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 | This article may be confusing or unclear to readers.(October 2007) |
The keyhole problem, in the context of astronomy, refers to the difficulty that azimuth-elevation type telescopes or antenna gimbal systems encounter in crossing the zenith.
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| This article may be confusing or unclear to readers.(October 2007) |
The keyhole problem, in the context of astronomy, refers to the difficulty that azimuth-elevation type telescopes or antenna gimbal systems encounter in crossing the zenith.
To track celestial objects as they move across the sky, these systems usually rotate on two axes. Often, a tilting mechanism (elevation) is mounted upon a panning base (azimuth). To cover the complete hemisphere of visible sky, a telescope gimbal can have a 360-degree azimuth range and a 0- to 90-degree elevation range. To visualize this shape, imagine drawing a quarter circle spanning from the horizon to directly above you and revolving it around the vertical axis. If, on the other hand, the gimbal has a range from 0 to slightly less than 90 degrees elevation, the telescope is unable to see a region of sky.
A variation on the keyhole problem involves defining behavior for gimbals with full-circle azimuth range, and at least 90-degree but less than 180-degree elevation range. Imagine a satellite on an orbital path that crosses directly overhead. If the gimbal tilts to track the object from the horizon but must stop at 90 degrees, the entire telescope must pan 180 degrees to follow the object from zenith down to the opposite horizon.
When there is a full-circle azimuth range and full 180-degree elevation range, all points can be reached without the need for an instantaneous 180-degree rotation of the azimuth. Passing directly through the zenith can be done smoothly. However, tracking an object that passes near (but not directly through) the zenith will require the azimuth to rotate increasingly faster as the zenith is approached. This will pose practical issues for a physical system with a motor than can only move the azimuthal axis at a limited rate and acceleration. And so the keyhole problem is a fundamental issue for any real azimuth-elevation type tracking system, even if designed to reach the whole range of half-hemispherical angles.
These are often-encountered difficulties in creating smooth automated tracking algorithms.
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified by three numbers, : the radial distance of the radial liner connecting the point to the fixed point of origin ; the polar angle θ of the radial line r; and the azimuthal angle φ of the radial line r.
An azimuth is the angular measurement in a spherical coordinate system which represents the horizontal angle from a cardinal direction, most commonly north.
The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles: altitude and azimuth. Therefore, the horizontal coordinate system is sometimes called the az/el system, the alt/az system, or the alt-azimuth system, among others. In an altazimuth mount of a telescope, the instrument's two axes follow altitude and azimuth.
The zenith is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction opposite to the gravity direction at that location (nadir). The zenith is the "highest" point on the celestial sphere.
A circle of latitude or line of latitude on Earth is an abstract east–west small circle connecting all locations around Earth at a given latitude coordinate line.
A theodolite is a precision optical instrument for measuring angles between designated visible points in the horizontal and vertical planes. The traditional use has been for land surveying, but it is also used extensively for building and infrastructure construction, and some specialized applications such as meteorology and rocket launching.
Gimbal lock is the loss of one degree of freedom in a multi-dimensional mechanism at certain alignments of the axes. In a three-dimensional three-gimbal mechanism, gimbal lock occurs when the axes of two of the gimbals are driven into a parallel configuration, "locking" the system into rotation in a degenerate two-dimensional space.
A telescope mount is a mechanical structure which supports a telescope. Telescope mounts are designed to support the mass of the telescope and allow for accurate pointing of the instrument. Many sorts of mounts have been developed over the years, with the majority of effort being put into systems that can track the motion of the fixed stars as the Earth rotates.
In astronomy, the meridian is the great circle passing through the celestial poles, as well as the zenith and nadir of an observer's location. Consequently, it contains also the north and south points on the horizon, and it is perpendicular to the celestial equator and horizon. Meridians, celestial and geographical, are determined by the pencil of planes passing through the Earth's rotation axis. For a location not on this axis, there is a unique meridian plane in this axial-pencil through that location. The intersection of this plane with Earth's surface defines two geographical meridians, and the intersection of the plane with the celestial sphere is the celestial meridian for that location and time.
An altazimuth mount or alt-azimuth mount is a simple two-axis mount for supporting and rotating an instrument about two perpendicular axes – one vertical and the other horizontal. Rotation about the vertical axis varies the azimuth of the pointing direction of the instrument. Rotation about the horizontal axis varies the altitude angle of the pointing direction.
An equatorial mount is a mount for instruments that compensates for Earth's rotation by having one rotational axis, called polar axis, parallel to the Earth's axis of rotation. This type of mount is used for astronomical telescopes and cameras. The advantage of an equatorial mount lies in its ability to allow the instrument attached to it to stay fixed on any celestial object with diurnal motion by driving one axis at a constant speed. Such an arrangement is called a sidereal drive or clock drive. Equatorial mounts achieve this by aligning their rotational axis with the Earth, a process known as polar alignment.
In photography, a tripod is a portable device used to support, stabilize and elevate a camera, a flash unit, or other videographic or observational/measuring equipment. All photographic tripods have three legs and a mounting head to couple with a camera. The mounting head usually includes a thumbscrew that mates to a female-threaded receptacle on the camera, as well as a mechanism to be able to rotate and tilt the camera when it is mounted on the tripod. Tripod legs are usually made to telescope, in order to save space when not in use. Tripods are usually made from aluminum, carbon fiber, steel, wood or plastic.
The meridian circle is an instrument for timing of the passage of stars across the local meridian, an event known as a culmination, while at the same time measuring their angular distance from the nadir. These are special purpose telescopes mounted so as to allow pointing only in the meridian, the great circle through the north point of the horizon, the north celestial pole, the zenith, the south point of the horizon, the south celestial pole, and the nadir. Meridian telescopes rely on the rotation of the sky to bring objects into their field of view and are mounted on a fixed, horizontal, east–west axis.
A solar tracker is a device that orients a payload toward the Sun. Payloads are usually solar panels, parabolic troughs, Fresnel reflectors, lenses, or the mirrors of a heliostat.
The Pfund telescope, originated by A.H. Pfund, provides an alternative method for achieving a fixed telescope focal point in space regardless of where the telescope line of sight is pointed.
In amateur astronomy, "GoTo" refers to a type of telescope mount and related software that can automatically point a telescope at astronomical objects that the user selects. Both axes of a GoTo mount are driven by a motor and controlled by a computer. It may be either a microprocessor-based integrated controller or an external personal computer. This differs from the single-axis semi-automated tracking of a traditional clock-drive equatorial mount.
Polar alignment is the act of aligning the rotational axis of a telescope's equatorial mount or a sundial's gnomon with a celestial pole to parallel Earth's axis.
Sun path, sometimes also called day arc, refers to the daily and seasonal arc-like path that the Sun appears to follow across the sky as the Earth rotates and orbits the Sun. The Sun's path affects the length of daytime experienced and amount of daylight received along a certain latitude during a given season.
In spherical astronomy, the parallactic angle is the angle between the great circle through a celestial object and the zenith, and the hour circle of the object. It is usually denoted q. In the triangle zenith—object—celestial pole, the parallactic angle will be the position angle of the zenith at the celestial object. Despite its name, this angle is unrelated with parallax. The parallactic angle is zero or 180° when the object crosses the meridian.
The Rayleigh sky model describes the observed polarization pattern of the daytime sky. Within the atmosphere, Rayleigh scattering of light by air molecules, water, dust, and aerosols causes the sky's light to have a defined polarization pattern. The same elastic scattering processes cause the sky to be blue. The polarization is characterized at each wavelength by its degree of polarization, and orientation.
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