Question:
A satellite is revolving around the earth in a circular orbit of radius $4$ times that of the parking orbit. The time period of the satellite is :
A satellite is revolving around the earth in a circular orbit of radius $4$ times that of the parking orbit. The time period of the satellite is :
Updated On: Jul 27, 2022
- 16 day
- 2 day
- 4 day
- 8 day
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The Correct Option is D
Solution and Explanation
Applying Keplers law $T \propto r^{3 / 2}$ We know that time period of parking orbit is 1 day (given: $T_{s}=r$ parking orbit)
Hence, $\frac{T_{s}}{T_{\text {parking }}}=\left(\frac{4 r_{\text {parking ortit }}}{r_{\text {parkhing orbit }}}\right)^{3 / 2}$
$=(4)^{3 / 2}=8$
$T_{s}=8 \times T_{\text {parking }}$
$=8 \times 1=8$ days
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Concepts Used:
Keplers Laws
Kepler’s laws of planetary motion are three laws describing the motion of planets around the sun.
Kepler First law – The Law of Orbits
All the planets revolve around the sun in elliptical orbits having the sun at one of the foci.
Kepler’s Second Law – The Law of Equal Areas
It states that the radius vector drawn from the sun to the planet sweeps out equal areas in equal intervals of time.
Kepler’s Third Law – The Law of Periods
It states that the square of the time period of revolution of a planet is directly proportional to the cube of its semi-major axis.
T2 ∝ a3