Chord (astronomy)

Last updated
Transit of mercury chord across the sun Transit of Mercury, 2006-11-08 2.jpg
Transit of mercury chord across the sun

In the field of astronomy the term chord typically refers to a line crossing an object which is formed during an occultation event. By taking accurate measurements of the start and end times of the event, in conjunction with the known location of the observer and the object's orbit, the length of the chord can be determined giving an indication of the size of the occulting object. By combining observations made from several different locations, multiple chords crossing the occulting object can be determined giving a more accurate shape and size model. This technique of using multiple observers during the same event has been used to derive more sophisticated shape models for asteroids, whose shape can be highly irregular. A notable example of this occurred in 2002 when the asteroid 345 Tercidina underwent a stellar occultation of a very bright star as seen from Europe. During this event a team of at least 105 observers recorded 75 chords across the asteroid's surface allowing for a very accurate size and shape determination. [1]

Contents

In addition to using a known orbit to determine an objects size, the reverse process can also be used. In this usage the occulting object's size is taken to be known and the occultation time can be used to determine the length of the chord the background object traced across the foreground object. Knowing this chord and the foreground object's size, a more precise orbit for the object can be determined.

This usage of the term "chord" is similar to the geometric concept (see: Chord (geometry)). The difference being that in the geometric sense a chord refers to a line segment whose ends lie on a circle, whereas in the astronomical sense the occulting shape is not necessarily circular.

Observation process

Because an occultation event for an individual object is quite rare, the process of observing occultation events begins with the creation of a list of candidate targets. The list is generated from a computer by analyzing the orbital motions of a large collection of objects with known orbital parameters. Once a candidate event has been chosen whose ground track passes over the site of an observer, the preparations for the observation begin. A few minutes before the event is expected to happen the observing telescope is targeted to the target star and the star's lightcurve is recorded. The recording of the lightcurve continues during and for a short time after the predicted event. This extra recording time is due in part to uncertainties in the occulting objects orbit but also due to the possibility of detecting other objects orbiting the primary object (for example in the case of a binary asteroid, also the ring system around the planet Uranus was detected this way [2] ).

The exact method of lightcurve determination is dependent on the specific equipment available to the observer and the goals of the observation, however in all occultation events accurate timing is an essential component of the observation process. The exact time that the foreground object eclipses the other can be used to work out a very precise position along the occulting object's orbit. Also, since the duration of the drop in the measured lightcurve gives the object's size and since occultation events typically only last somewhere on the order of a few seconds, very fast integration times are required to allow for high temporal resolution along the lightcurve. A second method of achieving very high temporal accuracy is to actually use a long exposure and allow the target star to drift across the CCD during the exposure. This method, known as the trailed image method, produces a streak along the photograph whose thickness corresponds to the brightness of the target star with the distance along the streak direction indicates time; this allows for very high temporal accuracy even when the target star may be too dim for the method described above using high frequency short exposures. [3] With high enough temporal resolution even the angular size of the background star can be determined. [3]

Once the lightcurve has been recorded the chord across the occulting object can be determined via calculation. By using the start and end times of the occultation event the position in space of both the observer and the occulting object can be worked out (a process complicated by the fact that both the object and the observer are moving). Knowing these two locations, combined with the direction to the background object, the two endpoints of the chord can be determined using simple geometry.

Related Research Articles

2 Pallas Large asteroid of the main asteroid belt

Pallas is the second asteroid to have been discovered, after 1 Ceres. It is the third-largest asteroid in the Solar System by both volume and mass, and is a likely remnant protoplanet. With an estimated 7% of the mass of the asteroid belt, it is three quarters the mass of 4 Vesta and slightly under a quarter the mass of Ceres. It is about 510 kilometers (320 mi) in diameter, only slightly smaller than Vesta.

