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Question
An unknown planet orbits the Sun with a distance twice the semi-major axis distance of the Earth’s orbit. If the Earth’s time period is T1, what is the time period of this unknown planet?
Solution
By Kepler’s 3rd law T2 ∝ a3
Time period of unknown planet = T2
Time period of Earth = T1
Distance of unknown planet from the Sun = a2
Distance of the Earth from the Sun = a1
`"T"_1^2/"T"_2^2= "a"_1^3/"a"_2^3`
T2 = `("a"_2/"a"_1)^(3/2) "T"_1`
a2 = 2a,
T2 = `("2a"_1/"a"_1)^(3/2) "T"_1`
T2 = `2sqrt2"T"_1`
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