IOAA 2019, theory — Задача 9. Distance of the Lagrangian point L2 of the Earth–Moon system

Theory problem sheet · 20 т.

Условие

On 3 January 2019, the Chinese spacecraft Chang'e-4 landed on the far side of the Moon in the area of the von Kármán crater, which was named after the world famous Hungarian-born physicist Theodore von Kármán.

As the Earth remains below the horizon of the spacecraft all the time, a relay station is also necessary for the communication with mission control on the Earth. For this purpose, The Chinese Space Agency launched a spacecraft, Queqiao, which was placed into a halo orbit around the outer Lagrangian point of the Earth–Moon system, $L_2$, the far side of the Moon.

Calculate the distance ($h$) of this satellite above the surface of the Moon. The Moon's orbit should be considered as a perfect circle with a radius of $R = 384\ 400\ \mathrm{km}$. Neglect perturbations from the Sun and other planets.

Hint: You can use the following approximation: $1/(1+x)^2 \approx 1 - 2x$, if $|x| \ll 1$.

Решение

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Оригинал в Архива: TH-problem-final.pdf · официални решения: TH-solution-final.pdf