comets

• see also:
  • astrophotography
  • astrophotographic landscapes of the Milky Way
  • my photos of comet McNaught C/2006 P1
  • my photos of comet Lemmon (C2012/F6)
  • my photos of comet Leonard
  • my photos of Comet C/2023 A3 (Tsuchinshan-ATLAS) Oct 2024
  • COBS comet observations website
  • https://theskylive.com/comets
  • meteors
  • Solar System
  • NASA's asteroid and comet earth impact site
  • SkyHound

My photo of Comet G3 Atlas taken on 24th Jan 2025, Sonya7RIV with Sony 135mm f/1.8 lens tripod images stacked and cropped.

My photo of Comet 12P/Pons-Brook taken on 7th May 2024, Sonya7RIV with Sony 135mm f/1.8 lens 20x13sec images stacked and cropped.

My photo of comet McNaught taken 23rd Jan 2007, Olympus E330, 60sec, ISO400, Zuiko 50mm f/1.4 lens at F/2 in rural region see HERE for more of my photos and info on comet McNaught P1

• comets are small bodies (usually 1 billionth mass of earth) that orbit around the sun, the far majority are too faint to see with the naked eye, but every 5-10yrs or so a naked eye comet arrives.
• approx. 10-20 comets are discovered each year, previously most by amateurs but now most are by near earth object surveillance programs such as NEAT

• The new designation system gives the year of discovery followed by a letter, indicating the half-month in which it was discovered, and a number, indicating number of the discovery within the half-month. So C/1998 A2 would indicate the second comet discovered in the first half of January 1998. In the case of Comet Halley, the 1P indicates that it is the first numbered periodic comet. (There are well over 100 numbered periodic comets at the present time.) 
• The old-style system gave the year of perihelion passage and the Roman numeral specified the order of perihelion passage during that year. Hence, 1970 II was the second comet to pass perihelion in 1970.

• the solid, centrally located part of the comet is known as the “nucleus”. The nucleus is a repository of dust and frozen gases. When heated by the sun, the gases sublimate and produce an atmosphere surrounding the nucleus known as the coma which is later swept into the elongated tail.
• he sizes of cometary nuclei are mostly unknown because the measurement is a difficult one. We have reliable measurements of the sizes of about 10 nuclei. Most of them have diameters from a few km to 10 or 20 km. The nucleus of comet Schwassmann-Wachmann 1 is probably one of the largest (perhaps 20 km), as is the nucleus of comet Hale-Bopp (perhaps 40 km). Except in the special cases of comets Halley and Borrelly, whose potato-shaped nuclei were resolved by the cameras of passing spacecraft, the sizes are inferred.
• The composition of the nucleus is determined by measuring the composition of the coma. We know nothing directly about the internal structure. The dominant volatile is water, followed by CO, CO2 and a host of minor species present at the <1% level. There is some evidence for abundance variations among comets. The CO/H2O ratio reached 0.2 to 0.3 in Hale-Bopp but is typically 4 or 5 times smaller. The ratio of volatile mass to refractory mass is probably near 1.
• comet heads are often green and this appears to be due to gaseous dicarbon or C2 which is formed when the comet gets closer to the sun but then broken down by sunlight hence not present in the tail

• most have no tails, but some, as they approach the sun, develop a tail - actually a gas tail and a dust tail - both of which are always directed away from the sun due to the “solar wind”
• as earth passes through the persistently orbiting remnants of the dust tail, it results in periodic meteor showers as the dust impacts earth's atmosphere
  • in the case of the Leonids meteor showers, the parent comet is named Tempel-Tuttle and it makes an appearance in our skies every 33 years
• the largest on record is the Great Comet of 1843 which had a tail more than 2 A.U. in length
• tail of Halley's comet in 1910 grew at rate of 500,000miles/day until it reached 90 million miles long.

