Two planets orbit the same star. Planet 1 has a circular orbit, with period $t_1$ and radius $r$. Planet 2 has an elliptical orbit, with period $t_2$ and average radius $r$. Which of the following is correct?
D. The relationship between $t_1$ and $t_2$ cannot be found without more information.
I thought the answer was D, but it's A.
I'm confused because technically Kepler's 3rd law says $T^2 \propto a^3$ where $a$ is the semimajor axis for elliptical orbits, and we may replace $a$ with $r$ for circular orbits, giving $T^2 \propto r^3$.
But for this question, even though one orbit is circular and the other elliptical, they are saying that if the 'average radius' (what does this even refer to?) of the ellipse is equal to the radius of the circular orbit, then their periods will be the same. I cannot quite accept this, and I would love an explanation.