Тренинг Платформа Engee (LTC/MBD)
作者
Язык Julia
Небольшой проект
Цель: использовать максимум полученных знаний, чтобы проанализировать спектр звезды.
В следующей ячейке содержатся данные о спектрах нескольких звезд, значения интенсивности их излучения, измеренные в некотором диапазоне частот .
Выполните эту ячейку чтобы загрузить исходные данные.
In [ ]:
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lambdaStart = 630.02;
lambdaDelta = 0.14;
nObs = length(spectra[1])
Кроме спектров звезд нам даны минимальная частота в спектре (), шаг измерений () и количество измерений nObs.
Шаг 1
📗 Задание 1
Создайте переменную lambdaEnd (), в которой будет содержаться значение яркости спектра на последней зарегистрированной частоте.
Значение lambdaEnd можно рассчитать по формуле .
In [ ]:
Подсказка
Для расчёта выражения для lambdaEnd нужны только операторы + и *.
Решение
In [ ]:
lambdaEnd = lambdaStart + (nObs - 1)*lambdaDelta;
Шаг 2
📗 Задание 2
Определите переменную lambda, в которой будет находиться диапазон значений от lambdaStart до lambdaEnd с фиксированным шагом lambdaDelta.
In [ ]:
Подсказка
Оператор : позволит создать диапазон значений с фиксированным шагом.
Решение
In [ ]:
lambda = lambdaStart:lambdaDelta:lambdaEnd;
Шаг 3
Проанализируем один конкретный спектр из таблицы – спектр звезды HD94028. Вспомним, как мы использовали функцию findmin для получения минимального значения и его индекса в массиве. Этот индекс соответствует положению линии H-альфа () на спектре.
📗 Задание 3
- Поместите в переменную
spectrumшестой ряд значений из таблицыspectra.
- Создайте две переменные
sHaиidx, содержащие минимальное значение вектораspectrumи тот индекс, где оно встречается в векторе.
- Затем найдите частоту линии H-альфа, соответствующую найденному минимуму, получив ее из вектора
lambdaпо индексуidx. Сохраните результат в переменнуюlambdaHa().
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Подсказка
1. Создайте переменную spectrum и используйте адресацию через квадратные скобки, чтобы поместить в нее элемент вектора spectra под номером 6.
2. Вызовите функцию findmin с двумя выходными переменными: sHa,idx = ...
3. Затем используйте idx в качестве индекса [...] для получения значения из вектора lambda.
Решение
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spectrum = spectra[6]
(sHa, idx) = findmin( spectrum );
lambdaHa = lambda[idx]
Шаг 4
Как вы уже могли убедиться, H-альфа линия звезды HD94028 находится в области 656.62 нм, что характеризует наблюдаемую волну как более длинную, чем волна с периодом 656.28 нм.
Используя значение частоты линии H-альфа этой звезды, можно рассчитать коэффициент красного смещения (имеющею отношение к тангенциальной скорости движения звезды относительно Земли), используя формулу . После этого можно рассчитать саму скорость, умножив коэффициент смещения (z) на скорость света в вакууме (299792.458 km/s).
📗 Задание 4
Рассчитайте коэффициент красного смещения (z) и скорость (в км/с) тангенциального движения звезды относительно Земли – то есть скорость, с которой она удаляется от нас. Поместите значение коэффициента смещения в переменную z, а скорость – в переменную с названием speed.
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Подсказка
1. Рассчитайте значение z по формуле lambdaHa/656.28 − 1.
2. Поместите в переменную speed результат умножения переменной z на скорость света 299792.458.
Решение
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z = lambdaHa/656.28 - 1
speed = z*299792.458
Шаг 5
Положительное значение тангенциальной скорости означает, что звезда удаляется от нас (красное смещение спектра), а отрицательное значение означает, что звезда приближается к нам (синее смещение).
Условный блок if позволит нам автоматически различить между красным и синим смещением спектров.
📗 Задание 5
Создайте блок if, который будет проверять выражение speed. Если значение меньше 0, то должен выполниться код, выведет строку "Звезда удаляется от нас". Если скорость равна 0, выведите строку "Движения не зафиксировано". Если же скорость положительная, выведите строку "Звезда приближается к нам".
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Подсказка
Для вывода текста используйте команду: print("Звезда приближается к нам").
Решение
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if speed < 0
print("Звезда удаляется от нас")
elseif speed > 0
print("Звезда приближается к нам")
else
print("Движения не зафиксировано")
end
Шаг 6
Для удобства вычислений, создадим компактную функцию для вычисления относительной скорости движения звезды по ее спектру.
📗 Задание 4-6
- Создайте описание функции
getSpeed( spectrum )
- Поместите в него вычисление всех переменных от
sHaдоspeed
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Подсказка
Все вычисления уже произведены в предыдущих ячейках. Их нужно только скопировать внутрь описания функции.
Чтобы значение speed было возвращаемым значением функции, не обязательно писать return speed в конце тела функции. Хотя так, несомненно, будет гораздо нагляднее. Функция возвращает значение последнего выполненного шага вычислений.
Решение
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function getSpeed( spectrum )
(sHa, idx) = findmin( spectrum );
lambdaHa = lambda[idx];
z = lambdaHa/656.28 - 1;
speed = z*299792.458;
end
Шаг 7
Теперь попробуем получить относительную скорость всех остальных звезд. В следующей ячейке собраны названия звезд, выполните ее:
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starnames = ["HD30584", "HD10032", "HD64191", "HD5211", "HD56030", "HD94028", "SAO102986"]
Цикл for по вектору 1:length(starnames) позволит нам вычислить значения для всех спектров в векторе spectra и вывести их вместе с названиями звезд из вектора starnames.
📗 Задание 4-7
- Создайте цикл
for, в котором переменнаяiпройдет все значения от1доlength(starnames).
- Поместите внутрь команду вызова функции
getSpeed( … )для вычисления относительной скорости очередной звезды по ее спектру из массиваspectra. Результат вызова этой функции поместите в переменнуюspeed
- В том же цикле, выведите название звезды (
starnames[i]) и ее относительную скоростьspeed
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Подсказка
1. В первой строке кода внутри цикла for, поместите в переменную speed результат вызова функции getSpeed( spectra[i] ).
2. Второй строчкой, для вывода текста, используйте команду: println( starnames[i], ": ", speed ).
Решение
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for i = 1:length(starnames)
speed = getSpeed( spectra[i] )
println( starnames[i], ": ", speed )
end