SYNCHRONISED DOME ROTATION - Brayebrook Observatory

SETTING UP THE EQUATIONS (cont.)which is a quadratic of the form:( cos 2 e.sin 2 Az + cos 2 e.cos 2 Az + sin 2 e)d 2+ 2( X'cose.sin Az − Y'cose.cos Az + Z'sin e)d( ) = 0+ X' 2 +Y' 2 +Z' 2 −R 2but: l' 2 = X' 2 +Y' 2 +Z' 2& simplifying cos 2 e.sin 2 Az + cos 2 e.cos 2 Az + sin 2 esincesin 2 Az =1− cos 2 Azand sin 2 e = 1− cos 2 eby substitution:cos 2 e.sin 2 Az + cos 2 e.cos 2 Az + sin 2 e = cos 2 e 1− cos 2 Az ( ) + cos 2 e.cos 2 Az + 1− cos 2 e ( )and putting:= cos 2 e − cos 2 e.cos 2 Az + cos 2 e.cos 2 Az +1− cos 2 e= 1L = X'cose.sin Az −Y'cose.cos Az + Z'sin eM = l' 2 −R 2d 2 + 2Ld + M = 0from which d = −L ± L 2 − Mbut d is always positive: ∴ d = ( L 2 − M) − L11