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Physics
OpenStudy (anonymous):

The mean distance of Neptune from the Sun is 30.07 AU (=astronomical unit, means Earth-Sun distance), that of Pluto 39.4 AU. Are these two numbers connected? (Hint: Derive the ratio of the orbital periods!)

OpenStudy (jamesj):

These numbers behave like Kepler's 3rd law. Write D_n = 30.07 D_p = 39.4 The period of orbit of Neptune is P_n = 164.79 years; and Pluto's P_p = 247.92 years Now you can calculate and confirm that \[ \left(\frac{P_p}{P_n}\right)^2 = \left(\frac{D_p}{D_n}\right)^3 \] If the distance D were the length of the semi-major axis, this would exactly Kepler's 3rd law.

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