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?

Answer 1

Hello,

a^3/2=29.5
==>a=29.5^2/3
==>a=9.5473170...AU
in reality: 9.5388..AU (astronomic unit)

Answer 2

Answer: 9.54731702 astronomical units

Step-by-step explanation:

Given: The orbital period, P, of a planet and the planet’s distance from the sun, a, in astronomical units is related by the formula $P=a^{\frac{3}{2}$.

Saturn’s orbital period P = 29.5 years

Substitute this value in the equation above, we get

$29.5=a^{\frac{3}{2}}\\\Rightarrow(29.5)^{\frac{2}{3}}=a\\\Rightarrow\ a=9.54731702\text{ astronomical units}$

Hence, its distance from the sun = 9.54731702 astronomical units.