 |
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.
The method to use differs depending on whether the alignment is taking place in daylight or at night. Furthermore, the method differs if the alignment is done in the Northern Hemisphere or Southern Hemisphere. The purpose of the alignment also must be considered; for example, the value of accuracy is much more significant in astrophotography than in casual stargazing.
In the Northern Hemisphere, sighting Polaris the North Star is the usual procedure for aligning a telescope mount's polar axis parallel to the Earth's axis. [1] Polaris is approximately three-quarters of a degree from the North Celestial Pole, and is easily seen by the naked eye.
σ Octantis, sometimes known as the South Star, can be sighted in the Southern hemisphere to perform a polar alignment. At magnitude +5.6, it is difficult for inexperienced observers to locate in the sky. Its declination of -88° 57′ 23″ places it 1° 2′ 37" from the South Celestial Pole. An even closer star BQ Octantis of magnitude +6.9 lies 10' from the South Pole as of 2016. Although not visible to the naked eye, it is easily visible in most polar 'scopes. (It will lie its closest to the South Pole, namely 9', in the year 2027.
In the Northern Hemisphere, rough alignment can be done by visually aligning the axis of the telescope mount with Polaris. In the Southern hemisphere or places where Polaris is not visible, a rough alignment can be performed by ensuring the mount is level, adjusting the latitude adjustment pointer to match the observer's latitude, and aligning the axis of the mount with true south or north by means of a magnetic compass. (This requires taking the local magnetic declination into account). This method can sometimes be adequate for general observing through the eyepiece or for very wide angle astro-imaging with a tripod-mounted camera; it is often used, with an equatorially-mounted telescope, as a starting point in amateur astronomy.
There are ways to improve the accuracy of this method. For example, instead of reading the latitude scale directly, a calibrated precision inclinometer can be used to measure the altitude of the polar axis of the mount. If the setting circles of the mount are then used to find a bright object of known coordinates, the object should mismatch only as to azimuth, so that centering the object by adjusting the azimuth of the mount should complete the polar alignment process. Typically, this provides enough accuracy to allow tracked (i.e. motorized) telephoto images of the sky.
For astro-imaging through a lens or telescope of significant magnification, a more accurate alignment method is necessary to refine the rough alignment, using one of the following approaches.
An alignment suitable for visual observation and short exposure imaging (up to a few minutes) can be achieved with a polar scope. This is a low-magnification telescope mounted co-axially with the mount (and adjusted to maximize the accuracy of this alignment). A special reticle is used to align the mount with Polaris (or a group of stars near the polar region) in the Southern Hemisphere. While primitive polariscopes originally needed the careful adjustment of the mount to match the time of year and day, this process can be simplified using computer apps that calculate the correct position of the reticle. A new-style northern-hemisphere reticle uses a 'clock-face' style with 72 divisions (representing 20-minute intervals) and circles to compensate for the drift of Polaris over around thirty years. Use of this reticle can allow alignment to within an arc minute or two. [2]
Drift alignment is a method to refine the polar alignment after a rough alignment is done. The method is based on attempting to track stars in the sky using the clock drive; any error in the polar alignment will show up as the drift of the stars in the eyepiece/sensor. Adjustments are then made to reduce the drift, and the process is repeated until the tracking is satisfactory. For the polar axis altitude adjustment, one can attempt to track a star low in the east or west. For the azimuth adjustment, one typically attempts to track a star close to the meridian, with declination about 20° from the equator, in the hemisphere opposite of the observing location.
For telescopes combined with an imaging camera connected to a computer, it is possible to achieve very accurate polar alignment (within 0.1 minutes of arc). An initial rough alignment is first performed using the polar scope. An image can then be captured and a star database is used to identify the exact field of view when aimed at stars near the pole - 'plate solving'. The telescope is then rotated ninety degrees around its right ascension axis and a new 'plate solve' is carried out. The error in the point around which the images rotate compared to the true pole is calculated automatically and the operator can be given simple instructions to adjust the mount for a more accurate polar alignment. [3]
The polar error in elevation and azimuth can be calculated by pointing the telescope to two stars or taking two astrometric solves of two positions and the measured error in right ascension and declination. [4] From the difference between the right ascension and declination of the telescope encoder and the second's star position, the elevation and azimuth error of the polar alignment can be calculated. The basic formulas are as follows:
where
is Right ascension
is Declination
is Site latitude
is the hour angle of the reference point equals ( - Local sidereal time)
is Error in Right Ascension
is Error in Declination
is Polar error in elevation (altitude)
is Polar error in azimuth
The inverse can be calculated if the above formula is written in matrix notation. So the polar error expressed in Δe and Δa can be calculated from the Δα and Δδ between the telescope encoder and the second reference star.
Polar Alignment with Excel [5] [6] is a method for polar alignment of equatorial mountings for astronomical telescopes, using a digital camera and a computer.
A digital camera with a standard lens is mounted on the telescope and pointed at the celestial pole. Exposure is set at „B“ (Bulb) and an image is taken while the camera is slowly turned around the polar axis. [7] This yields a kind of star-trail image. The beginning and the end of the star trails must be clearly marked with a few seconds of static exposure. Due to the rotation, the information about the current direction of the axis is hidden in the image. Alternatively, two static images can be taken, which differ by a rotation around the polar axis.
For the evaluation of the images, a special Excel spreadsheet has been developed. For three stars, the rectangular X-Y-coordinates are measured at both ends of their trails or on both static images. In addition, we need the current right ascension and declination of the 3 stars, the longitude and latitude of the observatory, and the date and time the images were taken. The spreadsheet then outputs the necessary corrections of the azimuth and the pole height in degrees and, in an auxiliary field, the corresponding number of turns of the adjustment screws, thus allowing a direct approach to the correct alignment.
