Съдържание

IOAA 2023, Наблюдения, планетариум — Задача 2. Ретроградний Марс

Оригинал на условието (PDF)Съобщи за грешка

Всички материали от IOAA 2023

Planetarium Round · 20 т.

Procedure

You will have 30 minutes to read the questions and prepare, 30 minutes inside the planetarium and 30 minutes to process your observations and complete the answer sheet.

The preparation area is outside the planetarium. Go to the table matching the name of your team for the Group Competition. It will also be marked with the sector, row and seat number assigned to you inside the planetarium.

Open the envelope only when the supervisor gives the command to ‘START’. You have 30 minutes, the supervisor will give the remaining time e.g. “10 minutes left”, “2 minutes left”. On the command ‘STOP’, stop working but do not leave your place until you are shown the ‘GO NOW’ sign. Take only your question papers, clipboard and pen/pencil (leave the atlas). Follow the directions into the planetarium keeping your distance from other participants and take your place. Do not talk to other participants.

During the tasks you may stand up to get a better view, but do not move around, change seats, talk to other participants, or shine your light at others or at the sky. The light must be pointed down at all times.

The round is in 3 parts of 10 minutes each. The first part is for task 1. The second part is for task 2. The third part is for task 3. At 5, 2 and 1 minute before the end a warning will appear briefly on the sky.

At the end of the round wait in your seat until shown the ‘GO NOW’ sign. Follow the directions to the processing area and find the table matching your team as before (leave the light). Keep your distance from other participants and do not talk to them. After everybody is seated you will have 30 minutes to process your observations and complete the answer sheet (there will be a calculator, geometrical instruments etc. and a clock displaying the remaining time). At the end of 30 minutes place your answer sheets in the envelope and wait at your desk until told to leave the area.

Условие

Проектор відображатиме рух Марса відносно фонових зір впродовж одного сезону видимості ( $1.5$ роки) починаючи з геліакального сходу, обраного таким чином, щоб Марс знаходився на максимальній екліптичній широті під час опозиції.

Також буде показано екліптику, положення Сонця впродовж року та поточну дату. Сонце завжди буде під горизонтом.

Синодичний період Марса $= 780$ діб.

(Тривалість показу 10 хвилин)

Answer sheet for part (b): two perpendicular axes and a circle centred at their intersection; the Sun (symbol ⊙) is marked at the centre and the Earth (symbol ⊕) at the right-hand intersection of the circle with the horizontal axis.

(a) Запишіть наступні величини:

i.	дати квадратури (коли елонгація Марса становить $90^{\circ}$ )

ii.	дату початку ретроградного руху
	дату завершення ретроградного руху
iii.	дату протистояння
iv.	екліптичну широту в протистоянні
v.	за екліптичною довготою визначте ширину петлі, утворену планетою

[8 т.]

Базуючись на Ваших спостереженнях і припускаючи, що орбіти Землі та Марса є коловими,

(b) На Аркуші Відповідей позначте положення Сонця, Землі та Марса в моменти протистояння та квадратури в геліоцентричній системі та визначте радіус орбіти Марса в а.о. геометрично, без використання законів Кеплера. Покажіть свій метод у Аркуші Відповідей. [9 т.]

(c) Визначте нахил орбіти Марса до екліптики. [3 т.]

Отговори

Решение

Planetarium Round 2: ‘Retrograde Mars’

The projector will display Mars moving relative to the background stars over one season of visibility (1.5 years) starting from the heliacal rising, chosen so that Mars will be at maximum ecliptic latitude at opposition.

The ecliptic will also be displayed, marked with the positions of the Sun during the year and the current date. The Sun will always be below the horizon.

Synodic period of Mars $= 780$ days.

(Projection time 10 minutes)

(a) Record the following quantities:

i.	the dates of quadrature (when the elongation of Mars is $90^{\circ}$ )

ii.	the date of the beginning of retrograde motion
	and the date of the end of retrograde motion
iii.	the date of opposition
iv.	the ecliptic latitude at opposition
v.	the width in ecliptic longitude of the loop made by the planet

(8 points)

Based on your observations and assuming the orbits of Earth and Mars are circular,

(b) On the answer sheet, mark the positions of the Sun, Earth and Mars at the moments of opposition and quadrature in the heliocentric system and determine the radius of the orbit of Mars in a.u. geometrically, without using Kepler’s Laws. Show your method in the answer sheet.

(9 points)

(Total: 20 points)

Solution

(a) 2 points for correct date of opposition and 1 point for each other answer (total 8)

i.	the dates of quadrature (when the elongation of Mars is $90^{\circ}$ )	8 Nov 1915 $\pm$ 5 days
		15 May 1916 $\pm$ 5 days
ii.	the date of the beginning of retrograde motion	1 Jan 1916 $\pm$ 5 days
	and the date of the end of retrograde motion	21 Mar 1916 $\pm$ 5 days
iii.	the date of opposition	20 Feb 1916 $\pm$ 5 days
iv.	the ecliptic latitude at opposition	$4.5^{\circ}\ \pm\ 1^{\circ}$
v.	the width in ecliptic longitude of the loop made by the planet	$19^{\circ}\ \pm\ 2^{\circ}$

(b) radius 1.5 au.

Оригинал в Архива: planetarium_ukr.pdf · официални решения: planetarium_sol.pdf