The equation cap t squared is equal to cap A cubed shows the relationship between a planet’s orbital period, cap t , and the planet’s mean distance from the sun, cap A , in astronomical units, AU. If the orbital period of planet Y is twice the orbital period of planet X, by what factor is the mean distance increased?
Answer
A
2 raised to the 1 third power
B
2 raised to the 2 thirds power
C
2 raised to the 1 half power
D
2 raised to the 3 halves power
Explanation
Use the relationship t² = A³. If planet Y’s orbital period is twice planet X’s, then t² increases by a factor of 2² = 4. Since A³ must increase by the same factor, the mean distance increases by the cube root of 4, or 2^(2/3). Thus, the answer is choice B, 2 raised to the 2/3 power.
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