Ch.9 Astronomy

1. Neil F. Comins • William J. Kaufmann III
Discovering the UniverseDiscovering the Universe
Tenth EditionTenth Edition
CHAPTER 9CHAPTER 9
Vagabonds of the Solar SystemVagabonds of the Solar System

2. In this chapter, you will discover…In this chapter, you will discover…
 the properties of dwarf planets and small solar systemthe properties of dwarf planets and small solar system
bodiesbodies
 asteroids and meteoroidsasteroids and meteoroids——pieces of interplanetary rockpieces of interplanetary rock
and metaland metal
 cometscomets——objects containing large amounts of ice andobjects containing large amounts of ice and
rocky debrisrocky debris
 meteorsmeteors——space debris that falls through Earth’sspace debris that falls through Earth’s
atmosphereatmosphere
 meteoritesmeteorites——space debris that lands on Earthspace debris that lands on Earth
 the asteroid belt and the Kuiper belt, both filled with athe asteroid belt and the Kuiper belt, both filled with a
variety of debris, including orbiting pairs of objectsvariety of debris, including orbiting pairs of objects
 the impacts from space 250 million and 65 million yearsthe impacts from space 250 million and 65 million years
ago that caused mass extinctions of life on Earthago that caused mass extinctions of life on Earth
 wayward asteroids that could again threaten life on Earthwayward asteroids that could again threaten life on Earth

3. Different Classifications of Solar System Objects
Some of the definitions of the
different types of objects in the
solar system overlap. For
example, the largest asteroids
are also being classified as
dwarf planets; various trans-
Neptunian objects (TNOs) are
asteroids or comets; some
comets are satellites of Jupiter;
some Kuiper belt objects
(KBOs) are satellites of other
KBOs. Furthermore, TNOs
exist in two groups: Kuiper belt
objects and Oort comet cloud
bodies. Some moons are as
large as dwarf planets. Indeed,
some moons are as large as
small planets!

4. Objects with unusually high-eccentricity orbits are shown as cyan triangles.
Objects roaming among the outer planets, called Centaur objects, are orange
triangles. Plutinos are white circles. Miscellaneous objects are magenta circles,
and classical KBOs are red circles. Objects observed only once are denoted
by open symbols; objects with two separate observations are denoted by filled
symbols. Comets are filled and unfilled light-blue squares.
Current Positions of Known Dwarf Planets
and SSBs in the Outer Solar System

5. Dwarf Planet Pluto
These three Hubble Space Telescope images of the
dwarf planet Pluto show little detail but indicate that
the major features of Pluto’s surface each cover large
amounts of its area. Comparing these observations to
previous ones reveals that the surface changes in
color and brightness seasonally.

6. Discovery of Pluto
Pluto was discovered in 1930 by searching for a dim,
starlike object that slowly moved against the background
stars. These two photographs were taken one day apart.

7. Orbit of Pluto
(a) The high-eccentricity orbit of dwarf planet (and KBO) Pluto stands
out compared to the orbits of the outer three planets. Notice how many
significant events occurred on Earth during Pluto’s present orbit of the
Sun. (b) Details of Pluto’s passage inside the orbit of Neptune. The two
bodies will never collide.

8. Orbit of Pluto
(c) A nearly edge-on view of the ecliptic and Pluto’s orbit compared with it.

9. Discovery of Charon
Long ignored as just a
defect in the photographic
emulsion, the bump on the
upper left side of this image
of Pluto led astronomer
James Christy to discover
the moon Charon.

10. Pluto and Its Five Known Moons
Observations by the Hubble Space Telescope in 2005 revealed two intermediate-
sized moons, each about 5000 times dimmer than Pluto. Named Nix and Hydra,
they are each about 75 km (50 mi) across and between 2 and 3 times farther from
Pluto than its moon Charon. P4 and P5 are each about 25 km (15 mi) in diameter.

11. Comparison of Ceres with the Moon and Earth
Ceres, the Moon, and Earth are shown here to scale. Dwarf planet Ceres is
the largest asteroid but is so small that it is not considered a planet. Because
it does not orbit a body other than the Sun, it is also not classified as a moon.
This image of Ceres suggests it has regions of ice and rock on its surface.
The asteroid will be visited by the Dawn spacecraft in 2015.