• hyperbolic or parabolic:
  • these are inter-stellar visitors rather than a permanent member of our solar system and only visit us once
  • if inter-stellar objects are traveling fast enough they will not be trapped by the sun’s gravitational pull but just have their path bent by the sun
    • eg. comet 3I/ATLAS in 2025 will hit 25,000kph at perihelion at some 2AU from the sun
      • a scientific assessment of whether such an object could be natural vs alien technology - see https://lweb.cfa.harvard.edu/~loeb/HCL25.pdf
• near-parabolic:
  • they only visit us once every several thousand years although some may have their orbits altered by passing near Jupiter to change it into a short period comet with an elliptical orbit - at least 50 comets are known to have been affected in this way
• elliptical orbit:
  • these are the short-period and many of the long-period comets
  • those with periods of 5-12 years approach the orbit of Jupiter
  • those with periods of 80-100 years get as far out as Neptune eg. Halley's comet

• The heliocentric distance ® is much more important than the geocentric distance (delta) in terms of how bright a comet gets.
• The brightness formula of a comet is: 
  • m1 = m0 + 5log(delta) + 2.5nlogr
  • m1 =apparent visual magnitude of comet (including coma)
  • m0 =absolute magnitude of comet ie how bright the comet will appear if placed 1AU from sun and 1AU from earth.
  • delta=comets distance to the Earth in AU
  • r =comets distance to the sun in AU
  • n =rate of brightening. The higher the value of n, the more rapid the brightening. The average comet has n=4. First time comets tend to have n=3-4 whilst periodic comets tend to have n>4.

• the lifetimes of active comets are limited for at least two reasons:
  • first, the nuclei are losing mass at rates that cannot be sustained for very long. For example, a 5 km radius spherical nucleus would have a mass about 4×10¹⁵ kg. When near the sun, this nucleus might sublimate at 10^4 kg/s (10 tonnes per second), so the sublimation lifetime is 4×10¹¹ s = 1000 years. True, the comet might spend only part of each orbit near the sun, and so might be able to keep going for more than 1000 years, but it is simply unable to sustain mass-loss for the 4.5×10⁹ year age of the solar system.
  • second, the active comets are under the gravitational control of the planets. There is a finite chance that a comet will be either ejected from the solar system, injected to the sun, or absorbed by an impact with one of the planets (as happened in the famous case of Shoemaker-Levy 9 hitting Jupiter). The “dynamical” lifetime of a typical comet is about 0.5 million years.
  • given that the comets we see now cannot have been present in the inner solar system for more than a million years or so, we have two choices. Perhaps the comets are young, meaning that they are created somewhere and then dumped in the inner solar system where they become active and are discovered. The trouble with this is that we do not see any place in the solar system where comets could be formed at the present time. So, it seems more reasonable that the comets were formed with the rest of the solar system and have been stored since formation in a cold place where the nuclear ices would be stable. The two deep-freeze locations now under discussion are Oort Cloud and the Kuiper Belt.

• early astronomers generally regarded comets as atmospheric phemonena, a kind of exhalation of the earth and many regarded them as signs or omens of fortune - good or bad.
• the notion that they lay beyond the moon was not developed until Tycho Brahe studied the comet of 1577 which he believed must move in a circular path outside the orbit of Venus. His student Kepler, believed they moved in straight lines.
• the problem was resolved by Edmund Halley (see Halley's comet).  

• if you are really serious, see:
  • Richard Bennion's technique

• comet visibility function = (comet's extra-atmospheric luminance) exp(-extinction coeff x extinction function) / (twilight sky luminance + night sky luminance)¹⁾
• the main factors of whether a comet will be visible on a clear night are:
  • the brightness of the comet as viewed beyond earth's atmosphere
  • the optical extinction due to earth's atmosphere
    • dependent upon:
      • the comet's elevation above the horizon (the higher the better) - see sky transparency and atmospheric extinction
      • sky transparency - see sky transparency and atmospheric extinction
  • the limiting night sky brightness (if the sky is brighter than the comet, you will not see it):
    • light pollution
    • airglow
    • starlight
    • zodiacal light
    • moon light
    • (see also light pollution
  • if near twilight, the contours of background sky brightness during twilight
    • this depends upon:
      • depth of sun below the horizon
      • azimuth angle between sun and the comet
      • elevation of comet above horizon
      • see sky brightness and effects of twilight

