document_title: Tornado intensity

question_text: what level of tornado causes the most damage

text: Tornado intensity

text: History of tornado intensity measurements[edit]

text: For many years, before the advent of Doppler radar, scientists had nothing more than educated guesses as to the speed of the winds in a tornado. The only evidence indicating the wind speeds found in the tornado was the damage left behind by tornadoes which struck populated areas. Some believed they reach 400 mph (640 km/h); others thought they might exceed 500 mph (800 km/h), and perhaps even be supersonic. One can still find these incorrect guesses in some old (until the 1960s) literature, such as the original Fujita Intensity Scale developed by Dr. Tetsuya Theodore Fujita in the early '70s. However, one can find accounts (e.g. [1]; be sure to scroll down) of some remarkable work done in this field by a U.S. Army soldier, Sergeant John Park Finley.

text: In 1971, Dr. Tetsuya Theodore Fujita introduced the idea for a scale of tornado winds. With the help of colleague Allen Pearson, he created and introduced what came to be called the Fujita scale in 1973. This is what the F stands for in F1, F2, etc. The scale was based on a relationship between the Beaufort scale and the Mach number scale; the low end of F1 on his scale corresponds to the low end of B12 on the Beaufort scale, and the low end of F12 corresponds to the speed of sound at sea level, or Mach 1. In practice, tornadoes are only assigned categories F0 through F5.

text: The TORRO scale, created by the Tornado and Storm Research Organisation (TORRO), was developed in 1974 and published a year later. The TORRO scale has 12 levels, which cover a broader range with tighter graduations. It ranges from a T0 for extremely weak tornadoes to T11 for the most powerful known tornadoes. T0-T1 roughly correspond to F0, T2-T3 to F1, and so on. While T10+ would be approximately an F5, the highest tornado rated to date on the TORRO scale was a T8.[6][7] There is some debate as to the usefulness of the TORRO scale over the Fujita scale—while it may be helpful for statistical purposes to have more levels of tornado strength, often the damage caused could be created by a large range of winds, rendering it hard to narrow the tornado down to a single TORRO scale category.

text: Research conducted in the late 1980s and 1990s suggested that, even with the implication of the Fujita scale, tornado winds were notoriously overestimated, especially in significant and violent tornadoes. Because of this, in 2006, the American Meteorological Society introduced the Enhanced Fujita scale, to help assign realistic wind speeds to tornado damage. The scientists specifically designed the scale so that a tornado assessed on the Fujita scale and the Enhanced Fujita scale would receive the same ranking. The EF-scale is more specific in detailing the degrees of damage on different types of structures for a given wind speed. While the F-scale goes from F0 to F12 in theory, the EF-scale is capped at EF5, which is defined as "winds ≥200 mph (320 km/h)".[8] In the United States, the Enhanced Fujita scale went into effect on February 2, 2007 for tornado damage assessments and the Fujita scale is no longer used.

text: The first observation which confirmed that F5 winds could occur happened on April 26, 1991. A tornado near Red Rock, Oklahoma was monitored by scientists using a portable Doppler radar, an experimental radar device that measures wind speed. Near the tornado's peak intensity, they recorded a wind speed of 115–120 m/s (260–270 mph). Though the portable radar had uncertainty of ±5–10 m/s (11–22 mph), this reading was probably within the F5 range, confirming that tornadoes were capable of violent winds found nowhere else on earth.

text: Eight years later, during the 1999 Oklahoma tornado outbreak of May 3, 1999, another scientific team was monitoring an exceptionally violent tornado (one which would eventually kill 36 people in the Oklahoma City metropolitan area). At about 7:00 pm, they recorded one measurement of 301 ± 20 mph (484 ± 32 km/h),[9] 50 mph (80 km/h) faster than the previous record. Though this reading is just short of the theoretical F6 rating, the measurement was taken more than 100 feet (30 m) in the air, where winds are typically stronger than at the surface.[citation needed] In rating tornadoes, only surface wind speeds, or the wind speeds indicated by the damage resulting from the tornado, are taken into account. Also, in practice, the F6 rating is not used.