12. Dwarf Planet Eris
Three perpendicular views of the orbit of Eris and Dysnomia are
compared with the planets and Pluto. Eris and Dysnomia’s orbit
around the Sun ranges from 38 to 98 AU, with orbital eccentricity,
e = 0.44, and an orbital inclination of 44°.

13. Dwarf Planet Eris
This is a Keck Telescope image of dwarf planet
Eris and its moon Dysnomia.

14. Asteroid Orbits
(a) The orbits of belt asteroids Ceres, Pallas, and Juno are indicated to scale in this
diagram. Some asteroids that are not in the asteroid belt, such as Apollo and Icarus,
have highly eccentric paths that cross Earth’s orbit. Other non-belt asteroids, called
the Trojan asteroids, follow the same orbit as Jupiter, while other Trojans are in the
orbits of Neptune, Uranus, Mars, and Earth. (b) Actual positions of all known
asteroids at Jupiter’s orbit or closer. The locations of the belt asteroids are indicated
by green dots. Although the asteroids appear packed together in this drawing, they
are typically millions of kilometers apart. The small scale here is deceiving!

15. The Kirkwood Gaps
This graph displays the number of asteroids at various distances from the
Sun. Note that few asteroids have orbital periods that correspond to such
simple fractions as 1/3, 2/5, 3/7, and 1/2 of Jupiter’s orbital period. Resonant
orbits with Jupiter have deflected asteroids away from these orbits. The
Trojan asteroids accompany Jupiter as it orbits the Sun.

16. Jupiter’s Trojan Asteroids
Groups of asteroids orbit at
the two stable Lagrange
points along Jupiter’s orbit,
trapped by the combined
gravitational forces of
Jupiter and the Sun.

17. Discovering Asteroids
In 1998, the Hubble Space Telescope found this asteroid
while observing objects in the constellation Centaurus. The
exposure, tracking stars, shows the asteroid as a 19-arcsec
streak. This asteroid is about 2 km in diameter and was
located about 140 million km (87 million mi) from Earth.

18. Asteroid Vesta
(a) Imaged in 2012 by the Dawn spacecraft, Vesta’s northern and
southern hemispheres have different amounts of cratering. The rough
area on the bottom is the mountain at the south pole and its environs.
(b) Vesta’s internal structure, with iron at the center, surrounded by a
mantle of rock (in green) and a thick crust (in gray).

19. Collision Between Two Asteroids
Observed in 2010, this X-shaped “object” (inset) is believed to be the
collision of an asteroid about 125 m in diameter with a smaller piece of
debris, perhaps 10 m across. The event created dust that was pushed
away from the Sun, which is to the left and below this image. The
collision occurred 2 AU from the Sun and 1 AU from Earth.

20. Asteroid Toutatis
An asteroid whose orbit crosses Earth’s, Toutatis was
imaged by NASA’s Goldstone Solar System Radar in
December, 2012.

21. Ida and Its Satellite
The 55-km-long rocky asteroid Ida, shown here with its satellite
Dactyl, is about twice the size of the younger asteroid Gaspra (see
Figure 5-7). Inset: Dactyl is also heavily cratered.

22. Asteroid 2012 DA14
This image, taken on February 15, 2013, 7 hours before its
closest approach, shows the asteroid as a streak. The camera
tracked stars for 3 minutes in order to obtain the image. At
closest approach, 2012 DA14 was moving so fast that the
same image would have been made in only 15 seconds.

23. Asteroids
(a) Reflecting only half as much light as
a charcoal briquette, Mathilde is half as
dense as typical stony asteroids. Slightly
larger than Ida, irregularly shaped
Mathilde measures 66 km × 48 km × 46
km, rotates once every 17.4 days, and
has a mass equivalent to 110 trillion
tons. The part of the asteroid shown is
about 59 km × 47 km. The large crater in
shadow is about 20 km across.
(b) The near-Earth asteroid
Itokawa was visited by the
Japanese space probe
Hayabusa. Samples of dust
particles from it are now being
analyzed.

