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?\n9.5 au\n19.7 au\n44.3 au\n160.2 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?\n9.5 au\n19.7 au\n44.3 au\n160.2 au

Answer

Explanation:

Step1: Escribir la fórmula

Dada la fórmula $P = a^{\frac{3}{2}}$, donde $P = 29.5$.

Step2: Despejar $a$

Elevamos ambos lados de la ecuación a $\frac{2}{3}$: $a=P^{\frac{2}{3}}$.

Step3: Sustituir el valor de $P$

$a = 29.5^{\frac{2}{3}}=\sqrt[3]{29.5^{2}}=\sqrt[3]{870.25}\approx9.5$.

Answer:

A. 9.5 AU