- The World Pole is a fixed point on the celestial sphere where the stars appear to rotate due to the Earth’s rotation. The North Pole of the World aligns with the geographic north, while the South Pole of the World aligns with the geographic south. The North Pole is located in the constellation Ursa Minor, with Polaris being the closest star. The South Pole is located in the constellation Octans. Over time, due to precession, the positions of the World Poles shift by approximately 20 arcseconds per year.
Similar Ideas
The concept of the celestial sphere involves the projection of celestial bodies onto an imaginary sphere with a chosen radius. It is utilized to address a variety of astrometric issues. The observer’s eye serves as the center of the celestial sphere, whether they are located on Earth’s surface or in other areas of space (such as the center of the Earth). For an observer on Earth, the rotation of the celestial sphere mirrors the daily motion of the stars in the sky.
The celestial equator refers to a vast circle on the celestial sphere, positioned perpendicular to the axis of the Earth and aligning with the Earth’s equator. This celestial equator effectively divides the celestial sphere into two distinct hemispheres: the northern hemisphere, centered around the north pole of the Earth, and the southern hemisphere, centered around the south pole of the Earth. Any constellations that the celestial equator intersects are known as equatorial constellations.
In the field of astronomy, declination (δ) serves as one of the two coordinates within the equatorial coordinate system. It quantifies the angular distance between a celestial body and the plane of the celestial equator, typically measured in degrees, minutes, and seconds of arc. Declination is considered positive when north of the celestial equator, and negative when south of it.
The system of celestial coordinates known as ecliptic coordinates is based on the plane of the ecliptic as its principal plane and the pole of the ecliptic as its pole.
Ecliptic coordinates are used to observe the movement of celestial bodies in the solar system, many of which have orbital planes that are near the ecliptic plane. They are also used to observe the apparent motion of the Sun across the sky over the course of a year.
References in literary works
Even the ancient Egyptians were aware of the fact that the starry sky, after completing a full circle in 24 hours, returns to its original position. They also knew that there is a fixed point in the sky that remains stationary. This point is known as the North Pole of the world, and it is located almost exactly at the bright star Alpha of the Little Bear, which is commonly known as Polaris. The opposite point, where the axis of the Earth’s rotation intersects with the celestial sphere, is called the South Pole of the world. Unlike the North Pole, there are no bright stars in close proximity to the South Pole. It can be found in the constellation Octanthus. The poles of the world, due to a phenomenon known as precession, slowly move in relation to the stars. Their movement follows a circular path with a radius of approximately 23.5 degrees, centered at the pole of the ecliptic. A complete revolution takes about 25,770 years. Currently, the North Pole of the world is getting closer to Polaris. By 2102, the distance between them will be only 27.5 minutes of arc, and then the World Pole will start to move away from Polaris. In 7500 years, it will be aligned with another star, Alderamin (Alpha Cepheus), and in 13,500 years, it will be aligned with Vega (Alpha Lyra). The South Pole of the world moves accordingly.
The displacement magnitude is 50?3.1? per annum. A complete revolution of the vernal equinox point occurs every 25,729 years, meaning it will shift by 1° approximately every 72 years. The celestial sphere’s reference point is the North Pole of the Earth, which gradually moves around the ecliptic pole, gradually approaching Polaris. In the year 2000, the distance between them was 28?. In 12,000 years, the distance will be minimal, bringing them closest to Vega, the brightest star in the Northern Hemisphere.
Therefore, due to the phenomenon of precession, the Earth’s axis gradually changes its orientation over thousands of years, resulting in different stars being visible in different epochs. Currently, the Earth’s axis aligns closely with Polaris, also known as the North Star, which belongs to the constellation Ursa Minor. However, around 5000 years ago, a much fainter star in the constellation Draco served as the North Star, while in 12000 years, the star Vega in the constellation Lyra will take over this role. Vega’s brightness will make it a convenient reference point for travelers. Nevertheless, the Earth’s axis does not always point directly towards a bright star; often the axis lies far away from any prominent celestial objects. For instance, while Polaris currently marks the position of the North Pole, there is no notable star near the South Pole, making it more challenging to navigate using stars in the Southern hemisphere.
Continuation of Related Concepts
The field of astronomy relies on the celestial coordinate system to accurately describe the positions of celestial bodies in the sky. This system uses angular measurements to determine the location of objects on an imaginary celestial sphere. By utilizing two angular quantities, the coordinates of celestial bodies can be precisely determined. The celestial coordinate system is a type of spherical coordinate system, where the distance of objects is often unknown and irrelevant.
Astronomers also use the concept of culmination to track the motion of celestial bodies. Culmination refers to the moment when the center of a celestial body passes through the celestial meridian during its daily journey. It can also refer to the passing of the center of a celestial body through the point where its daily parallel intersects with the celestial meridian.
The galactic plane is the primary location of most of the mass in a disk galaxy. The perpendicular directions to the galactic plane indicate the poles of the galaxy. The terms galactic plane and galaxy poles are typically used to describe the plane and poles of the Milky Way.
Right Ascension (α, R. A. – from English right ascension) refers to the length of the arc on the celestial equator from the vernal equinox to the declination circle of a celestial object. Right ascension serves as one of the coordinates in the second equatorial system (the first system utilizes the hour angle). The second coordinate is known as declination.
A celestial luminary is an astronomical entity that emits its own light or reflects light. It is also known as a celestial body. In the field of spherical astronomy, a celestial luminary can be defined as the projection of an astronomical object on the celestial sphere. Celestial luminaries include the Sun, stars, the Moon, planets, satellites, asteroids, comets, and other celestial bodies. These names of celestial luminaries have also been used in fiction to describe other planets. For example, planets may be referred to as “suns”.
The movements of the Sun and planets in the sky reflect only their observable movements from the perspective of an Earth observer. These movements on the celestial sphere are not influenced by the daily rotation of the Earth, as the celestial sphere itself rotates.
The phenomenon known as the precession of the equinoxes refers to the gradual shift of the points of the vernal and autumnal equinoxes (the points where the celestial equator intersects the ecliptic) due to the Sun’s annual motion. Essentially, each year the vernal equinox occurs slightly earlier than the previous year, by approximately 20 minutes and 24 seconds. In terms of angular measurement, this corresponds to an offset of about 50.3″ per year, or 1 degree every 71.6 years. This shifting is a continuous process.
Ecliptica, derived from the Latin (linea) ecliptica, which in turn comes from the Greek word ἔκλειψις meaning “eclipse,” represents the grand circle that traces the path of the Sun’s visible annual motion along the celestial sphere. Similarly, the ecliptic plane signifies the plane of the Earth’s orbit around the Sun. A more precise modern definition of the ecliptic refers to its representation as the intersection of the celestial sphere and the plane of the Earth-Moon system’s barycenter orbit.
Epoch, a term borrowed from the Greek word έποχή meaning “stop,” holds significance in astronomy as a specific moment in time that serves as a reference point for defining astronomical coordinates or orbital elements. It is possible to convert astronomical coordinates from one epoch to another by taking into account factors such as precession and the object’s own motion.
The starry sky is a collection of celestial bodies that can be seen at night in the sky. These bodies are mostly stars. The human eye can see stars with a magnitude of up to 5-6. If the sky is clear and there are no clouds, it is possible to see up to 800 stars with a magnitude of up to 5, and up to 2.5 thousand stars with a magnitude of up to 6. Most of these stars are located near the Milky Way, which is a band of stars. It is worth noting that the total number of stars in our Galaxy is greater than the number of stars in the Milky Way alone.
