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: Isolate the variable a.

Given $P = a^{\frac{3}{2}}$, we can rewrite it as $a=P^{\frac{2}{3}}$.

Step2: Substitute the value of P.

Substitute $P = 29.5$ into the formula $a = P^{\frac{2}{3}}$, so $a=29.5^{\frac{2}{3}}=\sqrt[3]{29.5^{2}}=\sqrt[3]{870.25}$. Calculating $\sqrt[3]{870.25}\approx9.5$.

Answer:

A. 9.5 AU