Angular distance is the separation between two points from an observer’s point of view, expressed in degrees or radians. It is used in trigonometry to calculate height and distance, and in astronomy to describe an object’s position. The amateur can use it to locate astronomical objects, while the professional uses angular diameter to measure their apparent size. Military personnel use angular mil to express targeting calculations.
Angular distance is a measure of the apparent separation between two points from the observer’s point of view. Straight lines extended from any point to the observer intersect. The angle of intersection of these two lines is the angular distance and is typically expressed in degrees or radians. In trigonometry, this angle can be used to calculate height and distances. Astronomers often use angle to describe the apparent separation between celestial bodies without referring to their actual distance.
A common trigonometry problem involves calculating the height of a building. The angular distance of the line of sight between the top and bottom of the building at a known distance is sufficient information to determine its height. Calculations involving angular range are common in surveying and targeting. Instead of degrees or radians, military personnel often find it helpful to express targeting calculations in terms of angular mil. This is 1/6400th of the circumference of a circle, or more conveniently, the angular distance between two points separated by one meter at a distance of 1000 metres.
In astronomy, there are two basic ways to describe an object’s position in the sky. One is in reference to a coordinate system, the other is based on the object’s position relative to another body. In the equatorial coordinate system, the Earth’s poles and equator are projected into space as the celestial poles and celestial equator. A body’s position is described by its declination, degrees north or south of the celestial equator, and its hour angle. This is the angular distance along the celestial equator between the observer’s position and the celestial meridian, a circle which passes directly above the observer and through the celestial poles.
For the amateur, angular distance could be used to help locate an astronomical object in relation to a known body, or simply to note an interesting feature. Often, all that is needed is an outstretched hand. At arm’s length, the tip of the little finger subtends about one degree of arc. Three middle fingers subtend about four degrees and a clenched fist about ten. The distance from the little finger to the thumb of an open hand covers approximately 18 degrees.
Frequently, the professional and more serious observer uses a measure similar to angular distance called the angular diameter. This is the apparent size of an astronomical object as seen from Earth. These diameters are quite small and are usually measured in arcseconds, or 1/3600th of a degree. As with terrestrial measurement, if the distance to an object is known, its angular diameter can be used to calculate its true size.
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