A radiant is a specific area of the sky that appears to be the source of meteors. These meteors are observed when the Earth passes through a group of meteoric bodies that are all moving in the same orbit around the Sun.
The tilt of the axis of rotation refers to the deviation angle of a celestial body’s rotation axis from the perpendicular to its orbit plane. This means it is the angle between the equator plane of the celestial body and its orbit.
An orbital node is one of the two opposite points on the celestial sphere where a celestial body’s orbit intersects with a conventional reference plane. It also represents the geocentric projection of this point on the celestial sphere. For the planets of the solar system and the Moon, the ecliptic plane serves as this reference plane. Usually, the equatorial coordinate system and the celestial equator plane are utilized to track celestial objects. Since there are two such points, a distinction is made between them.
Octans is a small and very dim constellation located in the southern hemisphere of the sky, encompassing the South Pole of the world.
Goldfish (from Latin Doradus) is a constellation found in the southern hemisphere of the sky. It covers an area of 179.2 square degrees in the celestial sphere and contains 32 stars that can be seen with the naked eye.
Extraterrestrial Heavens refer to the view of space from the surface of celestial bodies other than Earth. This perspective may differ from what is observed from Earth’s surface due to various factors, with the most significant being the atmosphere or lack thereof. The color of the sky is influenced by the density and chemical makeup of the atmosphere, and the presence or absence of clouds, which can also vary in color. Additionally, there may be astronomical objects visible from the surface, including stars, satellites, planets, and rings.
Chinese constellations (星官, xīngguān) are arrangements of stars that are recognized and named in traditional Chinese culture. They differ significantly from the modern constellations that are based on ancient Greek astronomy. However, there are some similarities between certain groups, such as the Big Dipper and Orion.
Opposition is a term used to describe the position of a celestial body in the solar system when its ecliptic longitude is exactly 180 degrees away from the Sun. In this position, the body is approximately aligned with the Sun and Earth, appearing in the opposite direction to the Sun from our perspective on Earth. Opposition can only occur for planets and other celestial bodies that are located farther from the Sun than Earth.
An occultation occurs when one celestial body passes in front of another, blocking part of it, as seen from a specific vantage point.
An eclipse is a celestial event where one celestial body obscures the light from another.
The retrograde motion of planets refers to the observed movement of planets against the backdrop of stars on the celestial sphere, from east to west. This motion is opposite to the Sun’s (annual) and the Moon’s movement.
This list provides the brightest stars visible from Earth in the optical range, based on their apparent stellar magnitude. For multiple stars, the total stellar magnitude is provided.
Tidal capture, also known as synchronous rotation, refers to the phenomenon when a satellite’s orbit around its axis matches its orbit around the central body. As a result, the satellite always keeps the same side facing the central body, as it completes one rotation around its axis in the same time it takes to orbit around its partner. This tidal entrapment commonly occurs among the large natural satellites of planets in our solar system.
Stellar days denote the duration of a celestial body’s rotation around its own axis in an inertial reference frame, typically based on the reference frame associated with distant stars. In the case of Earth, it represents the time required for the Earth to complete one revolution around its axis relative to distant stars.
Serpentine (Latin: Ophiuchus) is a large constellation that intersects the ecliptic and is referred to as the 13th sign of the zodiac. However, it is not included in the zodiacal circle because in European astrology, the signs of the zodiac only have approximate correspondence to the constellations. This is due to the gradual shift in the Sun’s passage through the constellations since the creation of the zodiacal circle.
Fixed stars, also known as fixed luminaries (Latin: stellae fixae), are celestial objects that do not change their apparent position in relation to other luminaries over a relatively short period of time, comparable to a human lifetime. This designation applies to all stars except for the Sun. The Sun, planets, and the Moon are considered mobile stars or luminaries.
The pole of the ecliptic is a celestial point found at the intersection with the perpendicular to the ecliptic plane. It serves as the pole for the celestial coordinate system of the ecliptic.
In astronomy, the apex is a celestial point towards which the motion of an observer relative to any reference frame is directed. The point opposite to the apex is known as the antiapex.
Retrograde motion refers to motion in the opposite direction of direct motion. This term can describe the rotation of one celestial body around another in an orbit, as well as the rotation of a body around its axis, and other orbital parameters like precession and nutation. In planetary systems, retrograde motion typically signifies motion that goes against the rotation of the central body, which is the primary object within the system.
The constellation known as Compass, or Pyxis in Latin, can be found in the southern hemisphere of the sky. It covers an area of 220.8 square degrees and contains 43 stars that can be seen without the aid of a telescope. In Russia, this constellation is most visible in the southern and central regions. The best time to observe Compass is during the months of February and March.
Astronomical refraction, also known as atmospheric refraction, refers to the bending of light rays from celestial objects as they pass through the Earth’s atmosphere. This bending causes a shift in their apparent position in the sky.
The geographic poles are the points where the Earth’s axis of rotation intersects with its surface. There are two geographic poles: the North Pole, which is located in the Arctic Ocean, and the South Pole, which is located in Antarctica.
The astronomical unit (abbreviated as a.e. in Russian and since 2012 as au internationally, previously known as ua) is a unit of distance measurement in astronomy that has been historically established. Originally, it was defined as the major semi-axis of the Earth’s orbit, which is considered to be the average distance from the Earth to the Sun:126.
Gemini, also known as Ara in Latin, is a constellation that can be found in the southern hemisphere of the night sky. It covers an area of approximately 237.0 square degrees and contains a total of 60 stars that are visible to the naked eye. In the southern regions of Russia, specifically south of latitude 44° 30′, a small portion of Gemini can be observed rising very close to the horizon during the months of May and June. However, it should be noted that this particular area of the constellation lacks any bright stars. On the other hand, the star α Sacristan, which has a magnitude of 2.95, cannot be seen in Russia. Nevertheless, under ideal conditions, it is possible to catch a glimpse of this star near the horizon line in certain southern cities within the post-Soviet region, specifically those located south of latitude 40° 08′ such as Bukhara, Samarkand, and Nakhichevan.
Naugol (also known as Norma) is a constellation located in the southern hemisphere of the sky. It is situated southwest of Scorpius and north of the Southern Triangle, with a point of contact with Circulus. Both branches of the Milky Way pass through this constellation, although it is not particularly rich in bright stars. There are no stars in Naugol that have a visual sidereal magnitude brighter than 4.0, but it does contain 42 stars that are visible to the naked eye. The constellation covers a sky area of 165.3 square degrees. The best conditions for observing Naugol are in May and June, and it can be partially observed in southern Russia (south of 48 N). Constellation.
Angular size (sometimes referred to as angle of view) is the measurement of the angle between straight lines that connect the diametrically opposite extreme points of an observed object and the observer’s eye.
A transit, also known as an astronomical transit, is a fascinating event in astronomy where one celestial body passes in front of another from the perspective of an observer. This passage obscures a portion of the body being eclipsed.
Orbital elements, which consist of various parameters, play a crucial role in defining the orbit of a celestial body. These elements determine the size, shape, and location of the orbit in space, as well as the position of the celestial body within the orbit.
