Answer:
Distance of Saturn from sun is 9.5473 astronomical units
Step-by-step explanation:
We have given,
A formula relating the planet's orbital period and planet's distance from the sun. i.e p = ![a^{\frac{3}{2} }](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7B3%7D%7B2%7D%20%7D)
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^{\frac{3}{2} }](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7B3%7D%7B2%7D%20%7D)
Here, Orbital period , p = 29.5 , Let a be the distance between Saturn and sun.
29.5 = ![a^{\frac{3}{2} }](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7B3%7D%7B2%7D%20%7D)
Squaring both sides, we get :
29.5² = ![a^{3}](https://tex.z-dn.net/?f=a%5E%7B3%7D)
Taking cube root both sides, we get:
![29.5^{\frac{2}{3} } =a](https://tex.z-dn.net/?f=29.5%5E%7B%5Cfrac%7B2%7D%7B3%7D%20%7D%20%3Da)
a = 9.5473 astronomical units
Distance of Saturn from sun is 9.5473 astronomical units