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Diprotodon

Diprotodon (Ancient Greek: "two protruding front teeth") is an extinct genus of marsupial from the Pleistocene of Australia containing one species, D. optatum. The earliest finds date to 1.77 million to 780,000 years ago but most specimens are dated to after 110,000 years ago. Its remains were first unearthed in 1830 in Wellington Caves, New South Wales, and contemporaneous paleontologists guessed they belonged to rhinos, elephants, hippos or dugongs. Diprotodon was formally described by English naturalist Richard Owen in 1838, and was the first named Australian fossil mammal, and led Owen to become the foremost authority of his time on other marsupials and Australian megafauna, which were enigmatic to European science.

Diprotodon is the largest-known marsupial to have ever lived; it greatly exceeds the size of its closest living relatives wombats and koalas. It is a member of the extinct family Diprotodontidae, which includes other large quadrupedal herbivores. It grew as large as 1.8 m at the shoulders, over 4 m from head to tail, and likely weighed several tonnes, possibly as much as 3500 kg. Females were much smaller than males. Diprotodon supported itself on elephant-like legs to travel long distances, and inhabited most of Australia. The digits were weak; most of the weight was probably borne on the wrists and ankles. The hindpaws angled inward at 130°. Its jaws may have produced a strong bite force of 2300 N at the long and ever-growing incisor teeth, and over 11000 N at the last molar. Such powerful jaws would have allowed it to eat vegetation in bulk, crunching and grinding plant materials such as twigs, buds and leaves of woody plants with its bilophodont teeth.

It is the only marsupial and metatherian that is known to have made seasonal migrations. Large herds, usually of females, seem to have marched through a wide range of habitats to find food and water, walking at around 6 kph. Diprotodon may have formed polygynous societies, possibly using its powerful incisors to fight for mates or fend off predators, such as the largest-known marsupial carnivore Thylacoleo carnifex. Being a marsupial, the mother may have raised her joey in a pouch on her belly, probably with one of these facing backwards, as in wombats.

Diprotodon went extinct about 40,000 years ago as part of the Late Pleistocene megafauna extinctions, along with every other Australian animal over 100 kg; the extinction was possibly caused by extreme drought conditions and predation pressure from the first Aboriginal Australians, who likely co-exised with Diprotodon and other megafauna in Australia for several thousand years prior to its extinction. There is little direct evidence of interactions between Aboriginal Australians and Diprotodon—or most other Australian megafauna. Diprotodon has been conjectured by some authors to have been the origin of some aboriginal mythological figures—most notably the bunyip—and aboriginal rock artworks but these ideas are unconfirmable.

Research history

In 1830, farmer George Ranken found a diverse fossil assemblage while exploring Wellington Caves, New South Wales, Australia. This was the first major site of extinct Australian megafauna. Remains of Diprotodon were excavated when Ranken later returned as part of a formal expedition that was headed by explorer Major Thomas Mitchell.

At the time these massive fossils were discovered, it was generally thought they were remains of rhinos, elephants, hippos, or dugongs. They fossils were not formally described until Mitchell took them in 1837 to his former colleague English naturalist Richard Owen while in England publishing his journal. In 1838, while studying a piece of a right mandible with an incisor, Owen compared the tooth to those of wombats and hippos; he wrote to Mitchell designating it as a new genus Diprotodon. Mitchell published the correspondence in his journal. Owen formally described Diprotodon in Volume 2 without mentioning a species; in Volume 1, however, he listed the name Diprotodon optatum, making that the type species. Diprotodon means "two protruding front teeth" in Ancient Greek and optatum is Latin for "desire" or "wish". It was the first-ever Australian fossil mammal to be described. In 1844, Owen replaced the name D. optatum with "D. australis". Owen only once used the name optatum and the acceptance of its apparent replacement "australis" has historically varied widely but optatum is now standard.

In 1843, Mitchell was sent more Diprotodon fossils from the recently settled Darling Downs and relayed them to Owen. Owen, having interpreted the incisors as tusks, as well as comparing the flattening (anteroposterior compression) of the femur to the condition in elephants and rhinos, and the raised ridges of the molar to the grinding surfaces of elephant teeth, believed Diprotodon was an elephant related to or synonymous with Mastodon or Deinotherium. Later that year, he formally synonymised Diprotodon with Deinotherium as Dinotherium Australe, which he recanted in 1844 after German naturalist Ludwig Leichhardt pointed out that the incisors clearly belong to a marsupial. Owen still classified the molars from Wellington as Mastodon australis and continued to describe Diprotodon as likely elephantine. In 1847, a nearly complete skull and skeleton was recovered from the Darling Downs, the latter confirming this characterisation. The massive skeleton attracted a large audience while on public display in Sydney. Leichhardt believed the animal was aquatic and in 1844, he said it might still be alive in an undiscovered tropical area nearer the interior but as the European land exploration of Australia progressed, he became certain it was extinct. Owen later become the foremost authority of Australian palaeontology of his time, mostly working with marsupials.

Huge assemblages of mostly complete Diprotodon fossils have been unearthed in dry lakes and riverbeds; the largest assemblage came from Lake Callabonna, South Australia. Fossils were first noticed here by an aboriginal stockman working on a sheep property to the east. The owners, the Ragless brothers, notified the South Australian Museum, which hired Australian geologist Henry Hurst, who reported an enormous wealth of fossil material and was paid £250 in 1893 to excavate the site. Hurst found up to 360 Diprotodon individuals over a few acres; excavation was restarted in the 1970s and more were uncovered. American palaeontologist Richard H. Tedford said multiple herds of these animals had at different times become stuck in mud while crossing bodies of water while water levels were low during dry seasons.

In addition to D. optatum, several other species were erected in the 19th century, often from single specimens, on the basis of subtle anatomical variations. Among the variations was size difference: adult Diprotodon specimens have two distinct size ranges. In their 1975 review of Australian fossil mammals, Australian palaeontologists J. A. Mahoney and William David Lindsay Ride did not ascribe this to sexual dimorphism because males and females of modern wombat and koala species—its closest living relatives—are skeletally indistinguishable, so they assumed the same would have been true for extinct relatives, including Diprotodon. These other species are: In 2008, Australian palaeontologist Gilbert Price opted to recognise only one species D. optatum based most-notably on a lack of dental differences among these supposed species, and said it was likely Diprotodon was indeed sexually dimorphic, with the male probably being the larger form.
 * D. annextans was erected in 1861 by Irish palaeontologist Frederick McCoy based on some teeth and a partial mandible found near Colac, Victoria; the name may be a typo of annectens, which means linking or joining, because he characterised the species as combining traits from Diprotodon and Nototherium;
 * D. minorwas erected in 1862 by Thomas Huxley based on a partial palate; in 1991, Australian palaeontologist Peter Murray suggested classifying large specimens as D. optatum and smaller ones as "D. minor";
 * D. longiceps was erected in 1865 by McCoy as a replacement for "D. annextans";
 * D. bennettii was erected in 1873 by German naturalist Gerard Krefft based on a nearly complete mandible collected by naturalists George Bennet and Georgina King near Gowrie, New South Wales; and
 * D. loderi was erected in 1873 by Krefft based on a partial palate collected by Andrew Loder near Murrurundi, New South Wales.

Phylogeny
Diprotodon is a marsupial in the order Diprotodontia, suborder Vombatiformes (wombats and koalas), and infraorder Vombatomorphia (wombats and allies). It is unclear how different groups of vombatiformes are related to each other because the most-completely known members—living or extinct—are exceptionally derived (highly specialised forms that are quite different from their last common ancestor).

In 1872, American mammalogist Theodore Gill erected the superfamily Diprotodontoidea and family Diprotodontidae to house Diprotodon. New species were later added to both groups; by the 1960s, the first diprotodontoids dating to before the Pliocene were discovered, better clarifying their relationship to each other. Because of this, in 1967, American palaeontologist Ruben A. Stirton subdivided Diprotodontoidea into one family, Diprotodontidae, with four subfamilies; Diprotodontinae (containing Diprotodon among others), Nototheriinae, Zygomaturinae, and Palorchestinae. In 1977, Australian palaeontologist Michael Archer synonymised Nototheriinae with Diprotodontinae and in 1978, Archer and Australian palaeontologist Alan Bartholomai elevated Palorchestinae to family level as Palorchestidae, leaving Diprotodontoidea with families Diprotodontidae and Palorchestidae; and Diprotodontidae with subfamilies Diprotodontinae and Zygomaturinae.

