The distances of two planets from the sun are 10^12 m and 10^10 m respectiuely. Then the ratio of time periods of those planets is____?

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Answer 1 · 2018-04-24T13:39:00

#1000#

Kepler's law of periods:

#T^2 propto r^3#

#implies T_1/T_2 = sqrt( r_1^3/r_2^3 ) = sqrt( ((10^(12))^3)/(10^(10))^3) = 1000#

Answer 2 · 2018-04-24T13:43:20

#1000 : 1#

Kepler’s third Law: The square of period of revolution of a planet is directly proportional to the cube of radius of it’s orbit.

Mathematically,

#"T"^2 ∝ "r"^3#

#("T"_1/"T"_2)^2 = ("r"_1/"r"_2)^3 = ((10^12\ cancel"m")/(10^10\ cancel"m"))^3 = ((cancel(10^10) × 10^2)/(cancel(10^10)))^3 = 10^6#

#"T"_1/"T"_2 = sqrt(10^6) = 10^3 = 1000 : 1#