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Home » Orbital period squared is proportional to radius cubed. - Crankk.io

Orbital period squared is proportional to radius cubed. - Crankk.io

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 First, factor \( 360 \):

📌 = 36 \times 10 = (2^2 \cdot 3^2) \cdot (2 \cdot 5) = 2^3 \cdot 3^2 \cdot 5^1

📌 We seek divisors of \( 360 \) that are perfect squares. A divisor is a perfect square if all exponents in its prime factorization are even.

📌 Let a divisor \( d = 2^a \cdot 3^b \cdot 5^c \) be a perfect square, with:

📌 \( a \in \{0, 2\} \) (since \( a \leq 3 \), and even)

📌 \( b \in \{0, 2\} \) (since \( b \leq 2 \), even)

📌 \( c \in \{0\} \) (since \( c \leq 1 \), and only even choice is 0)

📌 So possible combinations:

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