Below is the Diprotodontoidea family tree according to Australian palaeontologists Karen H. Black and Brian Mackness, 1999 (top), and Vombatiformes family tree according to Beck et al. 2020 (bottom):

Evolution

Diprotodontidae is the most diverse family in Vombatomorphia; it was better adapted to the spreading dry, open landscapes over the last tens of millions of years than other groups in the infraorder, living or extinct. Diprotodon has been found in every Australian state, making it the most-widespread Australian megafauna in the fossil record. The oldest vombatomorph (and vombatiform) is Mukupirna, which was identified in 2020 from Oligocene deposits of the South Australian Namba Formation dating to 26–25 million years ago. The group probably evolved much earlier; Mukupirna was already differentiated as a closer relative to wombats than other vombatiformes, and attained a massive size of roughly 150 kg, whereas the last common ancestor of vombatiformes was probably a small, 1–5.5 kg creature.

Both diprotodontines and zygomaturines were both apparently quite diverse over the Late Oligocene to Early Miocene, roughly 23 million years ago, though the familial and subfamilial classifications of diprotodontoids from this period is debated. Compared to zygomaturines, diprotodontines were rare during the Miocene, the only identified genus being Pyramios. By the Late Miocene, diprotodontians became the commonest marsupial order in fossil sites, a dominance that endures to the present day; at this point, the most-prolific diprotodontians were diprotodontids and kangaroos. Diprotodontidae also began a gigantism trend, along with several other marsupials, probably in response to the lower-quality plant foods available in a drying climate, requiring them to consume much more. Gigantism appears to have evolved independently six times among the vombatiform lineages. Diprotodontine diversity returned in the Pliocene; Diprotodontidae reached peak diversity with seven genera, coinciding with the spread of open forests. In 1977, Archer said Diprotodon directly evolved from the smaller Euryzygoma, which has been discovered in Pliocene deposits of eastern Australia predating 2.5 million years ago.

In general, there is poor resolution on the ages of Australian fossil sites. While the geochronology of Diprotodon is one of best for Australian megafauna, it is still incomplete and the majority of remains are undated. Price and Australian palaeontologist Katarzyna Piper reported the earliest, indirectly dated Diprotodon fossils from the Nelson Bay Formation at Nelson Bay, New South Wales, which dates to 1.77 million to 780,000 years ago during the Early Pleistocene. These remains are 8–17% smaller than those of Late Pleistocene Diprotodon but are otherwise indistinguishable. The oldest directly dated Diprotodon fossils come from the Boney Bite site at Floraville, New South Wales; they were deposited approximately 340,000 years ago during the Middle Pleistocene based on U-series dating and luminescence dating of quartz and orthoclase. Floraville is the only-identified Middle Pleistocene site in tropical northern Australia. Beyond these, almost all dated Diprotodon material comes from Marine Isotope Stage 5 (MIS5) or younger—after 110,000 years ago during the Late Pleistocene.

Skull
Diprotodon has a long, narrow skull. Like other marsupials, the top of the skull of Diprotodon is flat or depressed over the small braincase and the sinuses of the frontal bone. Like many other giant vombatiformes, the frontal sinuses are extensive; in a specimen from Bacchus Marsh, they take up 2675 cc—roughly 25% of skull volume—whereas the brain occupies 477 cc—only 4% of the skull volume. Marsupials tend to have smaller brain-to-body mass ratios than placental mammals, becoming more disparate the bigger the animal, which could be a response to a need to conserve energy because the brain is a calorically expensive organ, or is proportional to the maternal metabolic rate, which is much less in marsupials due to the shorter gestation period. The expanded sinuses increase the surface area available for the temporalis muscle to attach, which is important for biting and chewing, to compensate for a deflated braincase as a result of a proportionally smaller brain. They may also have helped dissipate stresses produced by biting more efficiently across the skull.

The occipital bone, the back of the skull, slopes forward at 45 degrees unlike most modern marsupials, where it is vertical. The base of the occipital is significantly thickened. The occipital condyles, a pair of bones that connect the skull with the vertebral column, are semi-circular and the bottom half is narrower than the top. The inner border, which forms the foramen magnum where the spinal cord feeds through, is thin and well-defined. The top margin of the foramen magnum is somewhat flattened rather than arched. The foramen expands backwards towards the inlet, especially vertically, and is more-reminiscent of a short neural canal—the tube running through a vertebral centrum where the spinal cord passes through—than a foramen magnum.

A sagittal crest extends across the midline of the skull from the supraoccipital—the top of the occipital bone—to the region between the eyes on the top of the head. The orbit (eye socket) is small and vertically oval-shaped. The nasal bones slightly curve upwards until near their endpoint, where they begin to curve down, giving the bones a somewhat S-shaped profile. Like many marsupials, most of the nasal septum is made of bone rather than cartilage. The nose would have been quite mobile. The height of the skull from the peak of the occipital bone to the end of the nasals is strikingly almost uniform; the end of the nasals is the tallest point. The zygomatic arch (cheek bone) is strong and deep as in kangaroos but unlike those of koalas and wombats, and extends all the way from the supraoccipital.

Jaws

As in kangaroos and wombats, there is a gap between the jointing of the palate (roof of the mouth) and the maxilla (upper jaw) behind the last molar, which is filled by the medial pterygoid plate. This would have been the insertion for the medial pterygoid muscle that was involved in closing the jaw. Like many grazers, the masseter muscle, which is also responsible for closing the jaw, seems to have been the dominant jaw muscle. A probable large temporal muscle compared to the lateral pterygoid muscle may indicate, unlike in wombats, a limited range of side-to-side jaw motion means Diprotodon would have been better at crushing rather than grinding food. The insertion of the masseter is placed forwards, in front of the orbits, which could have allowed better control over the incisors. Diprotodon chewing strategy appears to align more with kangaroos than wombats: a powerful vertical crunch was followed by a transverse grinding motion.

As in other marsupials, the ramus of the mandible, the portion that goes up to connect with the skull, angles inward. The condyloid process, which connects the jaw to the skull, is similar to that of a koala. The ramus is straight and extends almost vertically, thickening as it approaches the body of the mandible where the teeth are. The depth of the body of the mandible increases from the last molar to the first. The strong mandibular symphysis, which fuses the two halves of the mandible, begins at the front-most end of the third molar; this would prevent either half of the mandible from moving independently of the other, unlike in kangaroos which use this ability to better control their incisors.

Teeth

The dental formula of Diprotodon is. In each half of either jaw are three incisors in the upper jaw and one in the lower jaw; there are one premolar and four molars in both jaws but no canines. A long diastema (gap) separates the incisors from the molars.

The incisors are scalpriform (chisel-like). Like those of wombats and rodents, the first incisors in both jaws continuously grew throughout the animal's life but the other two upper incisors did not. This combination is not seen in any living marsupial. The cross-section of the upper incisors is circular. In one old male specimen, the first upper incisor measures 11 in of which 8.5 in is within the tooth socket; the second is 4 in and 1 in is in the socket; and the exposed part of the third is 2.6 in. The first incisor is convex and curves outwards but the other two are concave. The lower incisor has a faint upward curve but is otherwise straight and has an oval cross-section. In the same old male specimen, the lower incisor measures 10 in, of which $2/3$ is inside the socket.

The premolars and molars are bilophodont, each having two distinct lophs (ridges). The premolar is triangular and about half the size of the molars. As in kangaroos, the necks of the lophs are coated in cementum. Unlike in kangaroos, there is no connecting ridge between the lophs. The peaks of these lophs have a thick enamel coating that thins towards the base; this could wear away with use and expose the dentine layer, and beneath that osteodentine. Like the first premolar of other marsupials, the first molar of Diprotodon and wombats is the only tooth that is replaced. D. optatum premolars were highly morphologically variable even within the same individual.

Vertebrae
Diprotodon had seven cervical (neck) vertebrae. The atlas, the first cervical (C1), has a pair of deep cavities for insertion of the occipital condyles. The diaphophyses of the atlas, an upward-angled projection on either the side of the vertebra, are relatively short and thick, and resemble those of wombats and koalas. The articular surface of the axis (C2), the part that joints to another vertebra, is slightly concave on the front side and flat on the back side. As in kangaroos, the axis has a low subtriangular hypophysis projecting vertically from the underside of the vertebra and a proportionally long odontoid—a projection from the axis which fits into the atlas—but the neural spine, which projects vertically the topside of the vertebra, is more forwards. The remaining cervicals lack a hypophysis. As in kangaroos, C3 and C4 have a shorter and more-compressed neural spine, which is supported by a low ridge along its midline in the front and the back. The neural spine of C5 is narrower but thicker, and is supported by stronger-but-shorter ridges.. C7 had a forked shape on top of the neural spine.