Astronomical conjunction is a phenomenon that occurs when celestial bodies align with each other, having equal ecliptic longitudes. In some cases, the concept of conjunction can also refer to the alignment based on direct ascent, rather than ecliptic longitude. During a conjunction, the two bodies are in close proximity to each other on the celestial sphere, although the exact moment of conjunction may not coincide with the moment of closest approach. It’s worth noting that the term conjunction is also used in astrology.
The International Celestial Reference System (ICRS), also known as the International Astronomical Reference System, has been the standard celestial coordinate system since 1998. It was officially adopted at the 23rd ICA congress in 1997. The ICRS is centered around the barycenter of the Solar System and its coordinates closely align with the equatorial coordinates of the J2000.0 epoch, with only a slight difference in arc seconds.
Solar days refer to the period of time it takes for a celestial body to complete one rotation around its axis relative to the center of the Sun. More precisely, it is the time between two culminations (upper or lower) of the Sun’s center passing through the meridian in a specific location on Earth (or any other celestial body).
- A geographic pole is the point where the Earth’s axis of rotation intersects with its surface. There are two geographic poles: the North Pole, located in the Arctic (the central part of the Arctic Ocean), and the South Pole, located in Antarctica.
All meridians converge at the geographic pole, so it does not have a specific longitude. The North Pole has a latitude of +90 degrees, and the South Pole has a latitude of -90 degrees.
At the geographic poles, there are no cardinal directions. Day and night do not change at the poles because they do not experience the daily rotation of the Earth.
At the geographic pole, the Sun’s angle of elevation never exceeds 23.5°; as a result, the temperature at the pole is extremely low.
Associated ideas
Astronomical culmination – the moment when the center of a celestial body crosses the celestial meridian during its daily motion. Alternatively, it can refer to the point where the center of a celestial body intersects with the daily parallel of the celestial meridian.
The Earth’s axis rotation causes a visible daily movement of stars around a point on the celestial sphere known as the Pole of the World. The geographical north aligns with the North Pole of the world, while the geographical south aligns with the South Pole of the world. Polaris, also known as the North Star, can be found in the constellation of the Little Bear, marking the North Pole of the world. The South Pole of the world is located in the constellation Octanthus. Due to the precession of the Earth’s axis, the positions of the world’s poles shift by about 20 arcseconds per year.
Nutation, derived from the Latin word nutatio meaning “oscillation; rocking, nodding,” refers to a slight and irregular movement of a rotating solid object undergoing precession. This movement can be compared to a “wobble” of the rotation axis and involves a subtle change in the nutation angle, which is the angle between the axes of the object’s own rotation and its precessional rotation.
The term meridian, derived from the Latin word meridianus meaning “noon,” is commonly used in geography and astronomy to describe the line formed by the intersection of a surface with a plane that passes through the axis of rotation or symmetry.
Rotational axis inclination refers to the angle by which the rotation axis of a celestial body deviates from being perpendicular to the plane of its orbit. In simpler terms, it is the angle between the equatorial plane of a celestial body and its orbital plane.
The geographic poles, both north and south, are the points where the imaginary axis of the Earth intersects with the Earth’s surface.
Our planet, Earth, has a rotational axis, which is an imaginary line around which it spins. This axis intersects with the Earth’s surface at two specific points, known as the North and South geographic poles. If we were to extend the direction of the Earth’s axis, it would pass close to Polaris, the North Star. This is why Polaris appears stationary, while the celestial sphere seems to rotate around an imaginary axis.
March 21 is a unique day because it marks the moment when the boundary between light and shadow on Earth passes through both the North and South poles. If you hold a globe and position it correctly under a lamp, you will notice that the boundary of light follows the Earth’s meridian, intersecting the equator and all parallel circles at right angles. If you rotate the globe in this position while illuminating it, each point on the surface will trace a circle, with half of it in shadow and the other half in light. This means that during this time of year, the length of the day is equal to the length of the night. This phenomenon is observed worldwide, from the North Pole to the South Pole. Since the day lasts 12 hours, the Sun rises at 6 o’clock and sets at 18 o’clock everywhere (according to local time).
The 21st of March is a unique day because it is the only day of the year when the boundary between light and shadow on Earth passes through both the North and South poles. If you take a globe and position it correctly in relation to a lamp, you will see that the boundary between light and shadow follows the Earth’s meridian, crossing the equator and all parallel circles at right angles. By rotating the globe around its axis while illuminating it with the lamp, every point on the globe’s surface will trace a circle. Half of each circle will be in shadow, while the other half will be in light. This means that during this time of year, the length of the day is equal to the length of the night. This equality is observed from the North pole to the South pole. Since the day lasts 12 hours during this time, the Sun rises everywhere at 6 o’clock and sets at 18 o’clock (according to local time, of course).
Continuation of Related Concepts
The coordinate system of the ecliptic, or ecliptic coordinates:49, is a celestial coordinate system where the central plane is the plane of the ecliptic and the pole is the pole of the ecliptic. It is utilized in the study of the movement of celestial bodies within the solar system, many of which have orbital planes close to the ecliptic plane. It is also used in observing the apparent movement of the Sun across the sky throughout the year:30.
The prime meridian is a geographical meridian that serves as the reference point for measuring geographic longitude. Therefore, the longitude of this meridian in the accepted reference system is zero degrees.
The celestial sphere is a hypothetical sphere with an arbitrary radius upon which celestial objects are projected. This concept is utilized in order to address various astrometric issues. The observer’s eye is considered the center of the celestial sphere, and the observer can be located on the Earth’s surface or in other points in space (such as the center of the Earth). From the perspective of an observer on Earth, the rotation of the celestial sphere mirrors the daily motion of the celestial bodies in the sky.
The geoid, derived from the Greek words γῆ (earth) and εἶδος (species), is a closed convex surface that closely resembles the surface of calm water in seas and oceans and is perpendicular to gravity at any given point. It is a geometric shape that deviates from the ellipsoid of rotation and reflects the gravity potential properties of the Earth’s surface, making it a crucial concept in geodesy.
Stellar days refer to the period of rotation of a celestial body around its own axis in an inertial reference frame, typically the frame associated with distant stars. For the Earth, it represents the time it takes for one complete revolution on its axis relative to distant stars.
The celestial coordinate system is utilized in the field of astronomy to describe the precise location of celestial bodies in the sky or specific points on an imaginary celestial sphere. These coordinates are determined by two angular measurements that uniquely define the position of objects on the celestial sphere. Consequently, the celestial coordinate system functions as a spherical coordinate system, with the third coordinate, distance, often remaining unknown and insignificant.
Astronomical refraction, also known as atmospheric refraction, pertains to the bending of light rays emitted by celestial bodies as they pass through the Earth’s atmosphere. This refraction leads to a displacement of their apparent position in the sky.
The coordinate system that is used to observe stars and the motion of celestial bodies on the ground is known as the horizontal coordinate system. In this system, the main plane is the mathematical horizon and the poles are the zenith and nadir. It is commonly used with the naked eye, binoculars, or a telescope with an azimuth setting. The horizontal coordinates, such as azimuth and altitude, of celestial objects like the Sun, planets, and stars, change throughout the day due to the Earth’s rotation.
A celestial luminary refers to an astronomical entity that emits its own light or reflects light from other sources; it is also known as a “celestial body”. In the field of spherical astronomy, a celestial luminary can be seen as the projection of an astronomical object onto the celestial sphere. Celestial luminaries include the Sun, stars, the Moon, planets, their satellites, asteroids, comets, and other celestial bodies. In works of fiction, these names of celestial luminaries are often used to describe other planets, with “suns” being one such example.
