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Giải bài 6 trang 48 Chuyên đề học tập Toán 10 – Chân trời sáng tạo

Ngày 04/10/1957, Liên Xô đã phóng thành công vệ tinh nhân tạo đầu tiên vào không gian, vệ tinh mang tên Sputnik I.

Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Chân trờ꧃i sáng t💙ạo

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

Ngày 04/10/1957, Liên Xô đã phóng thành công vệ tinh nhân tạo đầu tiên vào không gian, vệ tinh mang tên Sputnik I. Vệ tinh đó có quỹ đạo hình elip (E) nhận tâm Trái Đất là một tiêu điểm. Cho biết khoảng cách xa nhất giữa vệ tinh và tâm Trái Đất là 7310 km và khoảng cách gần nhất giữa vệ tinh và tâm Trái Đất là 6586 km. Tìm tâm sai của quỹ đạo chuyển động của vệ tinh Sputnik I. (Nguồn:

Phương pháp giải - Xem chi tiết

Cho PTCT: \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\), \({F_1}( - c;0)\) là một tiêu điểm. + Tâm sai của elip: \(e = \frac{c}{a}\) Điểm M bất kì thuộc elip, khi đó: \(M{F_1}\) nhỏ nhất bằng \(a - c\) khi M trùng \({A_1}( - a;0)\) \(M{F_1}\) lớn nhất bằng \(a + c\) khi M trùng \({A_2}(a;0)\)

Lời giải chi tiết

Gọi PTCT của quỹ đạo hình elip đó là: \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\),Giả sử tâm Trái Đất là tiêu điểm \({F_1}( - c;0)\).Điểm M bất kì thuộc elip là vị trí của vệ tinh trong quỹ đạo, khi đó:\(M{F_1}\) nhỏ nhất bằng \(a - c = 6586\)\(M{F_1}\) lớn nhất bằng \(a + c = 7310\)\( \Rightarrow a = 6948;c = 362\)\( \Rightarrow \)Tâm sai của elip: \(e = \frac{c}{a} \approx 0,0521\)Vậy tâm sai của quỹ đạo chuyển động của vệ tinh là 0,0521. 

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Ph/hs Tham Gia Nhóm Để Cập Nhật Điểm Thi, Điểm Chuẩn Miễn Phí

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