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Question
The time period of a satellite revolving around the earth in a given orbit is 7 hours. If the radius of the orbit is increased to three times its previous value, then the approximate new time period of the satellite will be ______.
Options
40 hours
36 hours
30 hours
25 hours
MCQ
Fill in the Blanks
Solution
The time period of a satellite revolving around the earth in a given orbit is 7 hours. If the radius of the orbit is increased to three times its previous value, then the approximate new time period of the satellite will be 36 hours.
Explanation:
By Kepler's III law of motion, we have:
`T^2 ∝ R^3`
`(T_1/T_2)^2 = (R_1/R_2)^3`
Hence, `T_2^2 = (R_2/R_1)^3 xx T_1^2`
= `((3R)/R)^3 xx (7)^2`
= 27 × 49
= 1323
T = `sqrt(1323) = 36.37` hours
= 36 hours
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Introduction to Gravitation
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