The Earth ellipsoid is a shape resembling an ellipsoid of rotation, with its dimensions carefully chosen to closely match the shape of the quasigeoid for the Earth as a whole (known as the universal Earth ellipsoid) or specific regions of the Earth (known as reference ellipsoids).
The movements of the Sun and planets on the celestial sphere only show the visible movements, which are apparent to observers on Earth. These movements are not connected to the Earth’s daily rotation, as the rotation of the celestial sphere itself reproduces this rotation.
The longitude of the day is the time interval between sunrise and sunset when at least part of the solar disk is above the horizon.
Magnetic declination is the angle between the geographic and magnetic meridians at a specific point on the Earth’s surface. It represents the difference between the readings of a magnetic compass and the true northward direction at that point on the Earth’s surface during a particular historical period.
Solar days refer to the duration during which a celestial object completes one full rotation around its axis in relation to the center of the Sun. More precisely, it represents the time interval between two consecutive culminations (passages through the meridian) of the center of the Sun in a specific location on Earth (or any other celestial body).
A magnetic pole is a theoretical point located on the Earth’s surface, where the lines of force of the Earth’s magnetic field are oriented exactly at a 90-degree angle to the surface.
The celestial equator is a vast circle on the celestial sphere that is positioned perpendicular to the Earth’s axis and aligns with the plane of the Earth’s equator. It serves as a dividing line, separating the celestial sphere into two hemispheres: the northern hemisphere, centered around the north pole of the Earth, and the southern hemisphere, centered around the south pole of the Earth. The groupings of stars that the celestial equator intersects are known as equatorial constellations.
An orbital node is one of the two points on the celestial sphere where the orbit of a celestial body intersects with a reference plane. In the case of the planets in our solar system and the Moon, this reference plane is the ecliptic plane. The celestial equator and equatorial coordinate system are commonly used to track these orbital nodes. It is important to note that there are two distinct orbital nodes.
The movement of the equinoxes (known as praecessio aequinoctiorum in Latin) refers to the gradual change in the position of the vernal and autumnal equinoxes. These equinoxes are the points where the celestial equator intersects with the ecliptic, and they shift slightly each year in accordance with the apparent annual movement of the Sun. Simply put, the vernal equinox now occurs a little earlier each year, approximately 20 minutes and 24 seconds earlier than the previous year. In terms of angular units, this displacement is currently around 50.3″ per year, or 1 degree every 71.6 years. This represents the extent of the displacement.
The horizon, derived from the Greek word ὁρίζων, refers to the boundary where the sky meets the earth or water surface. It can also encompass the visible portion of this surface. The horizon can be divided into the visible horizon and the true horizon. The angle between the plane of the true horizon and the direction to the visible horizon is known as the horizon’s inclination, which can also be referred to as horizon depression.
Degree, minute, and second are commonly used units of measurement for plane angles. These measurements are also employed in cartography to determine the coordinates of any given point on the Earth’s surface, as well as to determine azimuth.
The Terminator (derived from the Latin word “terminare” meaning “to stop”) is a luminous boundary that separates the illuminated portion of a celestial body, such as a space body, from the unilluminated part. The terminator of a spherical body always appears as a semi-ellipse shape, resembling a straight line at the end of the first and the beginning of the last quarters.
Universal Time, also known as UT, is a time scale based on the rotation of the Earth. It serves as the modern replacement for Greenwich Mean Time (GMT), which is sometimes incorrectly used interchangeably with Coordinated Universal Time (UTC). Universal Time was introduced on January 1, 1925. It’s important to note that the term “world time” has multiple meanings, with UT1 and UTC being the primary versions (see below for more details).
The equation of time is the difference between the mean solar time (SSV) and the true solar time (TSV), which can be expressed as UT = SSV – TSV. This disparity remains consistent for all observers around the globe. One can acquire the equation of time from specialized astronomical publications, astronomical software, or by using the formula provided below.
Clockwise and counterclockwise refer to the observed rotation direction by comparing it with the movement of clock hands, which aligns with the shadow’s movement on a horizontal sundial (located in the northern hemisphere) and the sun’s trajectory across the sky (in the northern hemisphere). However, there are mechanical clocks with reversed hand movement. Such clocks, featuring Hebrew numerals, have been discovered within the Jewish community, for instance.
The motion of the planets observed from Earth against the background of the stars on the celestial sphere from east to west, in the opposite direction to the motion of the Sun (annual) and the Moon, is known as retrograde motion.
An eclipse is an astronomical event in which one celestial body blocks the light from another celestial body.
The pole of the ecliptic refers to a specific point on the celestial sphere where the perpendicular to the ecliptic plane intersects. This point serves as the pole for the ecliptic system of celestial coordinates.
In astronomy, a conjunction refers to the alignment of celestial bodies where their ecliptic longitudes are equal. Sometimes, conjunction can also be defined based on direct ascent rather than ecliptic longitude. This means that during a conjunction, two celestial bodies are relatively close to each other on the celestial sphere (although the moment of conjunction does not necessarily coincide with the moment of maximum approach). The term conjunction is also used in astrology.
The galactic coordinate system is a celestial coordinate system that has its origin at the Sun and its direction of origin from the center of the Milky Way galaxy. The plane of the galactic coordinate system aligns with the plane of the galactic disk. Similar to geographic coordinates, galactic coordinates consist of latitude and longitude.
The rise occurs when the top part of the luminary becomes visible above the horizon. The idea of sunrise can also encompass the entire process of the luminary’s visible disk crossing the horizon.
In astronomy, declination (δ) is one of the equatorial coordinate system’s two coordinates. It measures the angular distance on the celestial sphere from the plane of the celestial equator to the luminary and is typically expressed in degrees, minutes, and seconds of arc. Declination is positive when north of the celestial equator and negative when south of it.
Synchronous rotation, also known as tidal capture, occurs when a satellite’s rotational period matches its orbital period around a central body. As a result, the satellite always presents the same face towards the central body, as it completes one rotation on its axis in the same timeframe it takes to orbit around its partner. Tidal capture typically happens during mutual motion and is a common phenomenon among the large natural satellites of planets within the solar system.
Orbital parameters, also known as celestial body orbital elements, consist of a set of values that determine the size and shape of a celestial body’s orbit, as well as its position in space and the location of the celestial body within the orbit.
The northern magnetic pole is a specific point located in the polar region of the Earth’s surface. At this point, the Earth’s magnetic field is oriented directly downward, forming a 90-degree angle with the surface.
The Earth’s path around the Sun, also known as its orbit, has an average distance of approximately 149.6 million kilometers (152.1 million km at its farthest point, known as aphelion, and 147.09 million km at its closest point, known as perihelion).
An epoch in astronomy, derived from the Greek word έποχή meaning “stop,” refers to a specific moment in time when astronomical coordinates or orbital elements are determined. These coordinates can be recalculated from one epoch to another, taking into consideration precession and proper motion.
In navigation, observation, which comes from the Latin word observatio, involves a series of practical actions used to determine the position of a ship, vessel, aircraft, or vehicle. This is done by observing external landmarks or sources with known coordinates, such as coastal landmarks, radio navigation systems, and celestial luminaries.
