: On June 3, 2016, we are observing the star ( \eta ) Ursae Majoris (( \alpha = 13^h 47^m 29^s ), ( \delta = 49^\circ19'32'' )) from Villanova ( ( \phi = 40^\circ02'14'' \textN ), ( \lambda = 75^\circ20'57'' \textW )). What are the altitude and azimuth of the star at 11:00 PM local time?
But every observational astronomer should be able to derive these formulas and spot errors when software fails (e.g., near the zenith where (\cos h) near zero, or for circumpolar solutions).
Using the spherical trigonometric formulas from the PZX triangle, we get the star's altitude and azimuth. The final result is an altitude ( h = 75^\circ29'30'' ) and an azimuth ( A = 44^\circ59'03'' ). spherical astronomy problems and solutions
0=sinϕsinδ+cosϕcosδcosH0 equals sine phi sine delta plus cosine phi cosine delta cosine cap H Step 2: Solve for cosHcosine cap H
$$\cos c = \cos a \cos b + \sin a \sin b \cos C$$ : On June 3, 2016, we are observing
cos(90−δ)=cos(90−ϕ)cos(90−h)+sin(90−ϕ)sin(90−h)cos(A)cosine open paren 90 minus delta close paren equals cosine open paren 90 minus phi close paren cosine open paren 90 minus h close paren plus sine open paren 90 minus phi close paren sine open paren 90 minus h close paren cosine open paren cap A close paren
Update the coordinate epoch (e.g., B1950 to J2000) using standard IAU transformation matrices. Using the spherical trigonometric formulas from the PZX
Solve for $\cos A$: $$\cos A = \frac\sin \delta - \sin \phi \sin a\cos \phi \cos a$$