Two planets at mean distances d₁ and d₂ from the sun have their frequencies n₁ and n₂

Two planets at mean distances d₁ and d₂ from the sun have their frequencies n₁ and n₂ respectively. Then

(a) n₁²d₁²=n₂²d₂²
(b) n₁²d₁³=n₂²d₂³
(c) n₁d₁²=n₂d₂²
(d) n₁²d₁=n₂²d₂

n₁²d₁³=n₂²d₂³

Apply Kepler’s third law, T²∞R³
T²/R³=constant
Given: T=1/n and R=d
T²/R³=1/n².1/d³=constant
n²d³=constant
For the two planets,n₁²d₁³=n₂²d₂³

KL2002

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