you used a telescope and other mathematics to discover that jupiter is 5.20 au from the sun. use the…

you used a telescope and other mathematics to discover that jupiter is 5.20 au from the sun. use the equation to find its orbital period. round to the nearest tenth of a year. jupiter’s orbit: years done

you used a telescope and other mathematics to discover that jupiter is 5.20 au from the sun. use the equation to find its orbital period. round to the nearest tenth of a year. jupiter’s orbit: years done

Answer

Explanation:

Step1: Recall Kepler's third - law

Kepler's third - law is given by $T^{2}=a^{3}$, where $T$ is the orbital period in years and $a$ is the semi - major axis in astronomical units (au). Here, $a = 5.20$ au.

Step2: Substitute the value of $a$ into the formula

Substitute $a = 5.20$ into $T^{2}=a^{3}$. So, $T^{2}=(5.20)^{3}$. Calculate $(5.20)^{3}=5.20\times5.20\times5.20 = 140.608$.

Step3: Solve for $T$

Take the square root of both sides of the equation $T^{2}=140.608$. So, $T=\sqrt{140.608}\approx11.9$.

Answer:

$11.9$