• astronomic twilight is usually defined as ending or starting when the sun is 18deg below the horizon (ie. 60-90min before sunrise or after sunset depending upon latitude and month of the year) in which case by that time the sky is considered dark enough for all stars to become visible at a dark sky site
• assuming you would want a comet to be a further 5 deg at least above the horizon to reduce atmospheric haze, this means long exposure or high ISO images of comets require the comet to be at least 23-30deg from the sun vertically
• when the comet is closer than this, twilight will interfere and reduce contrast between the sky and the comet as well as lighten the sky enough that only short exposures at relatively low ISOs are only possible - this means the comet would need to be at least magnitude 1 in brightness to be visible in such twilight and the tail may be lost in the sky
• at 60min before sunrise a star near the sun would need to be brighter than mag 4.5 at 4deg above the horizon to be visible in standard photos, hence comets less bright would not be visible closer to the horizon and their tails which are usually less bright again would be washed out by twilight even higher above the horizon
• eg. a comet mag 4.7 at ~14deg vertical elevation from the sun and 25deg elongation from the sun will be about 3deg above horizon 1hr before sunrise and thus will not be visible due to the sky glow as it is too close to the sun for that brightness
• at sunset, if the comet if high enough above the horizon, and bright enough, it may become visible for some time as the twilight darkens just before the comet sets and atmospheric extinction obliterates it
• before sunrise, if the comet is bright enough and rises high enough to get past atmospheric extinction effects before twilight impacts, it may be visible for a short period until twilight obliterates it
• latitude may make all the difference
  • for a comet north of the ecliptic and close to the sun, a northern latitude means the comet will have much higher elevation and hence more visibility in twilight
  • for example comet C/2025 R3 Panstarrs on 16th April 2026:
    • declination +18deg with 28.6deg elongation from the sun which was at declination +10deg
    • at sunrise: in Melbourne, latitude 37.8degS, in was only 13deg above the horizon and invisible prior to sunrise due to twilight sky glow, while in Cairns, Australia, latitude 17degSth it was 21deg above the horizon making it an easier target, although even better further north (Rome at latitude 42degNth it was 25deg above the horizon, at Singapore on the equator, it was ~26deg above the horizon)

• most comets can be relatively easily photographed when they reach magnitude 8-9 or brighter although results will be very much dependent on light pollution and your ability to take guided images.
• a common setup is to piggyback mount a camera on a motorised telescope which is then used to track the comet, and in separate images to track the stars as the comet will slowly move in relation to the stars.
• you usually will need a good quality lens or telescope with effective focal length in 35mm terms of 200-400mm and aperture f/5.6 or brighter.
• thus, consider using the highest ISO that gives reasonably noise-free results and after ensuring lens or telescope is accurately focused, take:
  • perhaps 30 photos tracked on the comet using 2 minute exposures
  • perhaps 5 photos tracked on the stars using 2 minute exposures
  • some dark frame images using 2 minute exposures
• then post-process the images:
  • subtract the dark frame image from each of the comet and star images +/- adjust to minimise light pollution
  • use a median combine of the comet images with alignment on the comet nucleus (eg. Images Plus Sigma Clip Median) to produce the comet image and this will remove star trails, jet and satellite streaks.
  • use a median combine of the star images with alignment on the starfield
  • combine the two final images

• you should be able to get away with using a tripod and exposures of 5 to 20secs at f/2, 400ISO, although to register the dimmer parts of the tail, you may need to resort to the technique for comets magnitude 4 to 9.
• for really bright comets (magnitude 0 to minus 3) at sunset or sunrise:
• may be able to get away with a short exposure of 1/30th to 1/200th of a sec.
• the main problem is ensuring you are focused at infinity and the lack of contrast with the twilight sky requiring some adjustment of curves in PS.
• rarely, a comet may be bright enough to be photographed in daylight:
• usually in this case, the comet will be near the sun and need to be of magnitude -3 or so
• although not visible to the naked eye during daylight, a 10“ telescope may show it (take great care not to allow the telescope to include the sun in its field of view or immediate permanent blindness may result as well as cracking of eyepiece glass from the heat).
• may need to stack perhaps 10 images taken at prime focus on a 10” f/5.6 scope taken at 100ISO and about 1/100th to 1/4000th sec depending on brightness. 
• only the brightest parts of the tail will be able to be photographed in daylight.

