Because the sky is curved, standard flat geometry fails. Moving an inch near the celestial pole covers a vastly different angular distance than moving an inch near the celestial equator. The Solution
Calculations on the celestial sphere rely on spherical trigonometry rather than standard Euclidean geometry. On a sphere, the shortest distance between two points is a arc, which is a circle whose plane passes through the center of the sphere. spherical astronomy problems and solutions
An astronomer wants to know when the bright star Vega ( ) rises for an observer in London (Latitude Goal: Find the Hour Angle ( ) of Vega at the exact moment it skims the horizon. Because the sky is curved, standard flat geometry fails
Always pay close attention to signs. Southern latitudes ( ) and southern declinations ( On a sphere, the shortest distance between two
Rearrange the formula to solve for distance: d = 1 / p
cosa=cosbcosc+sinbsinccosAcosine a equals cosine b cosine c plus sine b sine c cosine cap A The Spherical Law of Cosines (for Angles)