24. Asteroid Eros
The Near-Earth Asteroid Rendezvous (NEAR) Shoemaker spacecraft took
these images of asteroid Eros in February 1999. (a) The top of the figure is the
asteroid’s north polar region. Eros’s dimensions are 33 km × 13 km × 13 km (21
mi × 8 mi × 8 mi) and it rotates every 5¼ h. Its density is 2700 kg/m3
, close to
the average density of Earth’s crust and twice as dense as asteroid Mathilde.
(b) This is an image taken while looking into the large crater near the top of (a),
which is 5.3 km (3.3 mi) across. (c) This is the penultimate image taken by
NEAR Shoemaker before it gently landed on Eros. Taken from an altitude of
250 m (820 ft), the image is only 12 m across. You can see rocks and boulders
buried to different depths in the regolith.

25. Kuiper Belt Objects
(a, b) These 1993 images show the discovery
(white lines) of 1 of more than 1524 known
KBOs. These two images of KBO 1993 SC
were taken 4.6 h apart, during which time the
object moved against the background stars.
(c) The KBO 1998
WW31 and its moon
(lower left).

26. Sedna’s Orbit
(a) The farthest known body in the solar system is in a highly elliptical
orbit (b) that orbits between the Kuiper belt and the Oort cloud.

27. The Structure of a Comet
The solid part of a typical comet (the nucleus) is roughly 10 km
in diameter. The coma can be as large as 105
to 106
km across,
and the hydrogen envelope is typically 107
km in diameter. A
comet’s tail can be enormous—even longer than 1 AU.

28. Comet Nuclei
(a) This image, taken by the Giotto spacecraft, shows the potato-
shaped nucleus of Comet Halley. Its dark nucleus measures 15 km in
its longest dimension and about 8 km in its shortest. The numerous
bright areas on the nucleus are icy outcroppings that reflect more
sunlight than surrounding areas of the comet. Two jets of gas can be
seen emanating from the left side of the nucleus. (b) The nucleus of
Hartley 2 is 2 km long. It spins on its short axis once every 18 hours,
while tumbling around its long axis.

29. Comet Wild 2
This picture shows two images combined. One is a high-resolution
photograph showing the surprisingly heavily cratered comet. The
other image is a longer photograph showing gas and dust jetting
from the comet. Its tails are millions of kilometers long.

30. Comet Wild 2
A substance called aerogel was used to capture particles from Comet
Wild 2’s dust tail. A piece of space debris pierced the aluminum foil
holding the aerogel and embedded in it, along with pieces of the foil.

31. Comet Wild 2
A 2-µm piece of comet dust, composed of a mineral called forsterite.
On Earth, this mineral is used to make gems called peridot.

32. Comet Hale-Bopp
In 1997, Comet Hale-Bopp had a hydrogen envelope 1 AU in
diameter (blue ovals). This gas was observed in the ultraviolet. The
visible light inset shows the scale of the visible tails (see also the
image at the opening of this chapter).

33. Comet West
Astronomer Michael M. West first noticed this comet on a photograph
taken with a telescope in 1975. After passing near the Sun, Comet
West became one of the brightest comets of the 1970s. This
photograph shows the comet in the predawn sky in March 1976.

34. The Orbit and Tails of a Comet
The sunlight and solar wind blow a comet’s dust particles
and ionized atoms away from the Sun. Consequently,
comets’ tails always point away from the Sun.

35. The Two Tails of Comet Mrkos
Comet Mrkos dominated the evening sky in August 1957.
These three views, taken at two-day intervals, show
dramatic changes in the comet’s gas tail. In contrast, the
slightly curved dust tail remained fuzzy and featureless.

36. The Head of Comet Brooks
This comet had an exceptionally large, bright coma.
Named after its discoverer, William R. Brooks, it
dominated the night skies in October 1911.

37. The Tail of Comet Ikeya-Seki
Named after its codiscoverers in Japan, this comet dominated the
predawn skies in late October 1965. The yellow in the tail comes from
emission by sodium atoms in the dust that was released by the comet.
Although its coma was tiny, its tail spanned over 1 AU.

38. Comet Tempel 1
(a) This composite image of Comet Tempel 1 has higher
resolution at the bottom, as the projectile from Deep Impact
headed in that direction. The smooth regions on the comet
have yet to be explained. (b) This image was taken 30 s
before the projectile struck the comet.

39. Comet Tempel 1
(c) Seconds after impact, hot debris explodes away from the comet
nucleus. The white horizontal half-ellipses are areas where the
CCDs were overloaded with light from the event. (d) Moments later,
the gases and dust were expanding outward. (e) This is an image
taken 67 s after impact. Within minutes, the cloud of debris
eventually became much larger than the entire nucleus.