Loxodromy, also known as loxodroma or loxodromic path, is a curved line on the rotating surface that intersects all meridians at a constant angle. The term “loxodromy” comes from the Greek words “loxos,” meaning “oblique” or “slanting,” and “dromos,” meaning “path.”
Earth is the third farthest planet from the Sun in the Solar System. It is the densest and fifth largest planet in terms of diameter and mass. Among the terrestrial group of planets, which includes Mercury, Venus, and Mars, Earth is the largest.
Mercury’s transit across the Sun’s disk is an astronomical event where Mercury moves directly between the Sun and the observer (whether it be Earth or a spacecraft). When viewed from Earth or its vicinity, Mercury appears as a small black dot moving across the surface of the Sun.
The equatorial coordinate system is a celestial coordinate system that uses the plane of the celestial equator as its main plane. One of the coordinates in this system is declination δ (sometimes referred to as polar distance p).
Another coordinate can be:
- hour angle t (in the first equatorial coordinate system)
- right ascension (in the second equatorial coordinate system)
The primary equatorial coordinate system
- Declinationδ is the angular distance from the celestial equator to a celestial body, or the angle between the plane of the celestial equator and the direction to the celestial body.
Declination is measured from 0° to 90° towards the North Pole and from 0° to -90° towards the South Pole.
- Polar distancep is the angular distance from the North Pole to a celestial body along the declination circle, or the angle between the Earth’s axis and the direction to the celestial body.
Polar distances are measured from 0° to 180° in the direction from the North Pole to the South Pole.
- Hour angles are measured in the direction of the celestial sphere’s daily rotation, which is towards the west of the upper point of the celestial equator. The range of measurement is from 0° to 360° (in degrees) or from 0 h to 24 h (in hours).
- Alternatively, hour angles can be measured from 0° to 180° (0 h to 12 h) towards the west and from 0° to -180° (0 h to -12 h) towards the east.
Another equatorial coordinate system
In this system, just like in the first equatorial system, the primary plane is the plane of the celestial equator, and one of the coordinates is the declination (δ) (less commonly referred to as polar distance p). However, the second coordinate is the right ascension (α), which is the arc of the celestial equator from the vernal equinox point to the luminary’s declination circle, or the angle between the direction to the vernal equinox point and the plane of the luminary’s declination circle. Therefore, the starting point is at the location where the Sun intersects the celestial equator during the spring (known as the vernal equinox point). This angle is measured eastward from the apparent position of the Sun’s center, which means it is measured in the opposite direction of the celestial sphere’s daily rotation, along the celestial equator. It can take values ranging from 0° to 360° (in degrees) or from 0h to 24h (in hours).
General characteristics
- Declination is measured in degrees, minutes, and seconds of arc. The positive direction represents the north of the celestial equator, while the negative direction represents the south. It is important to indicate the sign of declinations.
- An object located on the celestial equator has a declination of 0°
- The declination of the north pole of the celestial sphere is +90°
- The declination of the south pole is -90 °
- The declination of a celestial object that passes through the zenith is equal to the latitude of the observer.
In the case of the Northern Hemisphere on Earth, assuming a given latitude φ:
Due to precession, the plane of the celestial equator gradually changes its position, so an epoch is always provided for the equatorial coordinate system. This epoch determines the location of the major plane and, consequently, the direction to the point of the vernal equinox.
Sources
Wikimedia Foundation. 2010.
- Declination (δ) is one of the two coordinates in the equatorial coordinate system used in astronomy. It represents the angular distance on the celestial sphere from the plane of the celestial equator to a celestial body, and it is typically measured in degrees, minutes, and seconds of arc. Declination is considered positive when it is located north of the celestial equator and negative when it is located south of it.
* A celestial object located on the celestial equator has a declination of 0°
* The declination of the north pole of the celestial sphere is +90°.
The declination of the south pole is -90° The declination always carries a sign, even if it is positive.
The declination of a celestial object that passes through the zenith is equal to the latitude of the observer (considering northern latitudes with a + sign and southern latitudes with a – sign).
Related concepts
Right ascension (α, R. A. – derived from the English term right ascension) refers to the measurement of the arc on the celestial equator from the vernal equinox to the circle of declination of a celestial body. Right ascension serves as one of the coordinates in the second equatorial system (the first system uses hour angle as its coordinate). The second coordinate in this system is known as declination.
The celestial equator is a large circle on the celestial sphere, with its plane perpendicular to the axis of the Earth and coinciding with the Earth’s equatorial plane. It divides the celestial sphere into two hemispheres: the northern hemisphere, with its apex at the North Pole, and the southern hemisphere, with its apex at the South Pole. The constellations that the celestial equator passes through are referred to as equatorial constellations.
The celestial sphere serves as a useful tool in solving various astrometric problems, as it is an imaginary sphere on which celestial bodies are projected. It has an arbitrary radius and is centered around the observer’s eye, which can be located on the Earth’s surface or elsewhere in space. For a terrestrial observer, the celestial sphere’s rotation mirrors the daily motion of the stars in the sky.
In astronomy, an epoch refers to a specific moment in time that is used to define astronomical coordinates or orbital elements. These coordinates can be recalculated from one epoch to another, taking into account precession and proper motion.
The World’s Pole is a specific point on the celestial sphere where the visible daily movement of stars occurs because of the Earth’s rotation on its axis. The direction to the North Pole of the world aligns with the direction to the geographical north, while the direction to the South Pole of the world aligns with the direction to the geographical south. The North Pole of the world can be found in the constellation of the Little Bear, specifically with Polaris, also known as the North Star. On the other hand, the South Pole of the world is located in the constellation Octanthus. Due to the Earth’s axis precession, the poles of the world shift approximately 20 arc-seconds per year.
Citations in literature
Astrologers also utilize the equatorial coordinate system, which relies on the celestial equator. Within this system, the celestial body’s position is determined by two coordinates: right ascension (ά) and declination (δ).
Generally speaking, the motion of stars, while small, can be quite noticeable over long periods of time, especially for stars that are closest to us. An example of this is Alpha Centauri, which currently has an angular declination of approximately minus 60°. This means that it is not visible from latitudes in the middle of the Earth, as well as from subtropical northern latitudes. However, the ancient Egyptians were well acquainted with this star: in the 4th millennium BC, it was positioned in the sky just 30° south of the celestial equator. Celestial objects with a similar declination can be easily observed even in Crimea, not to mention in Egypt.
To utilize the illustration, one must possess knowledge of the magnitude of the angular separation (“declination”) between the Sun and the equator in various directions on different dates throughout the year. The relevant information is provided in the table located on page 23.
In order to make use of the diagram, it is imperative to be acquainted with the extent of the angular distance (“declination”) between the Sun and the equator in either direction on different dates throughout the year. The accompanying data can be found in the table on page 28.
Further Concepts (Continued)
The system of galactic coordinates is a celestial coordinate system that has its origin at the Sun and a reference direction from the center of the Milky Way galaxy. The galactic coordinate system’s plane aligns with the galactic disk’s plane. Similar to geographic coordinates, galactic coordinates consist of latitude and longitude.
Ecliptic (derived from the Latin term (linea) ecliptica, from the Greek word ἔκλειψις – eclipse) is a large circle on the celestial sphere that represents the visible annual movement of the Sun. Correspondingly, the ecliptic plane is the plane of the Earth’s orbit around the Sun. A more accurate definition of the ecliptic is the intersection of the orbital plane of the barycenter of the Earth-Moon system with the celestial sphere.
