Using law of cosines for angle $A$ (at Z):
Another problem in spherical astronomy is the effect of aberration and refraction on the apparent positions of celestial objects. Aberration is the apparent shift of an object's position due to the finite speed of light and the motion of the observer, while refraction is the bending of light as it passes through the Earth's atmosphere. spherical astronomy problems and solutions
cosa=cosbcosc+sinbsinccosAcosine a equals cosine b cosine c plus sine b sine c cosine cap A Using law of cosines for angle $A$ (at
An observer at latitude (\phi = 40^\circ) N sees a star with declination (\delta = 20^\circ) N at hour angle (H = 30^\circ) (west). Find its altitude and azimuth. Find its altitude and azimuth
This article introduces classic spherical‑astronomy problems, derives solutions, and provides worked examples you can follow. Topics covered: celestial coordinates, spherical triangles, object rise/transit/set times, hour angle and sidereal time, parallactic angle, conversion between coordinate systems, and small practical problems (angular separation, twilight limits). Equations assume a spherical Earth and standard astronomical conventions.
cos(θ)=sin(ϕ1)sin(ϕ2)+cos(ϕ1)cos(ϕ2)cos(Δλ)cosine open paren theta close paren equals sine open paren phi sub 1 close paren sine open paren phi sub 2 close paren plus cosine open paren phi sub 1 close paren cosine open paren phi sub 2 close paren cosine open paren cap delta lambda close paren
Light bends as it passes through Earth's atmosphere, making objects appear higher in the sky than they actually are. The Challenge