40. Transformation and
Evolution of a Long-
Period Comet
(a) The gravitational force of a
giant planet can change a
comet’s orbit. Comets initially
on highly elliptical orbits are
sometimes deflected into
more circular paths that keep
them in the inner solar
system. (b–d) These figures
show the evolution of a comet
into gas, dust, and rubble,
and why debris from some of
these comets strikes Earth.

41. The Fragmentation of Comet Schwassmann-Wachmann-3
This comet, with a 5.4-year orbit, has been coming apart for decades.
In 2006, it further fragmented after passing perihelion. One piece,
Fragment B, shed at least 30 smaller pieces, shown here.

42. Comet Hale-Bopp
Discovered on July 23, 1995, this comet was at its breathtaking best in mid-1997.
Inset: Jets of gas and debris were observed shooting out from Comet Hale-Bopp
several times. This image shows the comet nucleus (lower bright region), an
ejected piece of the comet’s surface (upper bright region), and a spiral tail. The
ejected piece eventually disintegrated, following the same spiral pattern as the tail.

43. Sungrazing Comet
Comet SOHO LASCO C3 is shown in the smaller box and magnified in the
larger one. Discovered in March 2004, it was the 750th
sungrazing comet
discovered from the SOHO data. It completely sublimated near perihelion.

44. Meteor
(a) This brilliant meteor is seen lighting up the dark desert skies of the California
desert area of Joshua Tree National Park. Just to the right of the meteor trail are the
Pleiades. (b) A spectacular bolide over Chelyabinsk, Russia. The fireball lasted about
30 seconds, leaving a smoke trail about 400 km across the sky, and (c) its impact
with the atmosphere produced a powerful shock wave that shattered over a million
square feet of glass, and damaged many buildings such as this zinc plant.

45. Meteorite Impact,
Poughkeepsie, NY, 1992

46. Aftermath of the Tunguska Event
In 1908, a stony asteroid traveling at supersonic speed
struck Earth’s atmosphere and exploded over the
Tunguska region of Siberia. Trees were blown down for
many kilometers in all directions from the impact site.

47. Meteor Crater
An iron meteor measuring 50 m across struck the ground in Arizona 50,000
years ago. The result was this beautifully symmetric impact crater.

48. The Origin of Meteor Showers
As comets dissipate, they leave debris behind that spreads out along
their orbits. When Earth plows through such material, many meteors
can be seen emanating from the same place within a very short time
—a meteor shower. As shown in this diagram, many comets have
high orbital inclinations.

49. Meteor Shower
This time exposure, taken in 1998, shows meteors streaking away from
the constellation Leo Major. They are part of the Leonid meteor
shower. This shower occurs because Earth is moving through debris
left by comet Temple-Tuttle.

50. Recent Impacts on the Moon
The locations A–F are places on the Moon where impacts were observed from
Earth in 1999 during the Leonid meteor shower. The impacting bodies hit the
Moon at around 260,000 km/hr (160,000 mph) and had masses of between 1 and
10 kg. Each impact created a short-lived cloud that momentarily heated to
between 5 × 104
and 10 × 104
K, much hotter than the surface of the Sun.

51. Pieces of the Moon and Mars on
Earth
(a) Meteorite from the Moon
composed of compacted regolith.
(b) A piece of the Tissint meteorite
that landed in Morocco in 2011.
Ejected from Mars as a result of an
impact 700,000 years ago, it is
Martian lava that was weathered
on Mars, primarily by water flow. It
contains trapped gases from
Mars’s atmosphere.

52. The Mass of Impacts on Earth
The Vatican Obelisk is about 300 tons, the amount of mass
that strikes Earth daily. As a result, Earth’s mass increases
by this amount every day.

53. Stony Meteorites
(a) Most meteorites that fall to
Earth are stones. Many freshly
discovered specimens, like the
one shown here, are coated with
thin, dark crusts. This stony
meteorite fell in Morocco.
(b) Some stony meteorites
contain tiny specks of iron, which
can be seen when the stones are
cut and polished. This specimen
was discovered in Ohio.

