Завдання теоретичного туру IV етапу VII Всеукраїнської олімпіади з астрономії
Молодша група
1. Спостерігаємо Сатурн. Під час спостережень із Землі максимальний блиск Сатурна досягає значення видимої зоряної величини –0m.47 при найбільшому за площею розкритті кілець. У моменти, коли розкриття кілець удвічі менше, а відстань до Сатурна більша на 1 а. о., його блиск зменшується до +0m.16 видимої зоряної величини. Враховуючи, що орбіти Землі, Юпітера та Сатурна колові і лежать в одній площині, знайдіть, у яких межах змінюється блиск Сатурна під час спостережень з орбіти Юпітера. Ефект впливу фазового кута на величину альбедо та екранувальний вплив Сонця не враховуйте. Вважайте, що альбедо верхніх шарів атмосфери Сатурна та кілець однакові. Радіус орбіти Юпітера 5.20 а.о., а Сатурна – 9.56 а.о.
2. Поверхнева густина галактики. Для деякої спіральної галактики, диск якої має видимі кутові розміри 7',6×2',7, було виміряне червоне зміщення для різних ділянок галактики. Виявилося, що найбільше та найменше зміщення дорівнювали 3,8∙10-3 і 2,9∙10-3 відповідно. Обчисліть середню поверхневу густину (маса на одиницю площі) диску галактики. Вважати форму галактики ідеальним тонким диском, одна з осей якого перпендикулярна до променя зору.
Вказівка: для спіральних галактик існує наближений зв’язок: M ~Vmax4, де M – маса, а Vmax – максимальна швидкість обертання галактики.
Вважати, що для Чумацького Шляху (Milky Way) VMW≈240км/с, MMW≈4,8∙1011Mʘ, H≈70км/с∙Мпк, Mʘ≈2,0∙1030кг.
3. Схід зорі. Зоря з екваторіальними координатами a=5h33m та d=0° на певній широті сходить о 20:00 за місцевим часом. Не користуючись картою, знайдіть приблизну дату, коли це відбувається.
4. Юпітер на небі Житомира. 25 березня екваторіальні координати планети Юпітер несуттєво змінюються в околі значень: δ=-22°39',α=17h32m. Знайдіть максимальну висоту над горизонтом, на якій може спостерігатися Юпітер у цей день на небі Житомира (північна широтаφ=50°15'). У якій частині небосхилу планета при цьому перебуватиме? Обчисліть також місцевий сонячний час, у який цього дня Юпітер буде на максимальній висоті. Рефракцію не враховувати.
5. Спостереження подвійної зорі. У шкільний телескоп з діаметром об’єктива 8 см вдалося побачити окремо компоненти подвійної зоряної системи. Відомо, що обидві зорі належать до V-го класу світності. Абсолютні зоряні величини дорівнюють Mabs1 = 1m та Mabs2 = 2m, період системи 1500 років. Яка відстань до цієї системи та яку зоряну величину мала би ця подвійна зоря під час спостережень неозброєним оком?
Примітка: Вважати орбіти зір коловими й такими, що лежать у картинній площини.
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)
Рис.1 Залежність Маса – Абсолютна зоряна величина
для зір головної послідовності.
Старша група
1. Спостерігаємо Сатурн. Під час спостережень із Землі максимальний блиск Сатурна досягає значення видимої зоряної величини –0m.47 при найбільшому за площею розкритті кілець. У моменти, коли розкриття кілець удвічі менше, а відстань до Сатурна більша на 1 а. о., його блиск зменшується до +0m.16 видимої зоряної величини. Враховуючи, що орбіти Землі, Юпітера та Сатурна колові і лежать в одній площині, знайдіть, у яких межах змінюється блиск Сатурна під час спостережень з орбіти Юпітера. Ефект впливу фазового кута на величину альбедо та екранувальний вплив Сонця не враховуйте. Вважайте, що альбедо верхніх шарів атмосфери Сатурна та кілець однакові. Радіус орбіти Юпітера 5.20 а.о., а Сатурна – 9.56 а.о.
2. З життя екзопланет. Екзопланета обертається навколо червоного карлика, маса якого удвічі менша від маси Сонця. Сидеричний період добового обертання екзопланети 301,1d. Видима зоряна величина материнської зорі з поверхні екзопланети змінюється на 2,39m внаслідок зміни відстані від планети до зорі. Коли екзопланета перебуває в периастрі своєї орбіти, з її поверхні можна спостерігати «ефект Ісуса Навина» – стояння зорі на небосхилі, під час якого протягом нетривалого проміжку часу не змінюється азимут зорі. Вважатимемо, що вісь добового обертання екзопланети перпендикулярна до площини орбіти планети, а орбітальний та добовий рухи відбуваються в одному напрямку.
- Знайдіть ексцентриситет і велику піввісь орбіти екзопланети.
- Яких значень міг би набувати сидеричний період добового обертання цієї екзопланети, щоб з її поверхні можна було спостерігати «ефект Ісуса Навина» хоча б в одній точці орбіти?
Гравітаційна стала G = 6,67·10-11 Н·м2/кг2; 1 а.о. = 149,6·106 км; маса Сонця МС = 1,99·1030 кг; тривалість року 365,25 середньої сонячної доби.
3. Пилове кільце. Навколо зорi, яка за всiми характеристиками близька до Сонця, виявили пилове кiльце з радiусом 1 а.о. Вважаючи, що пилинки є кульками i випромiнюють як абсолютно чорне тiло, оцiніть температуру пилинок i довжину хвилi, що вiдповiдає максимуму теплового випромiнювання кiльця. Вважайте, що максимальний потік випромінювання Сонця відповідає довжині хвилі 5000 Å при Teff = 5770 K.
4. Подвійна зоря. Максимальні значення модулів променевих швидкостей двох компонент подвійної зорі дорівнюють 70 та 100 км/с, період обертання 8 діб. Вважаючи орбіту коловою і такою, що лежить в одній площині з променем зору, знайдіть маси компонент. Враховуючи, що для зір головної послідовності виконуються співвідношення та , знайдіть найбільшу можливу амплітуду змін блиску під час затемнень у цій системі.
5. Юпітер на небі Житомира. 25 березня екваторіальні координати планети Юпітер несуттєво змінюються в околі значень: δ=-22°39',α=17h32m. Знайдіть максимальну висоту над горизонтом, на якій може спостерігатися Юпітер у цей день на небі Житомира (північна широтаφ=50°15'). У якій частині небосхилу планета при цьому перебуватиме? Обчисліть також місцевий сонячний час, у який цього дня Юпітер буде на максимальній висоті. Рефракцію не враховувати.