text: While scientists have long theorized that extremely low pressures might occur in the center of tornadoes, there were no measurements to confirm it. A few home barometers had survived close passes by tornadoes, recording values as low as 24 inHg (810 hPa), but these measurements were highly uncertain.[10] However, on June 24, 2003, a group of researchers successfully dropped devices called "turtles" into an F4 tornado near Manchester, South Dakota, one of which measured a pressure drop of more than 100 hPa (3.0 inHg) as the tornado passed directly overhead.[11] Still, tornadoes are widely varied, so meteorologists are still conducting research to determine if these values are typical or not.

text: Typical intensity[edit]

text: In the United States, F0 and F1 (T0 through T3) tornadoes account for 80% of all tornadoes. The rate of occurrence drops off quickly with increasing strength—violent tornadoes (stronger than F4, T8), account for less than 1% of all tornado reports.[5] Worldwide, strong tornadoes account for an even smaller percentage of total tornadoes. Violent tornadoes are extremely rare outside of the United States, Canada and Bangladesh.

text: F5 and EF5 tornadoes are rare, occurring on average once every few years. An F5 tornado was reported in Elie, Manitoba in Canada, on June 22, 2007. Before that, the last confirmed F5 was the 1999 Bridge Creek–Moore tornado, which killed 36 people on May 3, 1999.[12] Nine EF5 tornadoes have occurred in the United States, in Greensburg, Kansas on May 4, 2007; Parkersburg, Iowa on May 25, 2008; Smithville, Mississippi, Philadelphia, Mississippi, Hackleburg, Alabama and Rainsville, Alabama (four separate tornadoes) on April 27, 2011; Joplin, Missouri on May 22, 2011 and El Reno, Oklahoma on May 24, 2011. On May 20, 2013 a confirmed EF5 tornado again struck Moore, Oklahoma.

text: Typical damage[edit]

text:
Tornado rating classifications[4][13][14]

F0
EF0
F1
EF1
F2
EF2
F3
EF3
F4
EF4
F5
EF5

Weak
Strong
Violent

Significant

Intense

text: A typical tornado has winds of 110 mph (180 km/h) or less, is approximately 250 feet (76 m) across, and travels a mile (1.6 km) or so before dissipating.[citation needed] However, tornadic behavior is extremely variable; these figures represent only statistical probability.

text: Two tornadoes that look almost exactly the same can produce drastically different effects. Also, two tornadoes which look very different can produce similar damage. This is due to the fact that tornadoes form by several different mechanisms, and also that they follow a life cycle which causes the same tornado to change in appearance over time. People in the path of a tornado should never attempt to determine its strength as it approaches. Between 1950 and 2014 in the United States, 222 people have been killed by EF1 tornadoes, and 21 have been killed by EF0 tornadoes.[15][16]

text: Weak tornadoes[edit]

text: The vast majority of tornadoes are designated EF1 or EF0, also known as "weak" tornadoes. However, weak is a relative term for tornadoes, as even these can cause significant damage. F0 and F1 tornadoes are typically short-lived—since 1980 almost 75% of tornadoes rated weak stayed on the ground for 1 mile (1.6 km) or less.[12] However, in this time, they can cause both damage and fatalities.

text: EF0 (T0-T1) damage is characterized by superficial damage to structures and vegetation. Well-built structures are typically unscathed, sometimes sustaining broken windows, with minor damage to roofs and chimneys. Billboards and large signs can be knocked down. Trees may have large branches broken off, and can be uprooted if they have shallow roots. Any tornado that is confirmed but causes no damage (i.e. remains in open fields) is always rated EF0 as well.

text: EF1 (T2-T3) damage has caused significantly more fatalities than that caused by EF0 tornadoes. At this level, damage to mobile homes and other temporary structures becomes significant, and cars and other vehicles can be pushed off the road or flipped. Permanent structures can suffer major damage to their roofs.

text:
Weak tornadoes

E/F0 damage: The only significant damage to structures in this picture was caused by falling tree branches. Even though well-built structures are typically unscathed by E/F0 tornadoes, falling trees and tree branches can injure and kill people, even inside a sturdy structure. Between 35% to 40% of all annual tornadoes in the U.S. are E/F0 tornadoes.

