Answer to Question #280904 in Astronomy | Astrophysics for Cat.G

Question

A planet orbits the Sun every 430 years. What is its distance (semi-major axis of the orbit) from the Sun? (Give your answer in SI units and include the unit.)

Answer 1

Applying Kepler's third law to the Earth and the planet in the problem:

$$\frac{T_P^2}{T_E^2}=\frac{a_P^3}{a_E^3},\\\space\\ \frac{T_P^2}{1^2}=\frac{a_P^3}{1^3},\\\space\\ a_P=\sqrt[3]{T_p^2}=57\text{ AU}.$$