Diprotodon probably had 13 dorsal vertebrae and 14 pairs of closely spaced ribs. Like many other mammals, the dorsals initially decrease in breadth and then expand before connecting to the lumbar vertebrae. Unusually, the front dorsals match the short proportions of the cervicals, and the articular surface is flat. At the beginning of the series, the neural spine is broad and angled forward, and is also supported by a low ridge along its midline in the front and the back. In later examples, the neural spine is angled backwards and bifurcates (splits into two). Among mammals, bifurcation of the neural spine is only seen in elephants and humans, and only in a few of the cervicals and not in the dorsals. Compared to those of wombats and kangaroos, the neural arch is proportionally taller. As in elephants, the epiphysial plates (growth plates) and the neural arch, to which the neural spine is attached, are anchylosed—very rigid in regard to the vertebral centrum—which served to support the animal's immense weight.

Like most marsupials, Diprotodon likely had six lumbar vertebrae. They retain a proportionally tall neural arch but not the diapophyses, though L1 can retain a small protuberance on one side where a diapophysis would be in a dorsal vertebra; this has been documented in kangaroos and other mammals. The length of each vertebra increases along the series so the lumbar series may have bent downward.

Like other marsupials, Diprotodon had two sacral vertebrae. The base of the neural spines of these two were ossified (fused) together.

Girdles
The general proportions of the scapula (shoulder blade) align more closely with more-basal vertebrates such as monotremes, birds, reptiles, and fish rather than marsupials and placental mammals. It is triangular and proportionally narrow but unlike most mammals with a triangular scapula, the arm attaches to top of the scapula and the subspinous fossa (the fossa, a depression below the spine of the scapula) becomes bigger towards the arm joint rather than decreasing. The glenoid cavity where the arm connects is oval shaped as in most mammals.

Unlike other marsupials, the ilia, the large wings of the pelvis, are lamelliform (short and broad, with a flat surface instead of an iliac fossa). Lamelliform ilia have only been recorded in elephants, sloths, and apes, though these groups all have a much-longer sacral vertebra series whereas marsupials are restricted to two sacral vertebrae. The ilia provided strong muscle attachments that were probably oriented and used much the same as those in an elephant. The sacroiliac joint where the pelvis connects to the spine is at 35 degrees in reference to the long axis of the ilium. The ischia, which form part of the hip socket, are thick and rounded tailwards but taper and diverge towards the socket, unlike those in kangaroos, where the ischia proceed almost parallel to each other. They were not connected to the vertebra. The hip socket itself is well-rounded and almost hemispherical.

Long bones
Unlike those of most marsupials, the humerus of Diprotodon is almost straight rather than S-shaped, and the trochlea of the humerus at the elbow joint is not perforated. The ridges for muscle attachments are poorly developed, which seems to have been compensated for by the powerful forearms. Similarly, the condyles where the radius and ulna (the forearm bones) connect maintain their rounded shape and are quite-similarly sized, and unusually reminiscent of the condyles between the femur and the tibia and fibula in the leg of a kangaroo.

Like elephants, the femur of Diprotodon is straight and compressed anteroposteriorly (from headside to tailside). The walls of the femur are prodigiously thickened, strongly constricting the medullary cavity where the bone marrow is located. The proximal end (part closest to the hip joint) is notably long, broad, and deep. The femoral head projects up far from the greater trochanter. As in kangaroos, the greater trochanter is split into two lobes. The femoral neck is roughly the same diameter as the femoral head. Also as in kangaroos, the condyle for the fibula is excavated out but the condyle for the tibia is well-rounded and hemispherical. Like those of many other marsupials, the tibia is twisted and the tibial malleolus (on the ankle) is reduced.

Paws
Diprotodon has five digits on either paw. Like other plantigrade walkers, where the paws were flat on the ground, the wrist and ankle would have been largely rigid and inflexible. The digits are proportionally weak so the paws probably had a lot of padding. Similarly, the digits do not seem to have been much engaged in weight bearing.

The forepaw was strong and the shape of the wrist bones is quite similar to those of kangaroos. Like other vombatiformes, the metacarpals, which connect the fingers to the wrist, are broadly similar to those of kangaroos and allies. The enlarged pisiform bone takes up half the jointing surface of the ulna. The fifth digit on the forepaw is the largest.

The digits of the hindpaws turn inwards from the ankle at 130 degrees. The second and third metatarsals (the metatarsals connect the toes to the ankle) are significantly reduced, which may mean these digits were syndactylous (fused) like those of all modern diprotodontians. The first, fourth, and fifth digits are enlarged. The toes are each about the same length, except the fifth which is much stouter.

Size

Diprotodon is the largest-known marsupial to ever have lived. In life, adult Diprotodon could have reached 160–180 cm at the shoulders and 275–340 cm from head to tail. Accounting for cartilaginous intervertebral discs, Diprotodon may have been 20% longer than reconstructed skeletons, exceeding 400 cm.

As researchers were formulating predictive body-mass equations for fossil species, efforts were largely constrained to eutherian mammals rather than marsupials. The first person to attempt to estimate the living weight of Diprotodon was Peter Murray in his 1991 review of the megafauna of Pleistocene Australia; Murray made an estimate of 1150 kg using cranial and dental measurements, which he said was probably not a very precise figure. This made Diprotodon the largest herbivore in Australia. In 2001, Canadian biologist Gary Burness and colleagues did a linear regression between the largest herbivores and carnivores—living or extinct—from every continent (for Australia: Diprotodon, Varanus priscus, and Thylacoleo carnifex) against the landmass area of their continent, and another regression between the daily food intake of living creatures against the landmass of their continents. He calculated the food requirement of Diprotodon was 50–60% smaller than expected for Australia's landmass, which he believed was a result of a generally lower metabolism in marsupials compared to placentals—up to 20% lower—and sparser nutritious vegetation than other continents. The maximum-attainable body size is capped much lower than those for other continents.

In 2003, Australian palaeontologist Stephen Wroe and colleagues took a more-sophisticated approach to body mass than Murray's estimate. They made a regression between the minimum circumference of the femora and humeri of 18 quadrupedal marsupials and 32 placentals against body mass, and then inputted 17 Diprotodon long bones into their predictive model. The results ranged from 2,272–3,417 kg, for a mean of 2,786 kg, though Wroe said reconstructing the weight of extinct creatures that far outweighed living counterparts is problematic. For comparison, an American bison they used in their study weighed 1179 kg and a hippo weighed 1950 kg.

Diet

Like modern megaherbivores, most evidently the African elephant, Pleistocene Australian megafauna likely had a profound effect on the vegetation, limiting the spread of forest cover and woody plants. Carbon isotope analysis suggests Diprotodon fed on a broad range of foods and, like kangaroos, was consuming both C3—well-watered trees, shrubs, and grasses—and C4 plants—arid grasses. Carbon isotope analyses on Diprotodon excavated from the Cuddie Springs site in units SU6 (possibly 45,000 years old) and SU9 (350,000 to 570,000 years old) indicate Diprotodon adopted a somewhat-more-varied seasonal diet as Australia's climate dried but any change was subtle. In contrast, contemporary kangaroos and wombats underwent major dietary shifts or specialisations towards, respectively, C3 and C4 plants. The fossilised, incompletely digested gut contents of one 53,000-year-old individual from Lake Callabonna show its last meal consisted of young leaves, stalks, and twigs.

The molars of Diprotodon are a simple bilophodont shape. Kangaroos use their bilophodont teeth to grind tender, low-fibre plants as a browser as well as grass as a grazer. Kangaroos that predominantly graze have specialised molars to resist the abrasiveness of grass but such adaptations are not exhibited in Diprotodon, which may have had a mixed diet similar to that of a browsing wallaby. It may also have chewed like wallabies, beginning with a vertical crunch before grinding transversely, as opposed to wombats, which only grind transversely. Similarly to many large ungulates (hoofed mammals), the jaws of Diprotodon were better suited for crushing rather than grinding, which would have permitted it to process vegetation in bulk.

