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Giải bài 5 trang 65 Chuyên đề học tập Toán 10 – Chân trời sáng tạo

Mặt Trăng chuyển động theo một quỹ đạo là đường elip có tâm sai bằng 0,0549 và nhận tâm Trái Đất là một tiêu điểm.

ꦏTổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Mặt Trăng chuyển động theo một quỹ đạo là đường elip có tâm sai bằng 0,0549 và nhận tâm Trái Đất là một tiêu điểm. Biết khoảng cách gần nhất giữa tâm Trái Đất và tâm Mặt Trăng là 362 600 km. Tính khoảng cách xa nhất giữa tâm Trái Đất và tâm Mặt Trăng. Nguồn:

Phương pháp giải - Xem chi tiết

Cho M bất kì thuộc Elip  \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\) có một tiêu điểm là \({F_1}\) \(M{F_1}\) nhỏ nhất bằng \(a - c\) \(M{F_1}\) lớn nhất bằng \(a + c\)

Lời giải chi tiết

Gọi phương trình quỹ đạo chuyển động của Mặt Trăng là \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\)Giả sử tâm Trái Đất là tiêu điểm \({F_1}\)Khi đó:\(M{F_1}\) nhỏ nhất bằng \(a - c = 362600\)Tâm sai \(e = \frac{c}{a} = 0,0549\)Suy ra \(a \approx 383663,c \approx 21063\)\( \Rightarrow \) Khoảng cách xa nhất giữa tâm Trái Đất và tâm Mặt Trăng bằng \(a + c = 404726\) (km)

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