54. Iron Meteorites
(a) Irons are composed almost entirely
of iron-nickel minerals. The surface of
a typical iron is covered with
thumbprint-like depressions created as
the meteorite’s outer layers vaporized
during its high-speed descent through
the atmosphere. This specimen was
found in Argentina.
(b) When cut, polished, and
etched with a weak acid solution,
most iron meteorites exhibit
interlocking crystals in designs,
called Widmanstätten patterns.
This meteorite was found in
Australia.

55. Stony-Iron Meteorite
Stony-irons account for about 1% of all meteorites that fall to
Earth. This specimen, a variety of stony-iron called a pallasite,
was found in Antarctica. It has been sliced and polished.

56. Pieces of the Allende Meteorite
(b) Sliced open, the
Allende meteorite shows
round, rocky inclusions
called chondrules in a
matrix of dark rock.
(a) This carbonaceous chondrite fell
near Chihuahua, Mexico, in
February 1969. Note the meteorite’s
dark color, caused by a high
abundance of carbon. Geologists
believe that this meteorite is a
specimen of primitive planetary
material. The ruler is 15 cm long.

57. Finding a Meteorite in Antarctica
Good places to find meteorites include deserts and ice-covered
regions, such as Antarctica. By surveying such areas,
astronomers and geologists can accurately determine the
correct percentage of each of the different types of meteorites.

58. Iridium-Rich Layer of Clay
This photograph of strata in the Apennine Mountains of Italy shows a
dark-colored layer of iridium-rich clay sandwiched between white
limestone (bottom) from the late Mesozoic era and grayish limestone
(top) from the early Cenozoic era. The coin is the size of a U.S. quarter.

59. Confirming an Extinction-Level Impact Site
By measuring slight variations in the
gravitational attraction of different
materials under Earth’s surface,
geologists create images of
underground features. Concentric
rings of the underground Chicxulub
Crater (right inset) lie under a portion
of the Yucatán Peninsula. This crater
has been dated to 65 million years
ago and is believed to be the site of
the impact that led to the extinction of
the dinosaurs. A piece of 65-million-
year-old meteorite discovered in the
middle of the Pacific Ocean in 1998 is
believed to be a fragment of that
meteorite. The fragment, about 0.3
cm (0.1 in.) long, was cut into two
pieces for study (left inset).

60. Summary of Key IdeasSummary of Key Ideas

61. Asteroids
 Pieces of solar system debris larger than 10 m andPieces of solar system debris larger than 10 m and
composed primarily of rock and metal are calledcomposed primarily of rock and metal are called
asteroids.asteroids.
 Tens of thousands of belt asteroids with diameters largerTens of thousands of belt asteroids with diameters larger
than a kilometer are known to orbit the Sun between thethan a kilometer are known to orbit the Sun between the
orbits of Mars and Jupiter. The gravitational attraction oforbits of Mars and Jupiter. The gravitational attraction of
Jupiter depletes certain orbits within the asteroid belt.Jupiter depletes certain orbits within the asteroid belt.
The resulting Kirkwood gaps occur at simple fractions ofThe resulting Kirkwood gaps occur at simple fractions of
Jupiter’s orbital period.Jupiter’s orbital period.
 Jupiter’s and the Sun’s gravity combine to capture TrojanJupiter’s and the Sun’s gravity combine to capture Trojan
asteroids in two locations, called stable Lagrange points,asteroids in two locations, called stable Lagrange points,
along a planetalong a planet’s orbit. Jupiter, Neptune, Uranus, Mars,’s orbit. Jupiter, Neptune, Uranus, Mars,
and Earth are known to have Trojan asteroids.and Earth are known to have Trojan asteroids.

62. Asteroids
 The Apollo asteroids move in highly elliptical orbits thatThe Apollo asteroids move in highly elliptical orbits that
cross the orbit of Earth. Many of these asteroids willcross the orbit of Earth. Many of these asteroids will
eventually strike the inner planets.eventually strike the inner planets.
 A belt asteroid, Ceres, along with four KBOs (Pluto, Eris,A belt asteroid, Ceres, along with four KBOs (Pluto, Eris,
Haumea, and Makemake) are classified as dwarfHaumea, and Makemake) are classified as dwarf
planets.planets.
 Pluto, a KBO and dwarf planet, is an icy world that mayPluto, a KBO and dwarf planet, is an icy world that may
well resemble the moon Triton.well resemble the moon Triton.