In 2016, Australian biologists Alana Sharpe and Thomas Rich estimated the maximum-possible bite force of Diprotodon using finite element analysis. They calculated 2374 N at the incisors and 4118 to 11134 N across the molar series. For reference, the American alligator can produce forces upwards of 9500 N. Though these are likely overestimates, the jaws of Diprotodon were exceptionally strong, which would have allowed it to consume a broad range of plants, including tough, fibrous grasses.

Migration and sociality

In 2017, by measuring the strontium isotope ratio (87Sr/86Sr) at various points along the Diprotodon incisor QMF3452 from the Darling Downs, and matching those ratios to the ratios of sites across that region, Price and colleagues determined Diprotodon made seasonal migrations, probably in search of food or watering holes. This individual appears to have been following the Condamine River and, while apparently keeping to the Darling Downs during the three years this tooth had been growing, it would have been annually making a 200 km northwest-southeast round trip. This trek parallels the mammalian mass migrations of modern-day East Africa.

Diprotodon is the only identified metatherian that seasonally migrated between two places. A few modern marsupials, such as the red kangaroo, have been documented making migrations when necessary but it is not a seasonal occurrence. Because Diprotodon could do it, it is likely other Pleistocene Australian megafauna also had seasonal migrations.

Diprotodon apparently moved in large herds. Possible fossilised herds, which are most-commonly unearthed in south-eastern Australia, seem to be mostly or entirely female, and sometimes travelled with juveniles. Such sexual segregation is normally seen in polygynous species; it is a common social organisation among modern megaherbivores involving an entirely female herd save for their young and the dominant male, with which the herd exclusinvely breeds. Similarly, the skull is adapted to handling much-higher stresses than that which resulted from bite alone so Diprotodon may have subjected its teeth or jaws to more-strenuous activities than chewing, such as fighting other Diprotodon for mates or fending off predators, using the incisors. Like modern red and grey kangaroos, which also sexually segregate, bachelor herds of Diprotodon seem to have been less tolerant to drought conditions than female herds due to their larger size and nutritional requirements.

Gait

The locomotion of an extinct animal can be inferred using fossil trackways, which seldom preserve in Australia over the Cenozoic. Only the trackways of humans, kangaroos, vombatids, Diprotodon, and the diprotodontid Euowenia have been identified. Diprotodon trackways have been found at Lake Callabonna and the Victorian Volcanic Plain grasslands. The diprotodontid manus (forepaw) print is semi-circular and the pes (hindpaw) is reniform (kidney-shaped). Owing to proportionally small digits, most of the weight was borne on the carpus and tarsus—the bones connecting to respectively the wrist and the ankle. Diprotodontines seem to have had a much-more-erect gait, an adaptation to long-distance travel that is similar to that of elephants, rather than the more-sprawling posture of wombats and zygomaturines, though there are no fossil trackways of the latter to verify their reconstructed standing posture.

At Lake Callabonna, the single Diprotodon responsible for the impressions had an average stride length of 1500 mm, trackway width of 430 mm, and track dimensions 295x202 mm in length x width. The gleno-acetabular length—the distance between the shoulders and pelvis—could have been about 1125 mm; assuming a hip height of 900 mm, the maker of these tracks was probably moving at around 6.3 kph.

The single Diprotodon responsible for the impressions at the volcanic plain had an average stride length of 1310 mm, trackway width of 660 mm, and pes length of 450 mm. The gleno-acetabular length may have been about 1080 mm and assuming a hip height of 830 mm, the maker of the tracks was probably moving at around 5.5 kph. Its posture was much-more-sprawled than the example from Callabonna, aligning more with what might be expected of Zygomaturus. The animal may have been a female carrying a large joey in her pouch, the added weight on the stomach altering the gait. The first trackway continues for 62.8 m in a south-easterly direction towards a palaeo-lake. The animal seems to have hesitated while stepping down from the first sand bar on its path with the right pes making three overlapping prints here while shuffling around. The trackway vanishes for a 20 m stretch and reappears while the animal seemingly is stepping on wet sediment. Another diprotodontid trackway appears 50 m away, moving southerly, which may have been left by the same individual.

Life history
The marsupial metabolic rate is about 30% lower than that of placentals due to a lower body temperature of 34 to 36 C. Marsupials give birth at an earlier point in foetal development, relying on lactation to facilitate most of the joey's development; because pregnancy is much-more-energetically expensive, investing in lactation rather than longer gestation can be advantageous in a highly seasonal and unpredictable climate to minimise maternal nutritional requirements. Consequently, marsupials cannot support as large a litter size or as short a generation time.

Based on the relationship between female body size and life history in kangaroos, a 1000 kg Diprotodon female would have gestated for six-to-eight weeks, and given birth to a single 5 g joey. Given its massive size, Diprotodon may not have sat down to give birth as do smaller marsupials, possibly standing instead. Like koalas and wombats, the pouch may have faced backwards so the joey could crawl down across its mother's abdomen to enter and attach itself to a teat until it could see—perhaps 260 days—and thermoregulate. It would have permanently left the pouch after 860 days and suckled until reaching 270 kg after four or five years.

In large kangaroos, females usually reach sexual maturity and enter oestrus soon after weaning, and males need double the time to reach sexual maturity. A similar pattern could have been exhibited in Diprotodon. Assuming a lifespan of up to 50 years, a female Diprotodon could have given birth eight times.

Palaeoecology
Diprotodon was present across the entire Australian continent by the Late Pleistocene, especially following MIS5 approximately 110,000 years ago. The onset of the Quaternary glaciation, with the continuous advance and retreat of glaciers at the poles, created extreme climatic variability elsewhere. In Australia, the warmer, wetter interglacial periods were received by forests and woodlands; colder, dryer glacial periods were more conducive to grasslands and deserts. The continent progressively became dryer as the Asian monsoons became less influential over Australia: the vast interior had become arid and sandy by 500,000 years ago; the mega-lakes that were once prominent, especially during interglacials in north-western Australia, dried up; and the rainforests of eastern Australia gradually retreated. Aridity has hastened over the last 100,000 years, especially after 60,000 years ago with surging El Niño–Southern Oscillations.

The continent-wide distribution of Diprotodon indicates herds trekked across almost any habitat, much like modern African elephants south of the Sahara. Diprotodon was a member of a diverse assemblage of megafauna that were endemic to Pleistocene Australia; these also included the thylacine, modern kangaroos, sthenurines (giant short-faced kangaroos), a diversity of modern and giant koala and wombat species, the tapir-like Palorchestes, the giant turtle Meiolania, and the giant bird Genyornis. Diprotodon coexisted with the diprotodontid Zygomaturus trilobus, which appears to have remained in the forests, whereas Diprotodon foraged the expanding grasslands and woodlands. Other contemporaneous dipotodontids (Hulitherium, Z. nimborensia, and Maokopia) were insular forms that were restricted to the forests of New Guinea.

Predation
Due to its massive size, Diprotodon would have been a tough adversary for native carnivores. It contended with the largest-known marsupial predator Thylacoleo carnifex; while Diprotodon remains that were gnawed or bitten by T. carnifex have been identified, it is unclear if the 100 – marsupial predator was powerful enough to kill an animal surpassing 2000 kg. The modern jaguar, at half the size of T. carnifex, can kill a 500 kg bull so it is possible T. carnifex could have killed small Diprotodon. Similar to recent kangaroos with thylacines or quolls, juvenile Diprotodon may have been at high risk of predation by T. carnifex; it and fossils of juvenile Diprotodon have been recovered from the same caves.

The largest predators of Australia were reptiles, most notably the saltwater crocodile, the now-extinct crocodiles Paludirex and Quinkana, and the giant lizard megalania (Varanus priscus). At 7 m in length, megalania was the largest carnivore of Pleistocene Australia.

Extinction
As part of the Quaternary extinction event, Diprotodon and every other Australian land animal heavier than 100 kg became extinct. The timing and the exact cause are unclear because there is poor resolution on the ages of Australian fossil sites. Since their discovery, the extinction of the Australian megafauna has usually been blamed on the changing climate or overhunting by the first Aboriginal Australians. In 2001, Australian palaeontologist Richard Roberts and colleagues dated 28 major fossil sites across the continent, and were able to provide a precise date for megafaunal extinction. They found most disappear from the fossil record by 80,000 years ago but Diprotodon; the giant wombat Phascolonus; Thylacoleo; and the short-faced kangaroos Procoptodon, Protemnodon, and Simosthenurus was identified at Ned's Gully, Queensland, and Kudjal Yolgah Cave, Western Australia, which they dated to respectively 47,000 and 46,000 years ago. Thus, all of the Australian megafauna died out probably between about 50,000 and 41,000 years ago. There also seems to have been a diverse assemblage of megafauna just before their extinction, and all populations across at least western and eastern Australia died out at about the same time. As of 2021, there is still no solid evidence of megafauna surviving past approximately 40,000 years ago; their latest occurrence, including Diprotodon, is recorded at South Walker Creek mine in the north-east at about 40,100 ± 1,700 years ago.

