USAAAO 2022, I кръг — Задача 20

• C

Solution: The ratio of aphelion to perihelion distance for an elliptical orbit is $\frac{1+e}{1-e}$ where $e$ is the eccentricity of the orbit. Since, Pluto reflects light from the Sun, the reflected flux received at Earth scales as $\frac{1}{d_{SP}^2}\frac{1}{d_{EP}^2}$ where $d_{SP}$ is the Sun Pluto distance and $d_{EP}$ is the Earth - Pluto distance. Since the semi-major axis of Pluto is much larger than 1 A.U., we can approximate $d_{SP} \approx d_{EP}$.

The required change in magnitude is $-2.5\log\left(\frac{1-e}{1+e}\right)^4 = 2.2$.

Answer: C