The system of celestial coordinates known as ecliptic coordinates:49 utilizes the plane of the ecliptic as its main plane and the pole of the ecliptic as its pole. This coordinate system is employed when studying the movement of celestial bodies within the solar system, many of which have orbital planes that closely align with the ecliptic plane. Additionally, it is utilized when observing the apparent yearly movement of the Sun across the sky:30.
The celestial coordinate system is utilized in the field of astronomy to denote the location of celestial bodies in the sky or specific points on an imaginary celestial sphere. These coordinates are determined by two angular measures that distinctly identify the position of objects on the celestial sphere. Therefore, the celestial coordinate system functions as a spherical coordinate system, where the third coordinate, distance, is often unknown and insignificant.
An astronomical unit (Russian: a.e.; international: au since 2012; previously designated as ua) is a historically recognized unit of measurement used in the realm of astronomy to measure distances. Originally defined as the major semi-axis of the Earth’s orbit, it is commonly regarded as the average distance from Earth to the Sun:126.
Fifty-eight navigational stars hold a special position in the realm of astronomical navigation. Out of the approximately 6000 stars visible to the naked eye in ideal conditions, these stars have been chosen for their brightness and encompass 38 constellations on the celestial sphere, ranging from a declination of -70° to +89°. Many of these navigational stars were given names by ancient civilizations such as the Babylonians, Greeks, Romans, and Arabs.
The sideric orbital period (derived from the Latin word “sidus” meaning star, with the genitive case “sideris”) refers to the time it takes for a celestial satellite to complete a full revolution around its main body in relation to the stars. This concept of the “sideric period of revolution” applies to various bodies orbiting the Earth, including the Moon (sideric month) and artificial satellites, as well as planets, comets, and so on, orbiting the Sun.
The angular dimension, sometimes referred to as the angle of view, is the measurement of the angle between two straight lines that connect diametrically opposite extreme points of an observed object and the eye of the observer.
Octanthus, also known as Octans in Latin, is a small and faint constellation located in the southern hemisphere of the sky. It includes the South Pole of the Earth.
The precession of the equinoxes, known in Latin as praecessio aequinoctiorum, is a term used to describe the gradual shift of the vernal and autumnal equinoxes. These points mark the intersection of the celestial equator with the ecliptic and they move slightly each year due to the visible annual motion of the Sun. In other words, the vernal equinox occurs earlier each year by approximately 20 minutes and 24 seconds. This shift can be measured in angular units, with an offset of about 50.3″ per year, or 1 degree every 71.6 years. This is the displacement that occurs.
A radiant, derived from the Latin word “radians,” refers to an area on the celestial sphere that appears to be the origin of meteors. These meteors are observed when the Earth crosses paths with a group of meteor bodies that travel in a general orbit around the Sun.
An occultation is an astronomical event where one celestial body passes in front of another from the perspective of an observer at a specific location. This passing obscures a portion of the celestial body behind it.
In astronomy, culmination refers to the moment when the center of a celestial body crosses the celestial meridian during its daily movement. It can also refer to the moment when the center of the celestial body passes through the point of intersection between its daily parallel and the celestial meridian.
The list includes the most brilliant stars that can be seen from Earth in the optical range based on their apparent stellar magnitude. In the case of multiple stars, their total stellar magnitude is provided.
Stellar magnitude, also known as luminosity, is a dimensionless numerical measure of the brightness of an object, represented by the letter m (derived from the Latin word magnitudo meaning “magnitude, size”). This concept is primarily used in reference to celestial bodies. The stellar magnitude reflects the amount of energy flux emitted by the celestial body in question (i.e., the energy of all photons emitted per second) per unit area. Therefore, the apparent stellar magnitude is influenced by both the intrinsic characteristics of the object itself (such as its luminosity) and its distance from Earth. A lower value of stellar magnitude indicates a higher brightness.
The zodiacal constellations (derived from the Greek word ζωδιακός, meaning “animal”) consist of 13 constellations that are situated along the ecliptic, which is the apparent annual path of the Sun among the stars. These constellations have been named after animals since ancient times.
Earth mass (represented in astronomy as M⊕, where ⊕ is the symbol for Earth) refers to the mass of the planet Earth and is utilized as an off-system unit of measurement in astronomy. 1 M⊕ is equivalent to (5.9722 ± 0.0006) × 1024 kg.
Pheonix (known as Phoenix in Latin and abbreviated as Phe) is a constellation located in the southern hemisphere of the celestial sphere. It covers an area of 469.3 square degrees in the sky and contains 68 stars that are visible to the naked eye.
Spectral-double is a binary star system in which the duality is revealed through spectral observations. Typically, these systems consist of two stars that are located in close proximity to each other and have velocities that are too large to be observed separately with current telescopes. Due to the orbital motion of the stars around their common center of mass, one star approaches the observer while the other moves away, resulting in unequal radial velocities along the observer’s line of sight.
Naugol (Latin. Norma) is a celestial formation located in the southern hemisphere of the celestial sphere, positioned to the southwest of Scorpius and to the north of the Southern Triangle. It also shares a border with Circulus. This region of the sky is traversed by both branches of the Milky Way, although it is relatively lacking in prominent stars. None of the stars in this constellation have a visual sidereal magnitude brighter than 4.0, and there are a total of 42 stars that can be seen with the naked eye. The area of the sky occupied by Naugol spans 165.3 square degrees. The optimal time for observing this constellation is during the months of May and June, and it can be partially observed in southern Russia, specifically south of 48 N.
The constellation known as the Goldfish, which is derived from the Latin name Dorado, can be found in the southern hemisphere of the sky. It covers an area of approximately 179.2 square degrees. This constellation boasts a total of 32 stars that can be seen with the naked eye.
This compilation of stars closest to Earth, listed in order of increasing distance, encompasses stars that are located within 5 parsecs (which is equivalent to approximately 16.308 light-years) of our planet. At present, there are 57 known stellar systems, including our own Sun, that may reside within this proximity. Within these systems, there are a combined total of 64 stars and 13 brown dwarfs.
An astronomical phenomenon known as passage or astronomical transit occurs when one celestial body passes in front of another celestial body, casting a shadow over a portion of it. This event can be observed from a specific vantage point and is of great interest to astronomers.
Opposition is when a celestial body in the solar system is in a position where the difference in ecliptic longitudes between it and the Sun is exactly 180 degrees. This means that the body is approximately aligned with the “Sun – Earth” line and can be seen from the Earth in the opposite direction to the Sun. Opposition can occur for the outer planets and other bodies that are further from the Sun than the Earth.
Ascendant, also known as Auriga in Latin, is a constellation located in the northern hemisphere of the sky. The brightest star in this constellation is Capella, which has a visual sidereal magnitude of 0.1. The best conditions for visibility of this constellation are in December and January. It can be seen from all over Russia.
The synodic period of revolution (from the Greek σύνοδος – conjunction) is the time between two consecutive conjunctions of the Moon or any planet in the Solar System with the Sun as observed from Earth. The conjunctions of the planets with the Sun must occur in a specific linear sequence, which is particularly important for the inner planets. For example, it will be consecutive superior conjunctions when the planet passes behind the Sun.
Microscope (Latin: Microscopium) is a small constellation located in the southern hemisphere of the sky. It is situated to the south of Capricorn, to the north of Indian, to the east of Sagittarius, and to the west of South Pisces and Crane.
