Question

help!!!! please!The planet Jupiter revolves around the Sun in a period of about 12 years (3.79 X 10^ 8 seconds). What is its mean distance from the center of the Sun? The mass of the Sun is 1.99 X 10^ 30 kilograms. A)1.1 X10^ 11 meters B)1.5 X 10^ 11 meters C)2.3 X 10^ 11 meters D)5.8 X 10^ 11 meters E)7.8 X10^ 11 meters

Answer 1

By Kepler's Third Law:\[\text{(Planet's period in years)}\large ^2 = \normalsize
\text{(Planet's distance from the sun in AU)}\large ^3 \]Jupiter revolves around the Sun in a period of about 12 years.
Let the mean distance of Jupiter from the sun be "x" AU (Astronomical Units).
\[\large 12^2 = x^3 \\\large 144 = x^3\\ \large x = 144^{1/3} = 5.2 \text{ AU}
\\ \large
\text{ } \\ \large
1 \text{ AU} = 1.5 \times 10^{11}~\text{m} \\ \large
5.2 \text{ AU} = 5.2 \times 1.5 \times 10^{11} = 7.8 \times 10^{11}~\text{m}
\]

Answer 2

i still dont understand the math part /.\ why is it 144^1/3??

Answer 3

\[ \large
x^3 = 144 \\
\text{Take the cube root on both sides:} \\ \large
x = \sqrt[3]{144} = 144^{1/3} = 5.2\\
\]

Answer 4

ohh okaii /.\ thank u :) ur always so helpful!!

Answer 5

You are welcome.