Two satellites 
and 
revolve around a planet in coplanar circular orbits in the same sense. Their periods of revolutions are 1 h and 8 h, respectively. The radius of the orbit of 
is 
. With reference to the above situation, match the Column I (quantities) with Column II (approximate values).
Column I | Column II | ||
A. | Speed of in | I. | |
B. | Speed of in | II. | |
C. | Velocity of relative to when is closest to in | III. | |
D. | Angular speed of as observed by an astronaut in when is closest to in rad h | IV. |
Choose the correct answer from the options given below.
Text Solution
Verified by ExpertsA
Let the mass of the planet be M, that of 
be 
and of 
be 
. Let the radius of the orbit
of 
be 
and of 
be 
. Let 
and 
be the linear speeds of 
and 
with respect to the planet. The figure shows the situation.
If the period of revolutions of satellites 
and 
are 
and 
, respectively.
As the square of the time period is proportional to the cube of the radius,
Now, the time-period of 
is 1 h. So, 
Speed of 
… (i)
Similarly, speed of
… (ii)
At the closest separation, they are moving in the same direction. Hence, the velocity of 
with respect to 
is
As seen from 
, the satellite 
is at a distance 
at the closest separation. Also, it is moving at 
in a direction perpendicular to the line joining them. Thus, the angular speed of 
as observed by 
is
Hence, 
and 
.
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