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Asked in AIEEE 2004 · Modified force laws
A circular orbit means the assumed force is exactly what is needed to keep the planet turning.
k/(Rⁿ)=mRω², so ω²=k/(mRⁿ⁺¹).
Since T=(2π)/ω, T²∝ Rⁿ⁺¹ and T∝ R^(n+1)/2.
Setting n=2 gives T∝ R^3/2, the familiar Kepler result, which confirms the exponent.
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