Home > Horizontal coordinate system

The horizontal coordinates are:

• altitude (Alt), that is the angle between the object and the observer's local horizon.
• azimuth (Az), that is the angle of the object around the horizon (measured from the North point, toward the East).

The horizontal coordinate system is sometimes also called the Alt/Az coordinate system.

The horizontal coordinate system is fixed to the Earth, not the stars. Therefore, the altitude and azimuth of an object changes with time, as the object appears to drift across the sky. In addition, because the horizontal system is defined by your local horizon, the same object viewed from different locations on Earth at the same time will have different values of altitude and azimuth.

Horizontal coordinates are very useful for determining the rise and set times of an object in the sky. When an object's altitude is 0°, it is:

• rising (if its azimuth is less than 180°)
• setting (if its azimuth is greater than 180°)

and there are the following special cases:

• on the Poles, objects on the celestial equator turn around the horizon
• on the equator, objects on the celestial poles stay at one point on the horizon

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1 Transformation of Coordinates

It is possible to pass from the equatorial coordinate system to the horizontal coordinate system.

Let be the declination, the hour angle, the observer's latitude.

The equations of the transformation are:

Use the inverse trigonometric functions to get the values of the coordinates.

2 The position of the Sun

There are several ways to compute the apparent position of the Sun in horizontal coordinates.

Complete and accurate algorithms to obtain precise values can be found in Jean Meeus's book Astronomical Algorithms.

Instead a simple approximate algorithm is the following:

Given:

• the date of the year and the timeFor alternate uses of "time", see Time (disambiguation). Time quantifies or measures the interval between events, or the duration of events. Time has long been perceived as a dimension in which each event has a definite (but not necessarily unique) positi of the day
• the observer's latitude, longitudeMap of Earth showing vertical lines of longitude Longitude sometimes denoted λ, describes the location of a place on Earth east or west of a north-south line called the Prime Meridian. Longitude is given as an angular measurement ranging from 0° at and time zoneTime Zone was also an old historical computer game. Time zones are areas of the Earth that have adopted the same standard time. Formerly, people used local solar time (originally apparent and then mean), resulting in time differing slightly from town to t

You have to compute:

• The Sun declination of the corresponding day of the year, which is given by the following formula:

where is the number of days spent since January 1January 1 is the first day of the calendar year in both the Julian and Gregorian calendars. Here a calendar year refers to the order in which the months are displayed, January to December. The first day of the medieval Julian year was usually a day other.

• The true hour angle that is the angle which the earth should rotate to take the observer's location directly under the sun.
  • Let hh:mm be the time the observer reads on the clock.
  • Merge the hours and the minutes in one variable = hh + mm/60 measured in hours.
  • hh:mm is the official time of the time zone, but it is different from the true local time of the observer's location. has to be corrected adding the quantity + (Longitude/15 - Time Zone), which is measured in hours and represents the difference of time between the true local time of the observer's location and the official time of the time zone.
  • If it is summer and Daylight Saving Time is used, you have to subtract one hour in order to get Standard Time.
  • The value of the Equation of Time in that day has to be added. Since is measured in hours, the Equation of Time must be divided by 60 before being added.
  • The hour angle can be now computed. In fact the angle which the earth should rotate to take the observer's location directly under the sun is given by the following expression: = (12 - ) * 15. Since is measured in hours and the speed of rotation of the earth 15 degrees per hour, is measured in degrees. If you need measured in radians you just have to multiply by the factor 2π/360.

• Use the Transformation of Coordinates to compute the apparent position of the Sun in horizontal coordinates.

This article's initial version originated from 'Jason Harris' Astroinfo which comes along with KStars, a Desktop Planetarium for Linux/ KDE. See http://edu.kde.org/kstars/index.phtml