63. Comets
 Comet nuclei are fragments of ice and rock often orbiting at aComet nuclei are fragments of ice and rock often orbiting at a
great inclination to the plane of the ecliptic.great inclination to the plane of the ecliptic.
 Many comet nuclei orbit the Sun in the Kuiper belt, aMany comet nuclei orbit the Sun in the Kuiper belt, a
doughnut-shaped region beyond Neptune. Billions ofdoughnut-shaped region beyond Neptune. Billions of
cometary nuclei are also believed to exist in the sphericalcometary nuclei are also believed to exist in the spherical
Oort cloud located far beyond the Kuiper belt. Some nudgedOort cloud located far beyond the Kuiper belt. Some nudged
into orbits taking them close to the Sun, which is when weinto orbits taking them close to the Sun, which is when we
see their tails.see their tails.
 In the Kuiper belt and Oort cloud, comets have fairly circularIn the Kuiper belt and Oort cloud, comets have fairly circular
orbits. When close to the Sun, they generally move in highlyorbits. When close to the Sun, they generally move in highly
elliptical orbits.elliptical orbits.
 As an icy comet nucleus approaches the Sun, it develops aAs an icy comet nucleus approaches the Sun, it develops a
luminous coma surrounded by a vast hydrogen envelope. Aluminous coma surrounded by a vast hydrogen envelope. A
gas (or ion) tail and a dust tail extend from the comet, pushedgas (or ion) tail and a dust tail extend from the comet, pushed
away from the Sun by the solar wind and radiation pressure.away from the Sun by the solar wind and radiation pressure.

64. Meteoroids, Meteors, and Meteorites
 Boulder-sized and smaller pieces of rock and metal inBoulder-sized and smaller pieces of rock and metal in
space are called meteoroids. When a meteoroid entersspace are called meteoroids. When a meteoroid enters
EarthEarth’s atmosphere, it produces a fiery trail, and it is then’s atmosphere, it produces a fiery trail, and it is then
called a meteor. If part of the object survives the fall, thecalled a meteor. If part of the object survives the fall, the
fragment that reaches Earthfragment that reaches Earth’’s surface is called as surface is called a
meteorite.meteorite.
 Meteorites are grouped in three major classes accordingMeteorites are grouped in three major classes according
to their composition: iron, stony-iron, and stony meteorites.to their composition: iron, stony-iron, and stony meteorites.
Rare stony meteorites, called carbonaceous chondrites,Rare stony meteorites, called carbonaceous chondrites,
may be relatively unmodified material from the primordialmay be relatively unmodified material from the primordial
solar nebula. These meteorites often contain organicsolar nebula. These meteorites often contain organic
hydrocarbon compounds, including amino acids.hydrocarbon compounds, including amino acids.
 Fragments of rock from comets that have vaporized allFragments of rock from comets that have vaporized all
their ices produce meteor showers.their ices produce meteor showers.

65. Meteoroids, Meteors, and Meteorites
 An analysis of the Allende meteorite suggests that aAn analysis of the Allende meteorite suggests that a
nearby supernova explosion may have been involved innearby supernova explosion may have been involved in
the formation of the solar system some 4.6 billion yearsthe formation of the solar system some 4.6 billion years
ago.ago.
 An asteroid that struck Earth 65 million years ago probablyAn asteroid that struck Earth 65 million years ago probably
contributed to the extinction of the dinosaurs and manycontributed to the extinction of the dinosaurs and many
other species. Another impact may have caused theother species. Another impact may have caused the
“Great Dying” of life 250 million years ago. Such“Great Dying” of life 250 million years ago. Such
devastating impacts occur on average every 100 milliondevastating impacts occur on average every 100 million
years.years.

66. Key TermsKey Terms
amino acid
Apollo asteroid
asteroid belt
belt asteroid
carbonaceous chondrite
chondrites
coma (of a comet)
comet
dust tail
dwarf planet
gas (ion) tail
hydrogen envelope
impact crater
iron meteorite
Kirkwood gaps
long-period comet
meteor
meteor shower
meteorite
meteoroid
nucleus (of a comet)
Oort cloud
planet
radiation (photon)
pressure
short-period comet
small solar-system
bodies (SSSBs)
stable Lagrange
points
stony meteorite
stony-iron
meteorite
Trojan asteroid
Widmanstätten
Patterns