Question

The orbital period, P, of the planet's distance from the sun, a, in astronomical units is related by the formula p=a^3/2. If Saturn's orbital periodt n 29.5 years what is its distance from the sun?

Answer 1

Distance of Saturn from sun is 9.5473 astronomical units

Explanation:

We have given,

A formula relating the planet's orbital period and planet's distance from the sun. i.e p =
`a^{(3)/(2) }`

since we have, orbital period of Saturn = 29.5 years

And we need to find the distance of Saturn from the sun.

so we can use the given formula: p =
`a^{(3)/(2) }`

Here, Orbital period , p = 29.5 , Let a be the distance between Saturn and sun.

29.5 =
`a^{(3)/(2) }`

Squaring both sides, we get :

29.5² =
`a^(3)`

Taking cube root both sides, we get:

`29.5^{(2)/(3) } =a`

a = 9.5473 astronomical units

Distance of Saturn from sun is 9.5473 astronomical units