• stacked them in AstroPixelProcessor using comet registration mode, tidied up the stars with RC Astro BlurXterminator and StarShrink and finished it all off in Photoshop.
• see also options as for Milky Way astroscapes:
  • https://www.youtube.com/watch?v=6MfyumKaoro

• Comet 12/P Pons-Brooks - Apr 2024
• comet Leonard - Dec 2021
  • see Comet Leonard
• comet Neowise
  • https://petapixel.com/2021/12/06/photographer-captures-comet-aurora-and-milky-way-in-epic-panorama/
• comet ISON C/2012 S1 - Nov 2013
• my photos of comet Lemmon (C2012/F6) - Feb-Mar 2013
• comet C/2011 W3 Lovejoy - Dec 2011
• comet 17P/Holmes - Oct/Nov 2007
  • unexpectedly suddenly became brighter with an expanding halo some 7x the size of Jupiter with it being about 600x further than the moon yet appearing almost half the size of the moon but with no significant tail evident.
  • reached magnitude 2.3
  • unfortunately not visible from southern regions
• comet LONEOS (C/2007F1) - Nov 2007
  • expected to be a faint naked eye comet for the 1st week or so of Nov 2007 in Scorpius then rapidly become dim
• comet P1 McNaught - Jan 2007
  • the 2nd brightest comet in about 100 yrs, reached magnitude minus 5.5 and was able to be photographed in daylight through a 10“ telescope.
  • in addition to my photos above, see HERE for more of my photos and info
• comet Schwassmann-Wachmann 3 - May 2006
  • Two fragments of the disintegrating comet were visible in binoculars and small scopes at about 6th or 7th magnitude, a third was in reach of larger amateur scopes — and about 65 much fainter pieces have been detected. All are strung in a line, making their closest pass by Earth May 14–17 at a distance of just 10 million kilometers (6 million miles).
  • see http://skyandtelescope.com/observing/objects/comets/article_1704_1.asp 
• comet Pojmanski magnitude 5 at Feb 2006
  • see http://www.pbase.com/terrylovejoy/image/56461433 
• comet LINEAR T7
  • my pic of comet LINEAR T7 on 21st May 2004, a single 3 minute exposure 200mm f/3.5 400ISO Olympus 8080 digital camera, motor guided uncorrected

• Halley's comet:
  • English astronomer Edmund Halley (1656-1742) finally resolved that comets were orbiting the sun consistent with Newton's newly propounded law of gravitation. He calculated orbits for 24 of the brighter comets & noted the striking similarity between the orbits of the comets of 1531, 1607 & 1682. He predicted that these were the same comet and that it would return in 1758-59 but died before his prophecy was fulfilled.
  • it has a period of 77yrs, having been recorded as having returned as far back as the 5thC BC.
  • it is due to return in 2063.
  • my pic of Halley's comet in 1986 3min 200mm f/3.5 400ASA Olympus OM-1 film camera manual guided:

• - 10     C/1965 S1 (Ikeya-Seki)
• - 5.5    C/2006 P1 (McNaught) (Jan 14 2007) - best for southern hemisphere observers
•  -??      Daytime Comet 1910 (Halley's comet) - placed here for reference
• ? C/2011 W3 Lovejoy (Dec 2011) - another great comet for southern hemisphere observers
• - 3.0    C/1975 V1 (West)
• - 3.0    C/1947 X1 (Southern comet)
• - 0.8    C/1995 O1 (Hale-Bopp) - longest duration of unaided visibility on record - but mainly visible for N hemisphere observers
• - 0.5    C/1956 R1 (Arend-Roland)
• - 0.5    C/2002 V1 (NEAT)
• - 0.1    C/1996 B2 (Hyakutake) - one of the grandest comets of the millenium - but only for northern hemisphere observers 
• 0.0      C/1969 Y1 (Bennett)
• 0.0      C/1973 E1 (Kohoutek)
• 0.0      C/1948 V1 (Eclipse comet)
• 0.0      C/1962 C1 (Seki-Lines)
• 0.5      C/1998 J1 (SOHO)
• 1.0      C/1957 P1 (Mrkos)
• 1.0      C/1970 K1 (White-Ortiz-Bolelli)
• 1.7      C/1983 H1 (IRAS-Araki-Alcock)
• 2.0      C/1941 B2 (de Kock-Paraskevopoulos)
• 2.2      C/2002 T7 (LINEAR)
• 2.3      17P/Holmes - unexpected major outburst Oct 2007 but not visible in southern regions
• 2.4      1P/1982 U1 (Halley)
• 2.5      C/2000 WM_1 (LINEAR)
• 2.7      C/1964 N1 (Ikeya)
• 2.8      C/2001 Q4 (NEAT)
• 2.8      C/1989 W1 (Aarseth-Brewington)
• 2.8      C/1963 A1 (Ikeya)
• 2.9      153P/2002 C1 (Ikeya-Zhang)
• 3.0      C/2001 A2 (LINEAR)
• 3.3      C/1936 K1 (Peltier)
• 3.3      C/2004 F4 (Bradfield)
• 3.5      C/2004 Q2 (Machholz)
• 3.5      C/1942 X1 (Whipple-Fedtke-Tevzadze)
• 3.5      C/1940 R2 (Cunningham)
• 3.5      C/1939 H1 (Jurlof-Achmarof-Hassel)
• 3.5      C/1959 Y1 (Burnham)
• 3.5      C/1969 T1 (Tago-Sato-Kosaka)
• 3.5      C/1980 Y1 (Bradfield)
• 3.5      C/1961 O1 (Wilson-Hubbard)
• 3.5      C/1955 L1 (Mrkos)
• 3.6      C/1990 K1 (Levy)
• 3.7      C/1975 N1 (Kobayashi-Berger-Milon)
• 3.9      C/1974 C1 (Bradfield)
• 3.9      C/1937 N1 (Finsler)
• NB. this list was sent to an astronomy forum thread, not sure where it was derived from.