E/F1 damage: Cause major damage to mobile homes and automobiles, and can cause minor structural damage to well-constructed homes. This unanchored wood-frame home sustained major roof damage, and was pushed from its foundation while remaining intact. Around 35% of all annual tornadoes in the U.S. are E/F1 tornadoes.

text: Significant tornadoes[edit]

text: EF2 (T4-T5) tornadoes are the lower end of "significant", and yet are stronger than most tropical cyclones (though tropical cyclones affect a much larger area and their winds take place for a much longer duration). Well-built structures can suffer serious damage, including roof loss, and collapse of some exterior walls may occur at poorly built structures. Mobile homes, however, are totally destroyed. Vehicles can be lifted off the ground, and lighter objects can become small missiles, causing damage outside of the tornado's main path. Wooded areas will have a large percentage of their trees snapped or uprooted.

text: EF3 (T6-T7) damage is a serious risk to life and limb and the point at which a tornado statistically becomes significantly more destructive and deadly. Few parts of affected buildings are left standing; well-built structures lose all outer and some inner walls. Unanchored homes are swept away, and homes with poor anchoring may collapse entirely. Small vehicles and similarly sized objects are lifted off the ground and tossed as projectiles. Wooded areas will suffer almost total loss of vegetation, and some tree debarking may occur. Statistically speaking, EF3 is the maximum level that allows for reasonably effective residential sheltering in place in a first floor interior room closest to the center of the house (the most widespread tornado sheltering procedure in America for those with no basement or underground storm shelter).

text:
Significant tornadoes

E/F2 damage: At this intensity, tornadoes have a more significant impact on well-built structures, removing the roofs, and collapsing some exterior walls of poorly built structures. E/F2 tornadoes are capable of completely destroying mobile homes, and generating large amounts of flying debris. This frail wood-frame home sustained major structural damage, and it was moved slightly off its foundation, with its roof completely gone. Between 15% to 19% of all annual tornadoes in the U.S. are E/F2 tornadoes.

E/F3 damage: Here, the roof and all but some inner walls of this brick home have been demolished. While taking shelter in a basement, cellar, or inner room improves your odds of surviving a tornado drastically, occasionally even this is not enough. E/F3 and stronger tornadoes only account for about 6% of all annual tornadoes in the United States, and yet since 1980 they have accounted for more than 75% of tornado-related deaths.

text: Violent tornadoes[edit]

text: While isolated examples exist of people surviving E/F5 impacts in their homes—one survivor of the Jarrell F5 sheltered in a bathtub and was miraculously blown to safety as her house disintegrated[17]—surviving an E/F5 impact outside of a robust and properly constructed underground storm shelter is statistically unlikely.

text: EF4 (T8-T9) damage typically results in a total loss of the affected structure. Well-built homes are reduced to a short pile of medium-sized debris on the foundation. Homes with poor or no anchoring will be swept completely away. Large, heavy vehicles, including airplanes, trains, and large trucks, can be pushed over, flipped repeatedly or picked up and thrown. Large, healthy trees are entirely debarked and snapped off close to the ground or uprooted altogether and turned into flying projectiles. Passenger cars and similarly sized objects can be picked up and flung for considerable distances. EF4 damage can be expected to level even the most robustly built homes, making the common practice of sheltering in an interior room on the ground floor of a residence insufficient to ensure survival. A storm shelter, reinforced basement or other subterranean shelter is considered necessary to provide any reasonable expectation of safety against EF4 damage.

