IOAA Jr. 2022, Теория, тест с избираем отговор — Задача 3. The escape velocity

International Olympiad of Astronomy and Space Sciences for Juniors — Romania– Câmpulung Moldovenesc — October 31 - November 7 2022 — Theoretical Round — I. Multiple choice problems – 100 points · 31 октомври 2022 г.

I. Multiple choice problems – 100 points

For these problems, you have to choose only one correct answer. Please write your answer on answer-sheet. Don’t forget to write the number of the problem, i.e Grid 1. (c).

Условие

It is given: $V_0 \approx 30\,\dfrac{\mathrm{km}}{\mathrm{s}}$, the speed of the Earth in its circular orbit around the Sun; $v_0 \approx 7.9\ \frac{\mathrm{km}}{s}$, the speed of a terrestrial satellite orbiting the Earth in a very low circular orbit (the first cosmic speed).

It is known that: $\dfrac{M_{\mathrm{Earth}}}{R_{\mathrm{Earth}}} \ll \dfrac{M_{\mathrm{Sun}}}{R_{\mathrm{Earth-Sun}}}$.

The variation of the kinetic energy of the body, in relation to the Sun, is neglected during the motion of the body from the surface of the Earth to the limit of the gravitational attraction of the Earth.
The approximate minimum escape velocity of a body B, relative to the Sun, launched at a distance from the Sun equal to 1 AU, so that it leaves the Solar System forever, is:

a) $v_B \approx 45.52\ \frac{\mathrm{km}}{s}$

b) $v_B \approx 32.32\ \frac{\mathrm{km}}{s}$

c) $v_B \approx 22.22\ \frac{\mathrm{km}}{s}$

d) $v_B \approx 42.42\ \frac{\mathrm{km}}{s}$.

Отговори

Решение

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Оригинал в Архива: Multiple_Choice.pdf · официални решения: Grid_1.pdf · допълнителни данни: Grid_2.pdf · допълнителни данни: Grid_3.pdf · допълнителни данни: Grid_4.pdf · допълнителни данни: Grid_5.pdf · допълнителни данни: Grid_6.pdf · допълнителни данни: Grid_7.pdf · допълнителни данни: Grid_8.pdf · допълнителни данни: Grid_9.pdf · допълнителни данни: Grid_10.pdf