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?

Answer 1

By Kepler’s 3^rd 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`