Hour Angle - Solar Hour Angle

Solar Hour Angle

The hour angle (h or ha) of a point on the Earth's surface is the angle through which the earth would turn to bring the meridian of the point directly under the sun. The earth is rotating, so this angular displacement represents time.

So in observing the sun from earth, the solar hour angle is an expression of time, expressed in angular measurement, usually degrees, from the solar noon.

At solar noon, at the observer's longitude on earth, the hour angle is 0.000 degrees, with the time before solar noon expressed as negative degrees, and the local time after solar noon expressed as positive degrees.

The hour angle is the angular displacement of the sun east or west of the local meridian due to rotation of the earth on its axis at 15° per hour with morning being negative and afternoon being positive. For example, at 10:30 AM local apparent time the hour angle is -22.5° (15° per hour times 1.5 hours before noon).

The cosine of the hour angle (cos(h)) becomes an easy computation tool in determining the cosine term for the computation of the angle of the sun's altitude (or the complementary zenith angle) at any time during the day. At solar noon, h=0.000 so of course, cos(h)=1, and before and after solar noon the cos(± h) term = the same value for morning (negative hour angle) or afternoon (positive hour angle), i.e. the sun is at the same altitude in the sky at both 11:00AM and 1:00PM solar time, etc.