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The angle is typically measured in degrees from the mark of number 12 clockwise. The time is usually based on a 12-hour clock. A method to solve such problems is to consider the rate of change of the angle in degrees per minute. The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute.
The cosine of the hour angle (cos(h)) is used to calculate the solar zenith angle. At solar noon, h = 0.000 so 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), so that the Sun is at the same altitude in the sky at 11:00AM and 1:00PM solar time. [5]
Here, C is the difference between the angle moved at mean speed, and at the angle at the corrected speed projected onto the equatorial plane, and divided by 180° to get the difference in "half-turns". The value 23.44° is the tilt of the Earth's axis ("obliquity"). The subtraction gives the conventional sign to the equation of time.
In two dimensions, only a single angle is needed to specify a rotation about the origin – the angle of rotation that specifies an element of the circle group (also known as U(1)). The rotation is acting to rotate an object counterclockwise through an angle θ about the origin; see below for details.
An equation clock is a mechanical clock which includes a mechanism that simulates the equation of time, so that the user can read or calculate solar time, as would be shown by a sundial. The first accurate clocks, controlled by pendulums , were patented by Christiaan Huyghens in 1657.
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The bearing angle value will always be less than 90 degrees. [1] For example, if Point B is located exactly southeast of Point A, the bearing from Point A to Point B is "S 45° E". [3] For example, if the bearing between Point A and Point B is S 45° E, the azimuth between Point A and Point B is 135°. [1] [3] Azimuths and bearings.
The Sextant reading is known as the 'Sextant Altitude'. This is corrected by use of tables to a 'True Altitude'. The actual declination and hour angle of the celestial body are found from astronomical tables for the time of the measurement and together with the 'True Altitude' are put into a formula with the assumed latitude.