IOAA 2022, Теория — Задача 2. Circumbinary planet
International Olympiad on Astronomy and Astrophysics 2022 Georgia — Theoretical Competition · 16 август 2022 г. · 10 т.
Условие
A stellar system consists of two main-sequence stars each of orbiting with a period of 4 years in a circular orbit. A circumbinary planet orbits the center of the binary system in the same orbital plane and direction at a fixed distance of .
(a) Calculate the amount of time it takes for the planet to reappear at the same position relative to the binary system. [6 т.]
(b) At a given instant, what is the maximum fraction of the planet’s surface area which receives light from at least one of the stars? Neglect any atmospheric effects and the sizes of the stars. [4 т.]
Отговори
- (a) 4.4 years
- (b) 0.53
Решение
Equating gravitational force to centrifugal force, we get:
The period of planet can be calculated from the 3rd Kepler’s law of motion
One star always covers exactly the half of the planet’s surface. In the best case, the stars are located at the maximal angular distance from each other. So the fraction of illuminated surface is simply given by
Оригинал в Архива: Theory Problems.pdf · официални решения: Theory Solutions.pdf