Question #280904

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.)


1
Expert's answer
2021-12-17T18:15:04-0500

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


TP2TE2=aP3aE3, TP212=aP313, aP=Tp23=57 AU.\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}.


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