IOAA 2021, theory, 9. клас — Задача 1. Pluto Satellites (15 points).

Theory — Q9-1 English (Official) · 15 т.

Условие

9.1 The mass of Charon, the biggest satellite of Pluto, is 1/8th the mass of Pluto. Both bodies move in a circular orbit around a common center of mass. In addition, they both are tidally-locked. The distance between the center of the planet and the center of the satellite is $R = 19\,640\ \mathrm{km}$ and radius of the satellite is $r = 593\ \mathrm{km}$.

Let $g_0$ be the gravitational acceleration on the surface of Charon due only to its mass.Let A be the point on Charon surface directly facing Pluto, and B the point diametrically opposite. Compute the percentage difference between gravitational acceleration at A and B respect to $g_0$.

9.1 The mass of Charon, the biggest satellite of Pluto, is 1/8th the mass of Pluto. Both bodies move in a circular orbit around a common center of mass. In addition, they both are tidally-locked. The distance between the center of the planet and the center of the satellite is $R = 19\,640\ \mathrm{km}$ and radius of the satellite is $r = 593\ \mathrm{km}$.

Let $g_0$ be the gravitational acceleration on the surface of Charon due only to its mass.Let A be the point on Charon surface directly facing Pluto, and B the point diametrically opposite. Compute the percentage difference between gravitational acceleration at A and B respect to $g_0$. [15 т.]

Решение

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Оригинал в Архива: TQ-9-Q.pdf