IOAA 2019, theory — Задача 10. South → East → North

Theory problem sheet · 20 т.

Условие

Consider the Earth as a perfect, rigid, sphere with radius $R = 6378\ \mathrm{km}$. There exist some points on the surface of the Earth from which we can travel first 6378 km South, then 6378 km East, and after that 6378 km North, and as a result return to the original point of departure. Find such points and paths. Calculate the geographic coordinates of the turning points of your solutions and draw the paths.

For the sake of simplicity measure the geographic longitude from $0^{\circ}$ to $+360^{\circ}$ eastward from Greenwich, the geographic latitude from $0^{\circ}$ to $+90^{\circ}$ north of the Equator and from $0^{\circ}$ to $-90^{\circ}$ south of the Equator. Solutions resulting from rotational symmetry should not be considered to be different.

Решение

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