• absolute magnitude (Ho)
  • The brightness of a comet when it is at 1 AU from both the Earth and Sun. As this virtually never happens, this quantity is calculated from the comet's light curve. Unfortunately, this quantity is far from absolute. It can be different pre- and post-perihelion. It can also change from apparition to apparition (for periodic comets).
• anti-tail or anomalous tail
  • When a comet's tail appears to be pointing toward the Sun, this is called an anti-tail or anomalous tail. In reality, the tail only appears to be pointing toward the Sun. To get an anti-tail, the comet must produce large (“heavy”) dust particles. If this happens, these particles are left along the comet's orbit instead of being pushed away from the Sun and the comet's orbit by light pressure. Often dusty comets will produce particles of different sizes creating a fan-shaped appearance. The smallest dust will be pushed directly away from the Sun (like the gas tail) and the largest will be left in the comet's orbit. When a comet is close to the Sun, the angle of this fan can be 90 degrees or larger. If the Earth-comet-Sun geometry is correct, the dust in the comet's orbit will appear to point toward the Sun. [Try this…make a right (90 degree) angle with your thumb and index finger. Your index finger is the main tail and your thumb is the dust left in the comet's orbit. Point your finger and thumb directly away from you (keeping the angle 90 degrees). Your finger seems to be going in exactly the opposite direct from the thumb. This is what causes an anti-tail.]
• apparition
  • The time during which a comet is under observation. For periodic comets which have more than one appearance, the term apparition is often used with the year of perihelion passage, such “the 1910 apparition of Comet Halley.” The term probably is derived from the ghostly appearance of bright naked-eye comets.
• astronomical unit (AU)
  • Standard unit for measuring distance within the solar system. One AU is equal to the average distance between the Sun and Earth or about 93 million miles.
• coma or the comet's head
  • The comet's coma or head is the fuzzy haze that surrounds the comet's true nucleus. The coma (and tail) are really all that we see from Earth.
  • The shape of the coma can vary from comet to comet and for the same comet during its apparition. The shape depends on the comet's distance from the Sun and the relative amount of dust and gas production. For faint comets or bright comets producing little dust, the coma is usually round. Comets, which are producing significant quantities of dust, have a fan-shaped or parabolic comae. This is because different size dust is being released. The larger dust gets left along the comet's orbital path while smaller dust gets pushed away from the Sun by light pressure. The smaller the dust, the more directly away from the Sun the dust is pushed. With a distribution of both large and small dust sizes, a fan is created. For comets within 1 AU, the coma of a dusty comet often becomes parabolic in shape. Clearly, for comets with fan-shaped or parabolic comae, there is no obvious boundary between the coma and tail.
• coma diameter
  • The diameter of the coma is usually given in minutes of arc ('). If the coma is round, this is a straightforward definition. If the coma is elongated or has a tail, the measurement represents the smallest dimension of the coma (usually at a right angle to the tail) and transecting the brightest part of the coma.
• degree of condensation (DC)
  • DC is an indicator of how much the surface brightness of the coma increases toward the center of the coma. In general, DC=0 indicates totally diffuse and DC=9 means “stellar.” As the DC increases, the coma size usually decreses and becomes more sharply defined. A totally diffuse comet, with no brightening toward the center, is rated DC=0. With DC=3-5, there is a distinct brightening. By DC=7 you have a steep overall gradient and by DC=8 the coma is very small, dense,and intense with fairly well defined boundaries. With DC=9 the comet looks like a soft star or a planet in bad seeing.
• geocentric distance (delta)
  • The comet's distance from the Earth in astronomical units.
• heliocentric distance ®
  • The comet's distance from the Sun in astronomical units.
