Question

the orbital period, p, of a planet and the planet’s distance from the sun, a, in astronomical units is related by the formula $p = a^{\frac{3}{2}}$. if saturn’s orbital period is 29.5 years, what is its distance from the sun? 44.3 au 19.7 au 9.5 au 160.2 au

Explanation:

Step1: Dado la fórmula \( P = a^{\frac{3}{2}} \), sustituimos \( P = 29.5 \)

Tenemos \( 29.5 = a^{\frac{3}{2}} \)

Step2: Resolver para \( a \). Elevamos ambos lados a la potencia \( \frac{2}{3} \)

\( a = (29.5)^{\frac{2}{3}} \)
Calculamos \( 29.5^{\frac{2}{3}} \): Primero, \( 29.5^{\frac{1}{3}} \approx 3.09 \), luego elevamos al cuadrado: \( 3.09^2 \approx 9.5 \)

Answer:

9.5 AU (la opción con "9.5 AU")