The average distance from Earth to the sun is about \(150,000,000\) kilometers. This distance is called an astronomical unit, the \(AU\). The relationship of a planet's distance from the sun and it's orbital period is \(a^3=p^2\) where \(a\) is the given planet's average distance from the sun in astronomical units and \(p\) is the planet's period in Earth years.
Using the given information find the average distance from Jupiter to the sun in kilometers. Round to the nearest kilometer.
- Jupiter's period \(=12\) years
Hint: Solve for \(a\) then convert units. Do NOT round until your final answer.