phy105 - the celestial sphere - example problems - vik dhillon
from equatorial via rotation matrix $R$ (latitude $\phi$): Rotation about $y$-axis by $90^\circ - \phi$: $$\beginpmatrix \cos a \cos A \ \cos a \sin A \ \sin a \endpmatrix = \beginpmatrix \sin\phi & 0 & -\cos\phi \ 0 & 1 & 0 \ \cos\phi & 0 & \sin\phi \endpmatrix \beginpmatrix \cos\delta \cos H \ \cos\delta \sin H \ \sin\delta \endpmatrix$$ spherical astronomy problems and solutions
$a$ from (1): $\sin a = \sin35\sin10 + \cos35\cos10\cos45 = 0.0996 + 0.5739 = 0.6735$ → $a = 42.34^\circ$. phy105 - the celestial sphere - example problems
Angle at $P$ = hour angle $H$ (for upper culmination). Angle at $Z$ = $360^\circ - A$ if azimuth measured from north westward, but conventionally we use $A$ measured from north eastward. We adopt: Angle at Z = $A$ (azimuth) only after careful quadrant check. We adopt: Angle at Z = $A$ (azimuth)