Eagle (Latin: Aquila) is an equatorial constellation. Its western portion is situated in the eastern arm of the Milky Way, to the south of Arrow. The constellation has an area of 652.5 square degrees, and it contains 70 stars brighter than magnitude 6.
The International Celestial Reference System (ICRS), also known as the International Astronomical Coordinate System, has been the standard celestial coordinate system since 1998. It was officially adopted at the 23rd International Astronomical Union (IAU) congress in 1997. The origin of this system is the barycenter of the Solar System. The coordinates in the ICRS are designed to be as close as possible to the equatorial coordinates of the J2000.0 epoch, with any differences being only fractions of a second of arc.
Cassiopeia is a group of stars in the sky that can be seen from the Northern Hemisphere. Its brightest stars form a shape that looks like the letters “M” or “W”. The constellation covers a large area in the sky and contains around 90 stars that are visible to the naked eye. It is located within the Milky Way and has several star clusters.
When a variable star is not already designated by a letter of the Greek alphabet, it is given a special designation in the Bayer format, combined with the name of the constellation where it is found. (For a list of constellations and their Latin names in the genitive case, see List of constellations and their Latin name (genitive case)).
The major semi-axis is a fundamental geometric parameter of objects formed using a conic section.
Aries is a well-known constellation in the zodiac, even though it does not have any stars brighter than the second magnitude. The three primary stars, Hamal (“head of the ram”), Sheratan (“mark” or “sign”), and Mezartim (α, β, and γ of Aries, respectively), are easily located: they are located south of the Triangle. The star Mesartim, with a magnitude of four, was one of the first double stars to be discovered using a telescope (by Robert Hooke in 1664).
Stellar days refer to the duration of a celestial body’s rotation around its own axis in an inertial frame of reference, typically the frame of reference associated with distant stars. In the case of Earth, it represents the time taken for one complete revolution around its axis in relation to distant stars.
Absolute stellar magnitude is a measurable property that describes the brightness of an astronomical object. Various definitions of absolute magnitude exist for different types of celestial bodies.
Pictor is a small constellation located in the southern part of the sky. It covers an area of 247.7 square degrees and consists of 49 stars that can be seen without the aid of a telescope. In the southern region of Russia, specifically south of latitude +47°, a portion of the constellation can be observed, although it does not have any particularly bright stars. The first relatively bright star in Pictor is β Zhivopisets, with a magnitude of 3.85. This star rises to the south of latitude +38°56′ and can be seen in cities like Dushanbe, Astara, Ashgabat, and Kushka, which were part of the former USSR. It is worth noting that there is another star within the constellation known as the Painter.
Reticulum, also known as Ret, is a constellation located in the southern hemisphere of the sky. It covers an area of 113.9 square degrees and contains 22 stars that can be seen with the naked eye.
Pyxis (also known as Compass) is a constellation located in the southern hemisphere of the night sky. It covers approximately 220.8 square degrees and consists of 43 stars that can be seen without the use of a telescope. In Russia, Pyxis can be observed in its entirety in the southern regions, as well as in the southern parts of the central regions. The optimal time to observe this constellation is during the months of February and March.
The constellation Monoceros, also known as the Unicorn, is located in the equatorial region of the sky. Covering 481.6 square degrees, it is home to 146 stars that can be seen without the aid of a telescope. Although Monoceros lies within the Milky Way, it does not boast any particularly bright stars. However, its position inside the winter triangle, which is formed by the prominent stars Sirius, Procyon, and Betelgeuse, makes it easy to locate. Monoceros is one of the 15 constellations that the celestial equator passes through, and it is visible in the central and southern regions of the sky.
Tucana, also known as the Tucan, is a constellation found in the southern hemisphere of the sky. It covers an area of 294.6 square degrees and contains 44 stars that can be seen with the naked eye.
The tilt of the axis of rotation refers to the angle at which the axis of rotation of a celestial body deviates from being perpendicular to the plane of its orbit. In simpler terms, it is the angle between the equator plane of a celestial body and its orbit.
Continued References in Literature
In order to conveniently describe the boundaries of constellations, it was decided to depict them as broken lines that follow the grid of constant celestial coordinates – declination and right ascension. As a result, constellations started to resemble certain African countries and American states, whose borders are defined by parallels and meridians. This was considered a rational approach to easily define boundaries in a mathematical manner. However, over time, a minor flaw started to emerge in this elegant concept.
The gender of a noun in the 3rd declension can be determined by the specific infinitives of the nominative singular, which are associated with a particular gender within that declension. Therefore, in order to identify the gender of any noun in the 3rd declension, three factors must be considered:
Nouns in the 3rd declension were quite rare, such as os, corpus, caput, foramen, and dens. This systematic approach was completely justified. The 3rd declension is the most challenging to learn and has several distinct features that set it apart from the other declensions.
From an evolutionary perspective, man-made clocks measure incredibly small fractions of time – hours, minutes, and seconds. These clocks rely on fast dynamic processes such as the swinging of a pendulum, the unwinding of a spring, the oscillations of crystals, the burning of a candle, the flow of water from a vessel, the spilling of sand, and the rotation of the Earth (determined by the movement of the sun’s shadow). These processes occur at a consistent and known rate. For example, a pendulum swings at a known frequency determined by its length, rather than its amplitude or the mass of the weight at its end. Floor clocks utilize a pendulum connected to an anchor, which transmits motion to a gear wheel. This gear wheel, through a system of gears, drives the movement of the second, minute, and hour hands. Spring clocks operate in a similar manner. Quartz clocks, on the other hand, rely on the oscillation of specific crystals under the influence of energy supplied by a battery, essentially functioning like a pendulum. Water and fire clocks, although less accurate, were widely used before the invention of clocks based on constant motion. These clocks do not measure segments of time like pendulum or digital clocks, but rather measure volume. A sundial is an imprecise method of measuring time. However, the rotation of the Earth allows for a more accurate, albeit slow, clock known as a calendar. This is because at this scale, clocks shift from being measuring clocks (like sundials, which measure the changing declination of the sun) to counting clocks (counting the number of day/night cycles).
The authors of the collective work “Grundzüge einer deutschen Grammatik” also recognize a group of words called article words, but this does not mean that they reject the pronoun as a part of speech. They point out that article words (pronouns) have the characteristic of influencing the inflection of the following adjective: the adjective that comes after them undergoes a weak declension. Examples of these types of words include diese, alle, jede, welche, and others. These words behave in the same manner as the definite article. As we can see, the criteria for distinguishing article words vary: in Fater G., Grimm G.. – it is the impossibility of transposing the article without the noun, the impossibility of using another word before the article, and in the authors of “Grundzüge einer deutschen Grammatik” – it is the influence of the article on the adjective that follows it.
Astronomy utilizes celestial coordinate systems to describe the location of celestial bodies in the sky or specific points on an imaginary celestial sphere. These systems consist of two angular quantities that uniquely determine the position of objects on the celestial sphere. Celestial coordinate systems are essentially spherical coordinate systems, where the distance, or third coordinate, is often unknown and irrelevant. The choice of the principal plane and origin differentiate these systems from one another.
Depending on the specific task, it may be more convenient to use one coordinate system over another. The most commonly used systems include the horizontal and equatorial coordinate systems. Less frequently used systems include the ecliptic, galactic, and others.