2060 Chiron Centaur comet with 50 year orbit

2060 Chiron is a small Solar System body in the outer Solar System, orbiting the Sun between Saturn and Uranus. Discovered in 1977 by Charles Kowal, it was the first-identified member of a new class of objects now known as centaurs—bodies orbiting between the asteroid belt and the Kuiper belt.

Light curve graph of light intensity of a celestial object or region, as a function of time

In astronomy, a light curve is a graph of light intensity of a celestial object or region, as a function of time. The light is usually in a particular frequency interval or band. Light curves can be periodic, as in the case of eclipsing binaries, Cepheid variables, other periodic variables, and transiting extrasolar planets, or aperiodic, like the light curve of a nova, a cataclysmic variable star, a supernova or a microlensing event or binary as observed during occultation events. The study of the light curve, together with other observations, can yield considerable information about the physical process that produces it or constrain the physical theories about it.

Occultation occlusion of an object by another object that passes between it and the observer

An occultation is an event that occurs when one object is hidden by another object that passes between it and the observer. The term is often used in astronomy, but can also refer to any situation in which an object in the foreground blocks from view (occults) an object in the background. In this general sense, occultation applies to the visual scene observed from low-flying aircraft when foreground objects obscure distant objects dynamically, as the scene changes over time.

Observational astronomy field of astronomy concerned with recording data about the observable universe

Observational astronomy is a division of astronomy that is concerned with recording data about the observable universe, in contrast with theoretical astronomy, which is mainly concerned with calculating the measurable implications of physical models. It is the practice and study of observing celestial objects with the use of telescopes and other astronomical instruments.

90 Antiope main-belt double asteroid

Antiope is a double asteroid in the outer asteroid belt. It was discovered on October 1, 1866, by Robert Luther. In 2000, it was found to consist of two almost-equally-sized bodies orbiting each other. At average diameters of about 88 km and 84 km, both components are among the 500 largest asteroids. Antiope is a member of the Themis family of asteroids that share similar orbital elements.

9 Metis Main-belt asteroid

Metis is one of the larger main-belt asteroids. It is composed of silicates and metallic nickel-iron, and may be the core remnant of a large asteroid that was destroyed by an ancient collision. Metis is estimated to contain just under half a percent of the total mass of the asteroid belt.

13 Egeria main-belt asteroid

Egeria is a large main-belt G-type asteroid. It was discovered by Annibale de Gasparis on November 2, 1850. Egeria was named by Urbain Le Verrier, whose computations led to the discovery of Neptune, after the mythological nymph Egeria of Aricia, Italy, the wife of Numa Pompilius, second king of Rome.

39 Laetitia main-belt asteroid

Laetitia is a large main-belt asteroid that was discovered by French astronomer Jean Chacornac on 9 February 1856 and named after "Laetitia", one of the epithets of Ceres, Roman goddess of fertility and abundance. Photometric observations of this asteroid gathered between 1968–74 were used to build a light curve that provided shape and rotation information. It has the general shape of an elongated triaxial ellipsoid with ratios between the lengths of the axes equal to 15:9:5. Major surface features are on a scale of 10 km and the surface color does not vary significantly across the surface. In the ecliptic coordinate system, the pole of rotation is estimated to be oriented to the coordinates =.

41 Daphne main-belt asteroid

Daphne is a large asteroid from the asteroid belt. It is a dark-surfaced body 174 km in diameter is probably composed of primitive carbonaceous chondrites. The spectra of the asteroid displays evidence of aqueous alteration. It was discovered by H. Goldschmidt on May 22, 1856, and named after Daphne, the nymph in Greek mythology who was turned into a laurel tree. Incorrect orbital calculations initially resulted in 56 Melete being mistaken for a second sighting of Daphne. Daphne was not sighted again until August 31, 1862.

44 Nysa main-belt asteroid

Nysa is a large and very bright main-belt asteroid, and the brightest member of the Nysian asteroid family. It is classified as a rare class E asteroid and is probably the largest of this type.

