IOAA Jr. 2022, Теория, тест с избираем отговор — Задача 4. The Terrestrial Satellite

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

A small satellite (a luminous sphere) that orbits the Earth, in an equatorial circular orbit at the altitude $h$, is photographed with a camera on the ground, the lens of which is a converging lens with focal length $f$. The photography is made when the satellite aligns with the camera and the centre of the Earth.

It is given: the mass of the Earth, $M$; the gravitational constant, G, the radius of the Earth, R. During the photographic exposure the proper rotation of the Earth is neglected.

The length of the image on the photograph, after developing the photographic plate, placed in the focal plane of the objective lens, as indicated by the drawing in figure 1, if the exposure time of the camera was $\Delta t$, is given by the expression:

a) $l = \frac{f}{h-f} \cdot \sqrt{G\,\frac{M}{R+h}} \cdot \Delta t$

b) $l = \frac{f}{h+f} \cdot \sqrt{G\,\frac{M}{R+h}} \cdot \Delta t$

c) $l = \frac{f}{h-f} \cdot \sqrt{G\,\frac{M}{h-R}} \cdot \Delta t$

d) $l = \frac{f}{h-f} \cdot \sqrt{2G\,\frac{M}{R+h}} \cdot \Delta t$

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