• long-period comets
  • Comets with orbital periods greater than 200 years.
• “n”
  • The photometric parameter n in the power-law formula for comet brightness, m1 = Ho + 5 log (delta) + 2.5n log ®, indicates how fast the comet's brightness is changing with heliocentric distance, r. Specifically, n is the power in the power-law formula. That is, the comet's brightness varies as r to the -n power. When the comet's heliocentric brightness, m1 - 5 log (delta), is plotted against log ®, the slope of the straight line (assuming it is a straight line) is 2.5n.
• nucleus
  • The true nucleus of a comet has only been seen once (P/Halley by spacecraft). From the ground, the star-like nucleus always includes a cloud of dust and gas around the true nucleus. Hence, terms such as stellar condensation and nuclear condensation are often used when a star-like object is seen in the comet's coma. The magnitude of the “nucleus” is denoted m2 and usually isn't of much use because one is really not such what m2 represents. In general, the value of m2 will get fainter as more magnification is applied.
• observed magnitude (m1)
  • The observed magnitude of the comet represents the integrated brightness of the comet's coma or head as seen from Earth. This is normally obtained by comparing the comet's average surface brightness with that of defocused stars (matching the comet's size) of known brightness. Because comets have size (in contrast to stars which are pinpoints of light), a comet of a given brightness will appear less obvious than a star of the same brightness.
• opposition
  • The comet is in the midnight sky on the opposite side of the Earth from the Sun. A perfect opposition, which almost never happens, has the comet 180 degrees away from the Sun.
• outburst (in brightness)
  • An unexpected increase in brightness over a short period of time due to the release of dust and gas into the coma from the nucleus. For a visual observer, the nuclear condensation (a bright spot near the center of the coma) will appear to become star-like and brighter in the comet's coma. Over time (hours - days), the size of the nuclear condensation will increase as the dust moves away from the nucleus. The change in brightness can be as little as half a magnitude and as much as many magnitudes.
• perihelion
  • The point in a comet's orbit that it is closest to the Sun.
• perihelion date
  • The date (and time) the comet reaches perihelion.
• perihelion distance
  • The comet's distance from the Sun, usually expressed in Astronomical Units, at perihelion.
• periodic or short-period comets
  • Any comet with an orbital period of less than 200 years. These comets are indicated by a “P/” before the names. For example, P/Halley is Halley's comet or more properly known as periodic Comet Halley. Recently, the International Astronomical Union has started numbering periodic comets that have been seen at more than one apparition. Thus, Halley's Comet is 1P/Halley and P/de Vico is now known as 122P/de Vico.
• position angle (PA)
  • The PA of a tail or other cometary feature represents the direction on the sky (in degrees from north) toward which it is pointing. Thus, a comet in the morning sky (in the east) that has a tail pointing due west will have a PA of 270 degrees. A comet in with a tail poining toward the south-east will have a PA of 135 degrees. It must be stressed that the determination of the PA of a tail (or other feature) requires plotting it on an atlas and measuring the angle with a protractor. PAs should be measured to at least five degree resolution. It is not possible to look in an eyepiece and accurately estimate the PA of a tail. Also, the determination of PA in the polar regions of the sky is very tricky and may not be intuitive.
• solar conjunction
  • The comet is near the Sun in the sky. Usually, this means that the comet will not be observable from Earth.
• tail
  • The comet's tail is its most distinctive feature. Generally pointing away from the Sun, these appendages come in a variety of shapes and lengths. The lengths can vary from a small fraction of a degree (tails are always measured as the angular length either in degrees or minutes of arc [', 60' = one degree]) to the rare few that cover a significant fraction of the sky.