Coordinate System for Horizontal Positions
In this particular system, the primary plane is the mathematical horizon plane. One of the coordinates is the luminous body’s altitude, denoted as h, or its zenith distance, denoted as z. The other coordinate is the azimuth, denoted as A.
The height h of the luminous body represents the arc of the vertical circle from the mathematical horizon to the body, or the angle between the plane of the mathematical horizon and the direction towards the body. Altitudes are measured from 0° to +90° towards the zenith and from 0° to -90° towards the nadir.
The zenith distance z of a luminous body is the arc of the vertical circle from the zenith to the body, or the angle between the plumb line and the direction towards the body. Zenith distances are measured from 0° to 180° from zenith to nadir.
Azimuth A refers to the measurement of the angle between the south point and the vertical circle of a celestial body, or the angle between the noon line and the intersection of the mathematical horizon and the vertical circle. In celestial navigation, azimuths are measured in the direction of the daily rotation of the celestial sphere, typically ranging from 0° to 360°. However, there are cases where azimuths are measured from 0° to +180° to the west and from 0° to -180° to the east. (In geodesy, azimuths are measured from a point north.)
The primary equatorial coordinate system
In this system, the main plane is the plane of the celestial equator. One of the coordinates in this system is declination δ (occasionally referred to as polar distance p). Another coordinate is hour angle t.
Declination δ of a celestial body is the measurement of the arc from the celestial equator to the celestial body, or the angle between the plane of the celestial equator and the direction towards the celestial body. The declination is measured from 0° to +90° towards the north pole of the world and from 0° to -90° towards the south pole of the world.
The angular displacement t of the celestial body is the angle between the upper point of the celestial equator and the luminary’s declination circle. It can also be defined as the angle between the planes of the celestial meridian and the luminary’s declination circle. Hour angles are measured in the direction of the daily rotation of the celestial sphere, which is westward from the upper point of the celestial equator. They range from 0° to 360° (in degrees) or from 0 h to 24 h (in hours). Sometimes hour angles are measured from 0° to +180° (0 h to +12 h) in the west and from 0° to -180° (0 h to -12 h) in the east.
The alternative equatorial coordinate system
In this particular system, just like in the initial equatorial system, the primary plane is known as the celestial equator’s plane, with one of the coordinates being the declination β (less frequently referred to as the polar distance p). The other coordinate is the right ascension α.
The right ascension (RA, α) of a celestial object is the segment of the celestial equator starting at the vernal equinox and ending at the object’s declination circle, or the angle between the direction towards the vernal equinox and the plane of the object’s declination circle. Right ascensions are measured in the opposite direction of the daily rotation of the celestial sphere, ranging from 0° to 360° (in degrees) or from 0 h to 24 h (in hours).
RA corresponds to the astronomical equivalent of longitude on Earth. Both RA and longitude measure the east-west angle along the equator, with both starting from a zero point on the equator. In the case of longitude, the zero point is the prime meridian, while for RA, it is the location in the sky where the Sun crosses the celestial equator at the vernal equinox.
Declination (δ) in astronomy is one of the two coordinates in the equatorial coordinate system. It represents the angular distance on the celestial sphere from the plane of the celestial equator to the celestial body and is typically expressed in degrees, minutes, and seconds of arc. Declination is positive north of the celestial equator and negative south.
- An object on the celestial equator has a declination of 0°
- The declination of the north pole of the celestial sphere is +90°
- The south pole of the celestial sphere has a declination of -90°.
Declination always has a sign, even if it is positive.
The declination of a celestial object passing directly overhead (zenith) is equal to the observer’s latitude. In the northern hemisphere, a positive sign is used for northern latitudes and a negative sign for southern latitudes. For a given latitude φ in the northern hemisphere, celestial objects with a declination δ > 90° – φ do not set below the horizon, so they are referred to as non-sunset objects. If the declination of an object is δ < -90° + φ, then the object is called non-descending and is not observable at latitude φ. [1]
Ecliptic coordinate system
The ecliptic coordinate system revolves around the ecliptic plane. This system utilizes two coordinates: the ecliptic latitude β and the ecliptic longitude λ.
Ecliptic latitude β represents the angle between the ecliptic plane and the direction to the luminary. It can also be described as the arc of the circle of latitude from the ecliptic to the luminary. Ecliptic latitudes range from 0° to +90° towards the north pole of the ecliptic, and from 0° to -90° towards the south pole of the ecliptic.
Galactic coordinate system
In this system, the primary plane is the plane of our Galaxy. The coordinates in this system are known as galactic latitude (b) and galactic longitude (l).
Galactic latitude (b) of a celestial body refers to the arc of the galactic latitude circle from the ecliptic to the celestial body, or the angle between the plane of the galactic equator and the direction towards the celestial body.
Galactic latitudes range from 0° to +90° for the north galactic pole, and from 0° to -90° for the south galactic pole.
Galactic longitude l refers to the measurement of the angular distance along the galactic equator, starting from a reference point C and ending at the circle of galactic latitude of a celestial object. It can also be defined as the angle formed between the line connecting the reference point C and the plane of the circle of galactic latitude of the celestial object. When observing from the north galactic pole, galactic longitudes are counted in a counterclockwise direction, ranging from 0° to 360°, east of the reference point C.
The location C is near the direction of the center of the galaxy, but not exactly on it, as the latter is slightly below the galactic equator due to the solar system being slightly above the plane of the galactic disk. The chosen origin point C is positioned so that the intersection point of the galactic and celestial equators with a right ascension of 280° has a galactic longitude of 32.93192° (at epoch 2000).
The coordinates of the origin point C at epoch 2000 in the equatorial coordinate system are:
Changes in celestial coordinates during the rotation of the celestial sphere
The height h, zenith distance z, azimuth A, and hour angle t of celestial objects are constantly in flux as the celestial sphere rotates. This is because these coordinates are measured from points that are not affected by this rotation. On the other hand, the declination δ, polar distance p, and right ascension α of celestial objects remain unchanged during the rotation of the celestial sphere, although they may be subject to changes caused by the motions of the celestial objects that are not related to the daily rotation.
Origin and application
Ancient civilizations have long relied on celestial coordinates for various purposes. The concept of celestial coordinates can be traced back to the works of Euclid, an ancient Greek geometer, around 300 B.C. Euclid’s writings provide insights into different coordinate systems used during that time.
One notable example is the star catalog created by Hipparchus, which was later included in Ptolemy’s Almagest. This catalog documented the positions of 1022 stars using the ecliptic system of celestial coordinates.
The study of changes in celestial coordinates has led to significant discoveries in astronomy, which have greatly contributed to our understanding of the Universe. These discoveries include phenomena such as precession, nutation, aberration, parallax, and the proper motions of stars. Celestial coordinates play a crucial role in measuring time and determining the geographical coordinates of different locations on Earth’s surface. They are extensively used in creating star catalogs, studying the motion of celestial bodies in celestial mechanics and astrodynamics, and analyzing the distribution of stars in stellar astronomy problems.
The system of horizontal coordinates is employed to ascertain the direction towards the celestial body using angular instruments and when observing through a telescope mounted on an azimuthal rig.
The primary equatorial coordinate system is utilized for precise time determination and for observations made with a telescope mounted on an equatorial mount.
The secondary equatorial coordinate system is a widely-used coordinate system in astrometry. This system is employed to create star maps and to describe the positions of celestial bodies in catalogs.
The ecliptic coordinate system is employed in theoretical astronomy to determine the orbits of celestial bodies.
