}$.$\omega_{rel} = \frac{4\pi 	imes 10^3 - 2\pi 	imes 10^3}{8 	imes 10^3 - 2 	imes 10^3} = \frac{2\pi 	imes 10^3}{6 	imes 10^3} = \frac{\pi}{3}\, rad/h$.Comparing this with $\frac{\pi}{x}$,we get $x = 3$.

Column-$I$	Column-$II$
$(1)$ Polar satellite	$(a)$ Telecommunication
$(2)$ Geostationary satellite	$(b)$ Spying
	$(c)$ Weather forecasting

Similar Questions

$A$ spaceship approaches the moon (mass $= M$,radius $= R$) along a parabolic path which is almost tangential to its surface. At the moment of maximum approach,the brake rocket is fired to convert the spaceship into a satellite of the moon. Find the change in speed.

The orbit of a geo-stationary satellite is circular. The time period of the satellite depends on:
$(i)$ mass of the satellite
(ii) mass of the earth
(iii) radius of the orbit
(iv) height of the satellite from the surface of the earth
Which of the following is correct?

Match the types of satellites in Column-$I$ with their applications in Column-$II$.

Column-$I$ Column-$II$

$(1)$ Polar satellite $(a)$ Telecommunication

$(2)$ Geostationary satellite $(b)$ Spying

$(c)$ Weather forecasting

Vedclass Test Series

Exam Paper Generator

Online Exam Module