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^(3/2). If Saturn’s orbital period is 29.5 years, what is its distance from the sun?

9.5 AU
19.7 AU
44.3 AU
160.2 AU

Answer 1

9.5 AU is the correct answer to that question hope this helps you out

Answer 2

Answer: First option is correct.

Explanation:

Since we have given that

`P=a^{(3)/(2)}`

Here, P is the orbital period,

'a' denotes the planet's distance.

Since Orbital period of Saturn = 29.5 years

So, we need to find the value of 'a' for Saturn:

`29.5=a^{(3)/(2)}\\\\\text{Squaring both sides}\\\\29.5^2=a^3\\\\870.25=a^3\\\\\sqrt[3]{870.25}=a\\\\9.547=a`

Hence, Its distance from the sun is 9.5 AU.

Thus, First option is correct.