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Консультация № 201242
30.06.2021, 11:51
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:Космический корабль движется между Землёй и Луной таким образом, что всё время находится в точке, в которой силы гравитационного притяжения к Земле и к Луне в точности уравновешивают друг друга. Найдите примерный радиус орбиты этого корабля в системе отсчёта, связанной с Землёй. Считайте, что орбита Луны в этой системе отсчёта близка к круговой с радиусом 380000 км. Масса Земли примерно в 81 раз больше массы Луны. Ответ дайте в тысячах километров, округлив до целого числа.
Обсуждение
30.06.2021, 21:03
общий
это ответ
Здравствуйте, kuznetsova.79!
Предлагаю Вам следующее решение задачи.
Дано:
-- отношение массы Земли к массе Луны; 
м --- расстояние между центрами Земли и Луны, где 
-- расстояния соответственно от центров Земли и Луны до точки (космического корабля), находящейся на соединяющем их отрезке прямой, в которой силы гравитационного притяжения к Земле и Луне уравновешивают друг друга.
Определить:
-- радиус орбиты космического корабля в системе отсчёта, связанной с Землёй.
Обозначим массу космического корабля через
Тогда, согласно закону всемирного тяготения, космический корабль, находясь в точке круговой орбиты искомого радиуса 
притягивается к центру Земли с силой, модуль которой равен
а к центру Луны -- с силой, модуль которой равен
где
-- гравитационная постоянная. При этом, согласно условию задачи,
значит,
то есть
Решая систему уравнений
получим
(м)
тыс. км.
Ответ:
тыс. км.
Предлагаю Вам следующее решение задачи.
Дано:
-- отношение массы Земли к массе Луны; м --- расстояние между центрами Земли и Луны, где -- расстояния соответственно от центров Земли и Луны до точки (космического корабля), находящейся на соединяющем их отрезке прямой, в которой силы гравитационного притяжения к Земле и Луне уравновешивают друг друга.Определить:
-- радиус орбиты космического корабля в системе отсчёта, связанной с Землёй.Решение
Обозначим массу космического корабля через
Тогда, согласно закону всемирного тяготения, космический корабль, находясь в точке круговой орбиты искомого радиуса притягивается к центру Земли с силой, модуль которой равена к центру Луны -- с силой, модуль которой равен
где
-- гравитационная постоянная. При этом, согласно условию задачи,значит,
то есть
Решая систему уравнений
получим
(м) тыс. км.Ответ:
тыс. км.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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