At the time Roberts et al. published their paper, the earliest evidence of human activity in Australia was 56±4 thousand years old, which is close to their calculated date for the megafauna extinction; they hypothesised human hunting had eradicated the last megafauna within about 10,000 years of coexistence. Human hunting had earlier been blamed for the extinction of North American and New Zealand megafauna. Human activity was then generally regarded as the main driver of Australian megafaunal extinction, especially because the megafauna had survived multiple extreme drought periods during glacial periods. At the time, there did not seem to be any evidence of unusually extreme climate during this period. Due to the slowness of marsupial reproduction, even limited megafaunal hunting may have severely weakened the population.

In 2005, American geologist Gifford Miller noticed fire abruptly becomes more common about 45,000 years ago; he ascribed this increase to aboriginal fire-stick farmers, who would have regularly started controlled burns to clear highly productive forests and grasslands. Miller said this radically altered the vegetational landscape and promulgated the expanse of the modern-day fire-resilient scrub at the expense of the megafauna. Subsequent studies had difficulty firmly linking controlled burns with major ecological collapse. The frequency of fire could have also increased as a consequence of megafaunal extinction because total plant consumption rapidly fell, leading to faster fuel buildup.

In 2017, the human-occupied Madjedbebe rock shelter on the northern Australian coast was dated to about 65,000 years ago, which if correct would mean humans and megafauna had coexisted for over 20,000 years. Other authors have considered this dating questionable. In the 2010s, several ecological studies were published in support of major drought conditions coinciding with the final megafaunal extinctions. Their demise may have been the result of a combination of climatic change, human hunting, and human-driven landscape changes.

Fossil evidence
Despite the role the first Aboriginal Australians are speculated to have had in the extinction of Diprotodon and other mammalian megafauna in Australia, there is little evidence humans used them at all in the 20,000 years of coexistence. No fossils of mammalian megafauna suggestive of human butchery or cooking have been found.

In 1984, Gail Paton discovered an upper-right Diprotodon incisor (2I) bearing 28 visible cut marks in Spring Creek, south-western Victoria; Ron Vanderwald and Richard Fullager studied the incisor, which was split in half longitudinally, seemingly while the bone was still fresh but it was glued together before Vanderwald and Fullager could inspect it. Each piece measures 40 cm in length. The marks are aligned in a straight line, and measure 0.91–4.1 mm in length, 0.14–0.8 mm in width, and 0.02–0.24 mm in depth. They determined it was inconsistent with bite marks from scavenging Thylacoleo or mice, and concluded it was incised by humans with flint as a counting system or a random doodle. This specimen became one of the most-cited pieces of evidence humans and megafauna directly interacted until a 2020 re-analysis by Australian palaeoanthropologist Michelle Langley identified the engraver as most-likely a tiger quoll.

In 2016, Australian archaeologist Giles Hamm and colleagues unearthed a partial right radius belonging to a young Diprotodon in the Warratyi rock shelter. Because it lacks carnivore damage and the rock shelter is up a sheer face Diprotodon is unlikely to have climbed, they said humans were responsible for taking the bone to the site.

Mythology

When the first massive fossils in Australia were dug up, it was not clear what animals they might have represented because there were no serious scientists on the continent. Local residents guessed some may have been the remains of rhinos or elephants. European settlers, the most-vocal of whom was Reverend John Dunmore Lang, forwarded these fossils as evidence of the Genesis flood narrative. Aboriginal Australians also attempted to fit the finds into their own religious ideas, quickly associating Diprotodon with the bunyip, a large, carnivorous, lake monster. Many ethnologists and palaeontologists of the time believed the bunyip to be a tribal memory of the lumbering giant creature that probably frequented marshlands, though at the time it was uncertain whether Diprotodon and other megafauna were still extant because the Australian continent had not yet been fully explored by Europeans. Scientific investigation into the bunyip was stigmatised after a purported bunyip skull was sensationalised in 1846, and was put on display at the Australian Museum. The following year, however, Owen recognised it as the skull of a foal, and was surprised the burgeoning Australian scientific community could have erred so egregiously.

In 1892, Canadian geologist Henry Yorke Lyell Brown reported Aboriginal Australians identified Diprotodon fossils from Lake Eyre as those of the Rainbow Serpent, which he thought was a giant, bottom-dwelling fish. This notion became somewhat popularised after English geologist John Walter Gregory, who believed the god was a horned, scaly creature, conjectured it was a chimaera of Diprotodon—which he believed had a horn—and a crocodile. Later workers continued to report some link between the Rainbow Serpent and either Diprotodon or crocodiles.

These kinds of suppositions are not testable and require stories to survive in oral tradition for tens of thousands of years. If Pleistocene megafauna are the basis of some aboriginal mythology, it is unclear if the stories were based on the creatures when they were alive or their fossils being discovered long after their extinction.

Rock art representations
Aboriginal Australians decorated caves with paintings and drawings of several creatures but the identities of the subjects are often unclear. In 1907, Australian anthropologist Herbert Basedow found footprint petroglyphs in Yunta Springs and Wilkindinna, South Australia, which he believed were those of Diprotodon. In 1988, Australian historian Percy Trezise presented what he thought was a Quinkan depiction of Diprotodon to the First Congress of the Australian Rock Art Research Association. Both of these claims have their faults because the depictions bear several features that are inconsistent with what is known about Diprotodon. Unlike the more-naturalistic artwork of Early European modern humans, which are more easily identifiable as various animals, aboriginal artwork is much more stylistic and is mostly uninterpretable by an outsider. The subjects of aboriginal paintings can be mythological beings from the Dreaming rather than a corporeal subject.

title: Diprotodon


text:
Dirk Benedict

Dirk Benedict (born Dirk Niewoehner; March 1, 1945) is an American film, television and stage actor, and author. He is best known for playing the characters Lieutenant Starbuck in the original Battlestar Galactica film and television series and Templeton "Faceman" Peck in The A-Team television series. He is the author of Confessions of a Kamikaze Cowboy and And Then We Went Fishing.

Early life
Benedict was born Dirk Niewoehner in Helena, Montana, the son of George Edward Niewoehner, a lawyer, and his wife Priscilla Mella (née Metzger), an accountant. He grew up in White Sulphur Springs, Montana. He graduated from Whitman College in 1967. Benedict allegedly chose his stage name from a serving of Eggs Benedict he had prior to his acting career. He is of German extraction.

Career

Benedict's film debut was in the 1972 film Georgia, Georgia. When the New York run for Butterflies Are Free ended, he received an offer to repeat his performance in Hawaii, opposite Barbara Rush. While there, he appeared as a guest lead on Hawaii Five-O. The producers of a horror film called Sssssss (1973) saw Benedict's performance in Hawaii Five-O and promptly cast him as the lead in that movie. He next played the psychotic wife-beating husband of Twiggy in her American film debut, W (1974). Benedict starred in the television series Chopper One, which aired for one season in 1974. He made two appearances in Charlie's Angels. He also appeared on the Donny & Marie variety show.

Benedict's career break came in 1978 when he appeared as Lieutenant Starbuck in the movie and television series Battlestar Galactica. The same year Benedict starred in the TV film Cruise into Terror, and appeared in the ensemble movie Scavenger Hunt the following year.

1980s and 1990s
In 1980, Benedict starred alongside Linda Blair in an action-comedy movie called Ruckus. In 1983, Dirk gained further popularity as con man Templeton "Faceman" Peck in 1980s action television series The A-Team. He played "Face" from 1982 to 1986, although the series didn't air until January 1983, and the final episode wasn't shown until 1987 rebroadcasts. The second season episode "Steel" includes a scene at Universal Studios where Face is seen looking bemused as a Cylon walks by him as an in-joke to his previous role in Battlestar Galactica. The clip is incorporated into the series' opening credit sequence from season 3 onward.

In 1986, Benedict starred as low-life band manager Harry Smilac in the movie Body Slam along with Lou Albano, Roddy Piper, and cameo appearances by Freddie Blassie, Ric Flair, and Bruno Sammartino. His character Smilac ends up managing the pro-wrestler "Quick Rick" Roberts (Piper) and faces opposition by Captain Lou and his wrestling tag-team "the Cannibals".

