OWAO 2022, Теория — Задача 5. Follow the Shadow

• The Moon (and the star) is near the descending node of its orbit, which coincides with the autumnal equinox point; the occultation date is June 22.

  The official solution states the position (near the autumnal equinox) and the date, but prints no explicit numerical right ascension and declination of the star.

Let us look at the occultation of the star by the Moon from the star itself:

The Moon moves at an angle

to the celestial equator. Then it is clear that the Moon is near the descending node of its orbit, which coincided with the point of the autumnal equinox.

At the end of the occultation, the Sun is over the meridian opposite to the meridian of point E, because at the point E it is midnight at that moment. Therefore, the Sun is at the point of the summer solstice. The date is June 22.

Marking Scheme:

• The Moon is near the autumnal equinox (without justification, taking into account the inclination of the lunar orbit to the ecliptic) — 2 pt.
• The Moon is near a descending node of the orbit (as justification of the previous statement) — 2 pt.
• The Moon is in the first quarter (or equivalent statement) — 2 pt.
• The coordinates of the star — 2 pt.
• The occultation date — 2 pt.