Beatrix is a fairly large asteroid orbiting in the inner part of the main asteroid belt. It was discovered by Annibale de Gasparis on April 26, 1865. It was his last asteroid discovery. A diameter of at least 68 kilometres (42 mi) was determined from the Beatrician stellar occultation observed on June 15, 1983. It is named for Beatrice Portinari, beloved of Dante Alighieri and immortalized by him in La Vita Nuova and The Divine Comedy.

130 Elektra main-belt asteroid

Elektra is a large outer main-belt asteroid. It was discovered on 17 February 1873, by astronomer Christian Peters at Litchfield Observatory, New York, and named after Electra, an avenger in Greek mythology.

423 Diotima main-belt asteroid

Diotima is one of the larger main-belt asteroids. It is classified as a C-type asteroid and is probably composed of primitive carbonaceous material.

Gyptis, minor planet designation: 444 Gyptis, is a main-belt asteroid that was discovered by J. Coggia on March 31, 1899, in Marseilles. It is classified as a C-type asteroid and is probably composed of carbonaceous material. The spectra of the asteroid displays evidence of aqueous alteration.

617 Patroclus Jupiter trojan

617 Patroclus is a binary Jupiter trojan approximately 140 kilometers in diameter. It was discovered on 17 October 1906, by astronomer August Kopff at the Heidelberg Observatory in Germany. The asteroid was named after Patroclus from Greek mythology. It was the second trojan to be discovered and the only member of the Trojan camp named after a Greek character. The dark D-type asteroid is also slow rotator and one of the largest Jupiter trojans. Patroclus is one of five Jovian asteroids targeted by the Lucy space probe to be visited in 2033. In 2001, a moon – later named Menoetius, and slightly smaller than its primary – was discovered. It was the first discovery of a binary asteroid among the Jupiter trojans.

705 Erminia main-belt asteroid

705 Erminia is a minor planet orbiting the Sun. Its name derives from the comic opera Erminie. An occultation on December 8, 2014 gave 3 chords, with one measurement suggesting a small moon 6-10 kilometers wide at a distance of 400 kilometers to the primary.

976 Benjamina is a dark background asteroid from the outer regions of the asteroid belt, approximately 81 kilometers in diameter. It was discovered on 27 March 1922, by Russian-French astronomer Benjamin Jekhowsky at the Algiers Observatory in North Africa. The large X/D-type asteroid has a rotation period of 9.7 hours and is likely regular in shape. It was named after the discoverer's son.

Orbit determination

Orbit determination is the estimation of orbits of objects such as moons, planets, and spacecraft. One major application is to allow tracking newly observed asteroids and verify that they have not been previously discovered. The basic methods were discovered in the 17th century and have been continuously refined.

1437 Diomedes Trojan asteroid

1437 Diomedes is a large Jupiter trojan from the Greek camp, approximately 150 kilometers in diameter. It was discovered on 3 August 1937, by astronomer Karl Reinmuth at the Heidelberg-Königstuhl State Observatory in southwest Germany. The dark D/P-type asteroid belongs to the largest Jupiter trojans and has a notably elongated shape and a longer than average rotation period of 24.49 hours. Diomedes was the first Jupiter trojan successfully observed during an occultation event of star. It was named after the hero Diomedes from Greek mythology.

References

  1. ↑ "2002 European Asteroidal Occultation Results". euraster.net (a website for Asteroidal Occultation Observers in Europe). 2002-09-17. Retrieved 2008-12-03. (Chords)
  2. ↑ Elliot, J. L.; Dunham, E.; Mink, D. (1977). "The rings of Uranus". Nature. Cornell University. 267 (5609): 328–330. Bibcode:1977Natur.267..328E. doi:10.1038/267328a0.
  3. 1 2 Kravtsov, F. I.; Lukyanik, I. V. (2008). "Observations of Asteroid Occultations by the Trailed-Image Method". Kinematics and Physics of Celestial Bodies. 24 (6): 317–322. Bibcode:2008KPCB...24..317K. doi:10.3103/S0884591308060081.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.