Update orbit-motion.tex #194
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added intEnergy for eccentric anomaly
AShepelevv
requested changes
Jun 4, 2024
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| где $\nu$~--- истинная аномалия, а $p$~--- фокальный параметр. А также из (\ref{eq:kepler-eq-E-nu-2}) следует | ||
| \begin{equation} | ||
| v = \sqrt{\frac{GM}{a}}\sqrt{\frac{1+e\cos E}{1-e\cos E}}, |
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Давай распишем подстановку и преобразования, чтобы не было «очевидно, получается, что». Я вот в уме не смог подставить и получить результат :)
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Кажется, нужно использовать предыдущую формулу из уравнения Кеплера, нет? Могу быть не прав, поэтому и прошу расписать, собственно
| \begin{equation} | ||
| v = \sqrt{\frac{GM}{a}}\sqrt{\frac{1+e\cos E}{1-e\cos E}}, | ||
| \end{equation} | ||
| где $E$~--- эксцентрическая аномалия. | ||
| Найдем величину момента импульса пробной массы $m$ на эллиптической орбите. В силу постоянства данной величины, можно выбрать любую точку орбиты для её поиска. Проще всего рассмотреть перицентр или апоцентр, рассмотрим первый. |
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added intEnergy for eccentric anomaly