In 1987, Benedict took the title role of Shakespeare's Hamlet at the Abbey Theatre in Manhattan. Both his performance and the entire production were lambasted by critics. Benedict starred in the 1989 TV film Trenchcoat in Paradise.

In 1991, Benedict starred in Blue Tornado, playing Alex, call sign Fireball, an Italian Air Force fighter pilot. Benedict published an autobiography, Confessions of a Kamikaze Cowboy: A True Story of Discovery, Acting, Health, Illness, Recovery, and Life (Avery Publishing ISBN 0895294796). In 1993, Benedict starred in Shadow Force.

Benedict also appeared as Jake Barnes in the 1996 action-adventure film Alaska.

2000s and 2010s
In 2000, Benedict wrote and directed his first screenplay, Cahoots. Benedict appeared in the 2006 German film Goldene Zeiten ("Golden Times") in a dual role, playing an American former TV star as well as a German lookalike who impersonates him.

In 2006, he wrote an online essay criticizing the then-airing Battlestar Galactica re-imagined series and, especially, its casting of a woman as his character, Starbuck, writing that "the war against masculinity has been won" and that "a television show based on hope, spiritual faith, and family is unimagined and regurgitated as a show of despair, sexual violence and family dysfunction".

He appeared as a contestant on the 2007 UK series of Celebrity Big Brother 5, which he placed 3rd. He arrived on launch night in a replica of the A-Team van, smoking a cigar and accompanied by the A-Team theme tune.

In 2010, Benedict starred in a stage production of Prescription: Murder playing Lieutenant Columbo for the Middle Ground Theatre Company in the UK. Benedict also made a cameo appearance in the 2010 film adaptation of The A-Team as Pensacola Prisoner Milt.

In 2019, Benedict took on the role of Jack Strange in the B movie Space Ninjas, written and directed by Scott McQuaid. Dirk plays an eccentric TV host of a show called Stranger Than Fiction, which is like a hybrid of The Twilight Zone and The X-Files. The movie is a sci-fi comedy horror that follows a bunch of high school students trying to survive the night of a Space Ninja invasion.

Cancer
In the 1970s, Benedict survived a prostate tumor, which he refused to have tested for malignancy. Having rejected conventional medical treatment, he credited his survival to the adoption of a macrobiotic diet recommended to him by actress Gloria Swanson.

Marriage and family
In 1986, he married Toni Hudson, an actress with whom he has two sons, George and Roland. Hudson had previously appeared as Dana in the fourth season A-Team episode titled "Blood, Sweat and Cheers". They divorced in 1995.

In 1998, Benedict learned that he also has another son from an earlier relationship, who was placed for adoption.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Dirk Benedict


text:
User:DrBob/Major

Articles I have a major interest in:

 * Optics
 * Laser
 * Maser
 * Laser science
 * Laser construction
 * Reflection
 * Refraction
 * Population inversion
 * Snells law
 * Fresnel equations
 * Phase
 * Polarisation
 * Brewsters angle
 * David Brewster
 * Infrared
 * Ultraviolet
 * Absorption
 * Spontaneous emission
 * Stimulated emission
 * Laser applications
 * Microwave
 * Dispersion
 * Diffraction
 * Beer-Lambert law
 * Abbe number
 * Lens

 * Unit-related:
 * Radian
 * Steradian
 * Dyne
 * Erg

 * Other:
 * Larry Niven
 * Atari ST
 * Sinclair QL

 * See also : User:DrBob

title: User:DrBob/Major


text:
User:DrBob/Minor

Articles I have a minor interest in, i.e. have edited by did not write the majority of the content:

 * Table of Integrals
 * Peter F. Hamilton
 * SI supplementary unit
 * Teflon
 * Ohm
 * Electromagnetic spectroscopy
 * Decibel
 * Sinclair ZX Spectrum
 * Game of life
 * Boxes
 * Sinclair Research
 * Wave
 * PAL
 * X-ray
 * Rainbow
 * Refractive index
 * Mirror

 * See also : User:DrBob

title: User:DrBob/Minor


text:
User:DrBob/Figures

All the figures I have added to Wikipedia, so far as I can remember. Mostly here so I can keep an eye on them.

2004

2005

Now experimenting with SVG support:

2006
SVG versions of lens diagrams:

2007

+

All images drawn or taken by myself and are GFDL, except as noted.

title: User:DrBob/Figures


text:
User:DrBob/Todo

To do list:

 * More images for articles above.
 * Finish lens
 * Finish laser applications (medical, industrial apps to be added)
 * Finish absorption (not yet).
 * Quantum electronics
 * Move most of population inversion to laser science/quantum electronics
 * wave equation - need for nonlinear optics
 * expand optical fiber
 * possibly add article on optical communications, EDFA
 * nonlinear optics - flesh out stub
 * soliton

 * See also : User:DrBob

User watchlist: St*n*k related users:

title: User:DrBob/Todo


text:
Doppler effect

The Doppler effect (also Doppler shift) is the change in the frequency of a wave in relation to an observer who is moving relative to the source of the wave. The Doppler effect is named after the physicist Christian Doppler, who described the phenomenon in 1842. A common example of Doppler shift is the change of pitch heard when a vehicle sounding a horn approaches and recedes from an observer. Compared to the emitted frequency, the received frequency is higher during the approach, identical at the instant of passing by, and lower during the recession.

When the source of the sound wave is moving towards the observer, each successive cycle of the wave is emitted from a position closer to the observer than the previous cycle. Hence, from the observer's perspective, the time between cycles is reduced, meaning the frequency is increased. Conversely, if the source of the sound wave is moving away from the observer, each cycle of the wave is emitted from a position farther from the observer than the previous cycle, so the arrival time between successive cycles is increased, thus reducing the frequency.

For waves that propagate in a medium, such as sound waves, the velocity of the observer and of the source are relative to the medium in which the waves are transmitted. The total Doppler effect in such cases may therefore result from motion of the source, motion of the observer, motion of the medium, or any combination thereof. For waves propagating in vacuum, as is possible for electromagnetic waves or gravitational waves, only the difference in velocity between the observer and the source needs to be considered.

History
Doppler first proposed this effect in 1842 in his treatise "Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels" (On the coloured light of the binary stars and some other stars of the heavens). The hypothesis was tested for sound waves by Buys Ballot in 1845. He confirmed that the sound's pitch was higher than the emitted frequency when the sound source approached him, and lower than the emitted frequency when the sound source receded from him. Hippolyte Fizeau discovered independently the same phenomenon on electromagnetic waves in 1848 (in France, the effect is sometimes called "effet Doppler-Fizeau" but that name was not adopted by the rest of the world as Fizeau's discovery was six years after Doppler's proposal). In Britain, John Scott Russell made an experimental study of the Doppler effect (1848).

General
In classical physics, where the speeds of source and the receiver relative to the medium are lower than the speed of waves in the medium, the relationship between observed frequency $$f$$ and emitted frequency $$f_\text{0}$$ is given by: $$f = \left( \frac{c \pm v_\text{r}}{c \mp v_\text{s}} \right) f_0 $$ where
 * $$c $$ is the propagation speed of waves in the medium;
 * $$v_\text{r} $$ is the speed of the receiver relative to the medium. In the formula, $$v_\text{r} $$ is added to $$c$$ if the receiver is moving towards the source, subtracted if the receiver is moving away from the source;
 * $$v_\text{s} $$ is the speed of the source relative to the medium. $$v_\text{s} $$ is subtracted from $$c$$ if the source is moving towards the receiver, added if the source is moving away from the receiver.

Note this relationship predicts that the frequency will decrease if either source or receiver is moving away from the other.

Equivalently, under the assumption that the source is either directly approaching or receding from the observer: $$\frac{f}{v_{wr}} = \frac{f_0}{v_{ws}} = \frac{1}{\lambda}$$ where
 * $$v_{wr}$$ is the wave's speed relative to the receiver;
 * $$v_{ws}$$ is the wave's speed relative to the source;
 * $$\lambda$$ is the wavelength.

If the source approaches the observer at an angle (but still with a constant speed), the observed frequency that is first heard is higher than the object's emitted frequency. Thereafter, there is a monotonic decrease in the observed frequency as it gets closer to the observer, through equality when it is coming from a direction perpendicular to the relative motion (and was emitted at the point of closest approach; but when the wave is received, the source and observer will no longer be at their closest), and a continued monotonic decrease as it recedes from the observer. When the observer is very close to the path of the object, the transition from high to low frequency is very abrupt. When the observer is far from the path of the object, the transition from high to low frequency is gradual.

