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Giải bài 6.9 trang 7 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Định luật thứ ba của Kepler nói rằng bình phương của chu kì quỹ đạo \(p\)(tính bằng năm Trái Đất)

🗹Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Định luật thứ ba của Kepler nói rằng bình phương của chu kì quỹ đạo \(p\)(tính bằng năm Trái Đất) của một hành tinh chuyển động xung quanh Mặt Trời (theo quỹ đạo là một đường elip với 'Mặt Trời nằm ở một tiêu điểm) bẳng lập phương của bán trục lớn d (tính bằng đơn vị thiên văn \({\rm{AU}}\)). a) Tính \(p\)theo\(d\). b) Nếu Sao Thổ có chu kì quỹ đạo là 29,46 năm Trải Đất, hãy tinh bán trục lớn quỹ đạo của Sao Thổ đến Mặt Trời (kết quả tính theo đơn vị thiên văn và làm tròn đến hàng phần trăm).

Phương pháp giải - Xem chi tiết

Từ giả thiết ta có \({p^2} = {d^3}\, \Rightarrow \,p = \sqrt {{d^3}} \)

Lời giải chi tiết

a) Theo đinh luật thứ ba của Kepler, ta có:\({p^2} = {d^3}\,{\rm{hay}}\,p = \sqrt {{d^3}} \)b) Thay \(p = 29,46\)vào công thức\(p = \sqrt {{d^3}} \), ta được \(d = 9,54\) AU

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