Johannes Kepler discovered that a planet's mean distance $R$ from the sun (in astronomical units)is related to its period $T$ (in years)by the formula $R = \sqrt [ 3 ] { \frac { T ^ { 2 } } { k } }$ Find $R$ when $T = 1.881$ and $k = 1.002$ .
A)1.52 AU
B)1.22 AU
C)1.37 AU
D)1.35 AU
E)1.45 AU

Question

Quizplus · Accepted Answer

Plugging the given values into Kepler's formula, $R = \sqrt[3]{\frac{T^2}{k}} = \sqrt[3]{\frac{1.881^2}{1.002}}$, we find $R \approx 1.52$ AU.

Johannes Kepler Discovered That a Planet's Mean Distance RRR From the Sun (In Astronomical Units)is Related to Its Period

Johannes Kepler Discovered That a Planet's Mean Distance $R$ From the Sun (In Astronomical Units)is Related to Its Period