IOAA 2013, theory — Задача 2

*$7^{th}$ International Olympiad on Astronomy & Astrophysics 27 July – 5 August 2013, Volos Greece

Theoretical Exam - Long Questions · 27 юли 2013 г.*

Условие

Question 2

A spacecraft is orbiting the Near Earth Asteroid (2608) Seneca (staying continuously very close to the asteroid), transmitting pulsed data to the Earth. Due to the relative motion of the two bodies (the asteroid and the Earth) around the Sun, the time it takes for a pulse to arrive at the ground station varies approximately between 2 and 39 minutes. The orbits of the Earth and Seneca are coplanar. Assuming that the Earth moves around the Sun on a circular orbit (with radius $a_{\mathrm{Earth}}=1\ \mathrm{AU}$ and period $T_{\mathrm{Earth}}=1\ \mathrm{yr}$) and that the orbit of Seneca does not intersect the orbit of the Earth, calculate:

(1) the semi-major axis, $a_{\mathrm{Sen}}$ the eccentricity, $e_{\mathrm{Sen}}$ of Seneca’s orbit around the Sun

(2) the period of Seneca’s orbit, $T_{\mathrm{Sen}}$ and the average period between two consecutive oppositions, $T_{\mathrm{syn}}$ of the Earth-Seneca couple

(3) an approximate value for the mass of the planet Jupiter, $M_{\mathrm{Jup}}$ (assuming this is the only planet of our Solar system with non-negligible mass compared to the Sun). Assume that the presence of Jupiter does not influence the orbit of Seneca.

Решение

Теми и трудност

Трудност: неоценена.

Небесна механика · Закони на Кеплер · Синодични периоди

---

Оригинал в Архива: LongQuestions.pdf