If the speeds $$v_\text{s} $$ and $$v_\text{r} \,$$ are small compared to the speed of the wave, the relationship between observed frequency $$f$$ and emitted frequency $$f_\text{0}$$ is approximately where
 * $$\Delta f = f - f_0 $$
 * $$\Delta v = -(v_\text{r} - v_\text{s}) $$ is the opposite of the relative speed of the receiver with respect to the source: it is positive when the source and the receiver are moving towards each other.

$$

Consequences
Assuming a stationary observer and a wave source moving towards the observer at (or exceeding) the speed of the wave, the Doppler equation predicts an infinite (or negative) frequency as from the observer's perspective. Thus, the Doppler equation is inapplicable for such cases. If the wave is a sound wave and the sound source is moving faster than the speed of sound, the resulting shock wave creates a sonic boom.

Lord Rayleigh predicted the following effect in his classic book on sound: if the observer were moving from the (stationary) source at twice the speed of sound, a musical piece previously emitted by that source would be heard in correct tempo and pitch, but as if played backwards.

Sirens
A siren on a passing emergency vehicle will start out higher than its stationary pitch, slide down as it passes, and continue lower than its stationary pitch as it recedes from the observer. Astronomer John Dobson explained the effect thus:

"The reason the siren slides is because it doesn't hit you."

In other words, if the siren approached the observer directly, the pitch would remain constant, at a higher than stationary pitch, until the vehicle hit him, and then immediately jump to a new lower pitch. Because the vehicle passes by the observer, the radial speed does not remain constant, but instead varies as a function of the angle between his line of sight and the siren's velocity: $$v_\text{radial} = v_\text{s} \cos(\theta)$$ where $$\theta$$ is the angle between the object's forward velocity and the line of sight from the object to the observer.

Astronomy

The Doppler effect for electromagnetic waves such as light is of widespread use in astronomy to measure the speed at which stars and galaxies are approaching or receding from us, resulting in so called blueshift or redshift, respectively. This may be used to detect if an apparently single star is, in reality, a close binary, to measure the rotational speed of stars and galaxies, or to detect exoplanets. This effect typically happens on a very small scale; there would not be a noticeable difference in visible light to the unaided eye. The use of the Doppler effect in astronomy depends on knowledge of precise frequencies of discrete lines in the spectra of stars.

Among the nearby stars, the largest radial velocities with respect to the Sun are +308 km/s (BD-15°4041, also known as LHS 52, 81.7 light-years away) and −260 km/s (Woolley 9722, also known as Wolf 1106 and LHS 64, 78.2 light-years away). Positive radial speed means the star is receding from the Sun, negative that it is approaching.

Redshift is also used to measure the expansion of the universe. It is sometimes claimed that this is not truly a Doppler effect but instead arises from the expansion of space. However, this picture can be misleading because the expansion of space is only a mathematical convention, corresponding to a choice of coordinates. The most natural interpretation of the cosmological redshift is that it is indeed a Doppler shift.

Distant galaxies also exhibit peculiar motion distinct from their cosmological recession speeds. If redshifts are used to determine distances in accordance with Hubble's law, then these peculiar motions give rise to redshift-space distortions.

Radar
The Doppler effect is used in some types of radar, to measure the velocity of detected objects. A radar beam is fired at a moving target — e.g. a motor car, as police use radar to detect speeding motorists — as it approaches or recedes from the radar source. Each successive radar wave has to travel farther to reach the car, before being reflected and re-detected near the source. As each wave has to move farther, the gap between each wave increases, increasing the wavelength. In some situations, the radar beam is fired at the moving car as it approaches, in which case each successive wave travels a lesser distance, decreasing the wavelength. In either situation, calculations from the Doppler effect accurately determine the car's speed. Moreover, the proximity fuze, developed during World War II, relies upon Doppler radar to detonate explosives at the correct time, height, distance, etc.

Because the Doppler shift affects the wave incident upon the target as well as the wave reflected back to the radar, the change in frequency observed by a radar due to a target moving at relative speed $$\Delta v$$ is twice that from the same target emitting a wave: $$\Delta f=\frac{2\Delta v}{c}f_0.$$

Medical
An echocardiogram can, within certain limits, produce an accurate assessment of the direction of blood flow and the velocity of blood and cardiac tissue at any arbitrary point using the Doppler effect. One of the limitations is that the ultrasound beam should be as parallel to the blood flow as possible. Velocity measurements allow assessment of cardiac valve areas and function, abnormal communications between the left and right side of the heart, leaking of blood through the valves (valvular regurgitation), and calculation of the cardiac output. Contrast-enhanced ultrasound using gas-filled microbubble contrast media can be used to improve velocity or other flow-related medical measurements.

Although "Doppler" has become synonymous with "velocity measurement" in medical imaging, in many cases it is not the frequency shift (Doppler shift) of the received signal that is measured, but the phase shift (when the received signal arrives).

Velocity measurements of blood flow are also used in other fields of medical ultrasonography, such as obstetric ultrasonography and neurology. Velocity measurement of blood flow in arteries and veins based on Doppler effect is an effective tool for diagnosis of vascular problems like stenosis.

Flow measurement
Instruments such as the laser Doppler velocimeter (LDV), and acoustic Doppler velocimeter (ADV) have been developed to measure velocities in a fluid flow. The LDV emits a light beam and the ADV emits an ultrasonic acoustic burst, and measure the Doppler shift in wavelengths of reflections from particles moving with the flow. The actual flow is computed as a function of the water velocity and phase. This technique allows non-intrusive flow measurements, at high precision and high frequency.

Velocity profile measurement
Developed originally for velocity measurements in medical applications (blood flow), Ultrasonic Doppler Velocimetry (UDV) can measure in real time complete velocity profile in almost any liquids containing particles in suspension such as dust, gas bubbles, emulsions. Flows can be pulsating, oscillating, laminar or turbulent, stationary or transient. This technique is fully non-invasive.

Satellite navigation
The Doppler shift can be exploited for satellite navigation such as in Transit and DORIS.

Satellite communication
Doppler also needs to be compensated in satellite communication. Fast moving satellites can have a Doppler shift of dozens of kilohertz relative to a ground station. The speed, thus magnitude of Doppler effect, changes due to earth curvature. Dynamic Doppler compensation, where the frequency of a signal is changed progressively during transmission, is used so the satellite receives a constant frequency signal. After realizing that the Doppler shift had not been considered before launch of the Huygens probe of the 2005 Cassini–Huygens mission, the probe trajectory was altered to approach Titan in such a way that its transmissions traveled perpendicular to its direction of motion relative to Cassini, greatly reducing the Doppler shift.

Doppler shift of the direct path can be estimated by the following formula: $$f_{\rm D, dir} = \frac{v_{\rm mob}}{\lambda_{\rm c}}\cos\phi \cos\theta$$ where $$v_\text{mob}$$ is the speed of the mobile station, $$\lambda_{\rm c}$$ is the wavelength of the carrier, $$\phi$$ is the elevation angle of the satellite and $$\theta$$ is the driving direction with respect to the satellite.

The additional Doppler shift due to the satellite moving can be described as: $$f_{\rm D,sat} = \frac{v_{\rm rel,sat}}{\lambda_{\rm c}}$$ where $$v_{\rm rel,sat}$$ is the relative speed of the satellite.

Audio
The Leslie speaker, most commonly associated with and predominantly used with the famous Hammond organ, takes advantage of the Doppler effect by using an electric motor to rotate an acoustic horn around a loudspeaker, sending its sound in a circle. This results at the listener's ear in rapidly fluctuating frequencies of a keyboard note.

Vibration measurement
A laser Doppler vibrometer (LDV) is a non-contact instrument for measuring vibration. The laser beam from the LDV is directed at the surface of interest, and the vibration amplitude and frequency are extracted from the Doppler shift of the laser beam frequency due to the motion of the surface.

Robotics
Dynamic real-time path planning in robotics to aid the movement of robots in a sophisticated environment with moving obstacles often take help of Doppler effect. Such applications are specially used for competitive robotics where the environment is constantly changing, such as robosoccer.