The Excel spreadsheet and detailed instructions for use are available for free download at the website of the vhs-observatory Neumuenster. [8]
A crosshair eyepiece is an ordinary ocular with the only difference being that it has a crosshair for aiming and measurement of the angular distance. This is useful in any type of polar alignment, but especially in drift.
A small telescope usually with an etched reticle is inserted into the rotational axis of the mount.
Right ascension is the angular distance of a particular point measured eastward along the celestial equator from the Sun at the March equinox to the point in question above the Earth. When paired with declination, these astronomical coordinates specify the location of a point on the celestial sphere in the equatorial coordinate system.
Astronomicalcoordinate systems are organized arrangements for specifying positions of satellites, planets, stars, galaxies, and other celestial objects relative to physical reference points available to a situated observer. Coordinate systems in astronomy can specify an object's position in three-dimensional space or plot merely its direction on a celestial sphere, if the object's distance is unknown or trivial.
The equatorial coordinate system is a celestial coordinate system widely used to specify the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the centre of Earth, a fundamental plane consisting of the projection of Earth's equator onto the celestial sphere, a primary direction towards the vernal equinox, and a right-handed convention.
The galactic coordinate system is a celestial coordinate system in spherical coordinates, with the Sun as its center, the primary direction aligned with the approximate center of the Milky Way Galaxy, and the fundamental plane parallel to an approximation of the galactic plane but offset to its north. It uses the right-handed convention, meaning that coordinates are positive toward the north and toward the east in the fundamental plane.
Proper motion is the astrometric measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the center of mass of the Solar System, compared to the abstract background of the more distant stars.
A sundial is a horological device that tells the time of day when direct sunlight shines by the apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a flat plate and a gnomon, which casts a shadow onto the dial. As the Sun appears to move through the sky, the shadow aligns with different hour-lines, which are marked on the dial to indicate the time of day. The style is the time-telling edge of the gnomon, though a single point or nodus may be used. The gnomon casts a broad shadow; the shadow of the style shows the time. The gnomon may be a rod, wire, or elaborately decorated metal casting. The style must be parallel to the axis of the Earth's rotation for the sundial to be accurate throughout the year. The style's angle from horizontal is equal to the sundial's geographical latitude.
In astronomy, a planisphere is a star chart analog computing instrument in the form of two adjustable disks that rotate on a common pivot. It can be adjusted to display the visible stars for any time and date. It is an instrument to assist in learning how to recognize stars and constellations. The astrolabe, an instrument that has its origins in Hellenistic astronomy, is a predecessor of the modern planisphere. The term planisphere contrasts with armillary sphere, where the celestial sphere is represented by a three-dimensional framework of rings.
The great-circle distance, orthodromic distance, or spherical distance is the distance along a great circle.
The solar zenith angle is the zenith angle of the sun, i.e., the angle between the sun’s rays and the vertical direction. It is the complement to the solar altitude or solar elevation, which is the altitude angle or elevation angle between the sun’s rays and a horizontal plane. At solar noon, the zenith angle is at a minimum and is equal to latitude minus solar declination angle. This is the basis by which ancient mariners navigated the oceans.
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 astronomical navigation, the intercept method, also known as Marcq St. Hilaire method, is a method of calculating an observer's position on Earth (geopositioning). It was originally called the azimuth intercept method because the process involves drawing a line which intercepts the azimuth line. This name was shortened to intercept method and the intercept distance was shortened to 'intercept'.
Longitude by chronometer is a method, in navigation, of determining longitude using a marine chronometer, which was developed by John Harrison during the first half of the eighteenth century. It is an astronomical method of calculating the longitude at which a position line, drawn from a sight by sextant of any celestial body, crosses the observer's assumed latitude. In order to calculate the position line, the time of the sight must be known so that the celestial position i.e. the Greenwich Hour Angle and Declination, of the observed celestial body is known. All that can be derived from a single sight is a single position line, which can be achieved at any time during daylight when both the sea horizon and the sun are visible. To achieve a fix, more than one celestial body and the sea horizon must be visible. This is usually only possible at dawn and dusk.
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.
Angular distance or angular separation, also known as apparent distance or apparent separation, denoted , is the angle between the two sightlines, or between two point objects as viewed from an observer.
Setting circles are used on telescopes equipped with an equatorial mount to find celestial objects by their equatorial coordinates, often used in star charts and ephemerides.
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.
The Heliocentric Julian Date (HJD) is the Julian Date (JD) corrected for differences in the Earth's position with respect to the Sun. When timing events that occur beyond the Solar System, due to the finite speed of light, the time the event is observed depends on the changing position of the observer in the Solar System. Before multiple observations can be combined, they must be reduced to a common, fixed, reference location. This correction also depends on the direction to the object or event being timed.
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 position of the Sun in the sky is a function of both the time and the geographic location of observation on Earth's surface. As Earth orbits the Sun over the course of a year, the Sun appears to move with respect to the fixed stars on the celestial sphere, along a circular path called the ecliptic.
Astronomical nutation is a phenomenon which causes the orientation of the axis of rotation of a spinning astronomical object to vary over time. It is caused by the gravitational forces of other nearby bodies acting upon the spinning object. Although they are caused by the same effect operating over different timescales, astronomers usually make a distinction between precession, which is a steady long-term change in the axis of rotation, and nutation, which is the combined effect of similar shorter-term variations.
