the orbital period, $p$, of a planet and the planets distance from the sun, $a$, in astronomical units is…

the orbital period, $p$, of a planet and the planets distance from the sun, $a$, in astronomical units is related by the formula $p = a^{\frac{3}{2}}$. if saturns orbital period is 29.5 years, what is its distance from the sun?\no 9.5 au\no 19.7 au\no 44.3 au\no 160.2 au

the orbital period, $p$, of a planet and the planets distance from the sun, $a$, in astronomical units is related by the formula $p = a^{\frac{3}{2}}$. if saturns orbital period is 29.5 years, what is its distance from the sun?\no 9.5 au\no 19.7 au\no 44.3 au\no 160.2 au

Answer

Explanation:

Step1: Write the given formula and values

Given $P = a^{\frac{3}{2}}$, and $P = 29.5$. So, $29.5=a^{\frac{3}{2}}$.

Step2: Solve for $a$

Raise both sides to the $\frac{2}{3}$ power: $a = 29.5^{\frac{2}{3}}$. Using a calculator, $a=\sqrt[3]{29.5^{2}}=\sqrt[3]{870.25}\approx9.5$.

Answer:

A. 9.5 AU