Inverse Doppler effect
Since 1968 scientists such as Victor Veselago have speculated about the possibility of an inverse Doppler effect. The size of the Doppler shift depends on the refractive index of the medium a wave is traveling through. Some materials are capable of negative refraction, which should lead to a Doppler shift that works in a direction opposite that of a conventional Doppler shift. The first experiment that detected this effect was conducted by Nigel Seddon and Trevor Bearpark in Bristol, United Kingdom in 2003. Later, the inverse Doppler effect was observed in some inhomogeneous materials, and predicted inside a Vavilov–Cherenkov cone.

title: Doppler effect


text:
ΔT (timekeeping)

In precise timekeeping, ΔT (Delta T, delta-T, deltaT, or DT) is a measure of the cumulative effect of the departure of the Earth's rotation period from the fixed-length day of International Atomic Time (86,400 seconds). Formally, ΔT is the time difference $ΔT = TT − UT$ between Universal Time (UT, defined by Earth's rotation) and Terrestrial Time (TT, independent of Earth's rotation). The value of ΔT for the start of 1902 was approximately zero; for 2002 it was about 64 seconds. So Earth's rotations over that century took about 64 seconds longer than would be required for days of atomic time. As well as this long-term drift in the length of the day there are short-term fluctuations in the length of day ($Δτ$) which are dealt with separately.

Since early 2017, the length of the day has happened to be very close to the conventional value, and ΔT has remained within half a second of 69 seconds.

Calculation
Earth's rotational speed is $ν = 1⁄2π dθ⁄dt$, and a day corresponds to one period $P = 1⁄ν$. A rotational acceleration $dν⁄dt$ gives a rate of change of the period of $dP⁄dt = −1⁄ν^{2} dν⁄dt$, which is usually expressed as $α = ν dP⁄dt = −1⁄ν dν⁄dt$. This has units of 1/time, and is commonly quoted as milliseconds-per-day per century (written as ms/day/cy, understood as (ms/day)/cy). Integrating $α$ gives an expression for ΔT against time.

Universal time
Universal Time is a time scale based on the Earth's rotation, which is somewhat irregular over short periods (days up to a century), thus any time based on it cannot have an accuracy better than 1 in 108. However, a larger, more consistent effect has been observed over many centuries: Earth's rate of rotation is inexorably slowing down. This observed change in the rate of rotation is attributable to two primary forces, one decreasing and one increasing the Earth's rate of rotation. Over the long term, the dominating force is tidal friction, which is slowing the rate of rotation, contributing about $α = +2.3$ ms/day/cy or $dP⁄dt = +2.3$ ms/cy, which is equal to the very small fractional change $0$ day/day. The most important force acting in the opposite direction, to speed up the rate, is believed to be a result of the melting of continental ice sheets at the end of the last glacial period. This removed their tremendous weight, allowing the land under them to begin to rebound upward in the polar regions, an effect that is still occurring today and will continue until isostatic equilibrium is reached. This "post-glacial rebound" brings mass closer to the rotational axis of the Earth, which makes the Earth spin faster, according to the law of conservation of angular momentum, similar to an ice skater pulling their arms in to spin faster. Models estimate this effect to contribute about −0.6 ms/day/cy. Combining these two effects, the net acceleration (actually a deceleration) of the rotation of the Earth, or the change in the length of the mean solar day (LOD), is +1.7 ms/day/cy or +62 s/cy2 or +46.5 ns/day2. This matches the average rate derived from astronomical records over the past 27 centuries.

Terrestrial time
Terrestrial Time is a theoretical uniform time scale, defined to provide continuity with the former Ephemeris Time (ET). ET was an independent time-variable, proposed (and its adoption agreed) in the period 1948–1952 with the intent of forming a gravitationally uniform time scale as far as was feasible at that time, and depending for its definition on Simon Newcomb's Tables of the Sun (1895), interpreted in a new way to accommodate certain observed discrepancies. Newcomb's tables formed the basis of all astronomical ephemerides of the Sun from 1900 through 1983: they were originally expressed (and published) in terms of Greenwich Mean Time and the mean solar day, but later, in respect of the period 1960–1983, they were treated as expressed in terms of ET, in accordance with the adopted ET proposal of 1948–52. ET, in turn, can now be seen (in light of modern results) as close to the average mean solar time between 1750 and 1890 (centered on 1820), because that was the period during which the observations on which Newcomb's tables were based were performed. While TT is strictly uniform (being based on the SI second, every second is the same as every other second), it is in practice realised by International Atomic Time (TAI) with an accuracy of about 1 part in 1014.

Earth's rate of rotation
Earth's rate of rotation must be integrated to obtain time, which is Earth's angular position (specifically, the orientation of the meridian of Greenwich relative to the fictitious mean sun). Integrating +1.7 ms/d/cy and centering the resulting parabola on the year 1820 yields (to a first approximation) 32 × ( $year − 1820⁄100$ ) $2$ - 20 seconds for ΔT. Smoothed historical measurements of ΔT using total solar eclipses are about +17190 s in the year −500 (501 BC), +10580 s in 0 (1 BC), +5710 s in 500, +1570 s in 1000, and +200 s in 1500. After the invention of the telescope, measurements were made by observing occultations of stars by the Moon, which allowed the derivation of more closely spaced and more accurate values for ΔT. ΔT continued to decrease until it reached a plateau of +11 ± 6 s between 1680 and 1866. For about three decades immediately before 1902 it was negative, reaching −6.64 s. Then it increased to +63.83 s in January 2000 and +68.97 s in January 2018 and +69.361 s in January 2020, after even a slight decrease from 69.358 s in July 2019 to 69.338 s in September and October 2019 and a new increase in November and December 2019. This will require the addition of an ever-greater number of leap seconds to UTC as long as UTC tracks UT1 with one-second adjustments. (The SI second as now used for UTC, when adopted, was already a little shorter than the current value of the second of mean solar time. ) Physically, the meridian of Greenwich in Universal Time is almost always to the east of the meridian in Terrestrial Time, both in the past and in the future. +17190 s or about $4 3/4$ h corresponds to 71.625°E. This means that in the year −500 (501 BC), Earth's faster rotation would cause a total solar eclipse to occur 71.625° to the east of the location calculated using the uniform TT.

Values prior to 1955
All values of ΔT before 1955 depend on observations of the Moon, either via eclipses or occultations. The angular momentum lost by the Earth due to friction induced by the Moon's tidal effect is transferred to the Moon, increasing its angular momentum, which means that its moment arm (approximately its distance from the Earth, i.e. precisely the semi-major axis of the Moon's orbit) is increased (for the time being about +3.8 cm/year), which via Kepler's laws of planetary motion causes the Moon to revolve around the Earth at a slower rate. The cited values of ΔT assume that the lunar acceleration (actually a deceleration, that is a negative acceleration) due to this effect is $dn⁄dt$ = −26″/cy2, where $n$ is the mean sidereal angular motion of the Moon. This is close to the best estimate for $dn⁄dt$ as of 2002 of −25.858 ± 0.003″/cy2, so ΔT need not be recalculated given the uncertainties and smoothing applied to its current values. Nowadays, UT is the observed orientation of the Earth relative to an inertial reference frame formed by extra-galactic radio sources, modified by an adopted ratio between sidereal time and solar time. Its measurement by several observatories is coordinated by the International Earth Rotation and Reference Systems Service (IERS).

Current values
Recall $ΔT = TT − UT1$ by definition. While TT is only theoretical, it is commonly realized as TAI + 32.184 seconds where TAI is UTC plus the current leap seconds (TAI − UTC is 37 seconds as of 2024 ), so $ΔT = UTC − UT1 + (leap seconds) + 32.184 s$.

This can be rewritten as $ΔT = (leap seconds) + 32.184 s − DUT1$, where DUT1 is UT1 − UTC. The value of DUT1 is sent out in the weekly IERS Bulletin A, as well as several time signal services, and by extension serve as a source of the current $ΔT$.

Geological evidence
Tidal deceleration rates have varied over the history of the Earth-Moon system. Analysis of layering in fossil mollusc shells from 70 million years ago, in the Late Cretaceous period, shows that there were 372 days a year, and thus that the day was about 23.5 hours long then. Based on geological studies of tidal rhythmites, the day was 21.9±0.4 hours long 620 million years ago and there were 13.1±0.1 synodic months/year and 400±7 solar days/year. The average recession rate of the Moon between then and now has been 2.17±0.31 cm/year, which is about half the present rate. The present high rate may be due to near resonance between natural ocean frequencies and tidal frequencies.

title: ΔT (timekeeping)