multiple choice 17 points\nkeplers third law states $p = a^{\frac{3}{2}}$ where:\np = the time it takes the…

multiple choice 17 points\nkeplers third law states $p = a^{\frac{3}{2}}$ where:\np = the time it takes the planet to go around the sun, in years.\na = the planets distance from the sun, in astronomical units.\nif the orbital period of jupiter is 13.2 years, what is its distance from the sun to the nearest hundredth of an astronomical unit?\n5.31 units\n5.59 units\n6.21 units\n56 units

multiple choice 17 points\nkeplers third law states $p = a^{\frac{3}{2}}$ where:\np = the time it takes the planet to go around the sun, in years.\na = the planets distance from the sun, in astronomical units.\nif the orbital period of jupiter is 13.2 years, what is its distance from the sun to the nearest hundredth of an astronomical unit?\n5.31 units\n5.59 units\n6.21 units\n56 units

Answer

Explanation:

Step1: Rearrange the formula

Given $P = a^{\frac{3}{2}}$, we can solve for $a$ by raising both sides to the $\frac{2}{3}$ - power. So $a=P^{\frac{2}{3}}$.

Step2: Substitute the value of $P$

Substitute $P = 13.2$ into the formula $a = P^{\frac{2}{3}}$. Then $a=(13.2)^{\frac{2}{3}}=\sqrt[3]{13.2^{2}}=\sqrt[3]{174.24}$.

Step3: Calculate the value

Using a calculator, $\sqrt[3]{174.24}\approx5.59$.

Answer:

B. 5.59 units