# 尧代观象台的相关计算

$\hat{x} = \hat{x^\prime}\\ \hat{y}=\cos\beta \ \hat{y^\prime} +\sin\beta \ \hat{z^\prime}\\ \hat{z} = -\sin\beta \ \ \hat{y^\prime} + \cos\beta \ \hat{z^\prime}$

$\cos\theta = [\cos d \ \cos L \cos\beta + \sin L \sin\beta] \cos\phi + \sin\phi \sin d \cos L$

$\cos \alpha = \left[\cos\beta \sin L \cos d- \sin\beta \cos L\right] \cos\phi + \cos L \sin d \sin\phi$

$[\cos d \ \cos L \cos\beta + \sin L \sin\beta] \cos\phi + \sin\phi \sin d \cos L=0$

$\cos\theta = \left[ \sin L \sin\beta + \cos L \cos\beta \ \cos (\omega \ t) \right]\ \cos (\Omega\ t) + \cos L \sin (\omega\ t) \sin(\Omega\ t)$

$\left[ \sin L \sin\beta + \cos L \cos\beta \ \cos (\omega \ t) \right]\ \cos (\Omega\ t) + \cos L \sin (\omega\ t) \sin(\Omega\ t) =0$

$\frac{ \sin L \sin\beta + \cos L \cos\beta \ \cos (\omega \ t)}{\cos L \sin (\omega\ t)}=-\tan\Omega t$

$\cos \alpha = \left[\cos\beta \sin L \cos (\omega t)- \sin\beta \cos L\right] \cos (\Omega t) + \cos L \sin (\omega t) \sin (\Omega t)$

http://www.zhenzhubay.com/home.php?mod=space&uid=2&do=blog&id=36911

http://blog.sciencenet.cn/blog-684007-1123989.html

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GMT+8, 2019-10-23 21:30