text: EF5 (T10-T11) damage represents the upper limit of tornado power, and destruction is almost always total. An EF5 tornado pulls well-built, well-anchored homes off their foundations and into the air before obliterating them, flinging the wreckage for miles and sweeping the foundation clean. Large, steel reinforced structures such as schools are completely leveled. Tornadoes of this intensity tend to shred and scour low-lying grass and vegetation from the ground. Very little recognizable structural debris is generated by EF5 damage, with most materials reduced to a coarse mix of small, granular particles and dispersed evenly across the tornado's damage path. Large, multi-ton steel frame vehicles and farm equipment are often mangled beyond recognition and deposited miles away or reduced entirely to unrecognizable component parts. The official description of this damage highlights the extreme nature of the destruction, noting that "incredible phenomena will occur"; historically, this has included such awesome displays of power as twisting skyscrapers, leveling entire communities, and stripping asphalt from roadbeds. Despite their relative rarity, the damage caused by EF5 tornadoes represents a disproportionately extreme hazard to life and limb— since 1950 in the United States, only 58 tornadoes (0.1% of all reports) have been designated F5 or EF5, and yet these have been responsible for more than 1300 deaths and 14,000 injuries (21.5% and 13.6%, respectively).[12][18]

text:
Violent tornadoes

E/F4 damage: Brick homes reduced to piles of rubble. Above-ground structures are almost completely vulnerable to E/F4 tornadoes, which level well-built structures, toss heavy vehicles through the air, and uproot trees, turning them into flying missiles. Around 1.1% of annual tornadoes in the U.S. are E/F4 tornadoes.

E/F5 damage: These tornadoes cause complete destruction, obliterating and sweeping away almost anything in their paths, including those sheltering in open basements. However, they are extremely rare (making up less than 0.1% of annual tornadoes in the U.S.), and even a tornado rated as E/F5 usually only produces E/F5 damage across a relatively small portion of the damage path (with F4-F0 damage zones surrounding the central E/F5 core).[19] While isolated examples exist of people surviving E/F5 impacts in their homes—one survivor of the Jarrell F5 sheltered in a bathtub and was miraculously blown to safety as her house disintegrated[20]—surviving an E/F5 impact outside of a robust and properly constructed underground storm shelter is statistically unlikely.


document_title: Lost in Space (2018 TV series)

question_text: who stars in the netflix lost in space

question_tokens: who stars in the netflix lost in space

root

text: Lost in Space (2018 TV series)

text: Premise[edit]

text: In the year 2048 the Robinson family is selected for the 24th mission of the Resolute, an interstellar spacecraft which will carry selected families to colonize a new world. The Resolute was built after a celestial object, dubbed "The Christmas Star" by the media, crashed into Earth a few years earlier, threatening humanity's survival on Earth. Before they reach their destination, an alien robot breaches the Resolute's hull. Some of the families are forced to evacuate the mothership in their short range Jupiter spacecraft. The Robinsons and other colonists crash land on a nearby habitable planet where they battle the strange new environment and their own personal demons as they attempt to find a way back to the Resolute.[1]

tag: p

text: Cast[edit]

text: Main[edit]

text:
Molly Parker as Maureen Robinson, a fearless and brilliant aerospace engineer taking her family on the mission to colonize Alpha Centauri for a new life on a better world. She is a mission commander. She is married to John Robinson and is the mother of three children.[3]
Toby Stephens as John Robinson, a former U.S. Navy SEAL, and husband to Maureen. He is the biological father of Maureen's two youngest children.[4]
Maxwell Jenkins as Will Robinson, the 11-year-old son and youngest child of Maureen and John Robinson.[5]
Taylor Russell as Judy Robinson, Maureen's 18-year-old biracial daughter and eldest child. She is a mission doctor, having received accelerated medical training.[6][7]
Mina Sundwall as Penny Robinson, the 15-year old daughter and middle Robinson child.[7][8]
Ignacio Serricchio as Don West, a mechanic who also smuggles luxury goods. He has a chicken named Debbie, which he claims to be lucky.[9]
Parker Posey as Dr. Smith. She is a criminal and a sociopath who uses other people's identities to claim their belongings. Dr. Smith, whose real name is June Harris, stole her sister Jessica's identity and place on the colony ship. There she impersonates a Dr. Zachary Smith, to take his seat on an evacuating Jupiter ship. After landing on the planet, Dr. Smith attempts to sabotage the Jupiters' chances of being rescued by the Resolute while manipulating and gaslighting the survivors to avoid prosecution for her crimes.[10] The theft of the doctor's identity is a reference to the corresponding Dr. Smith character of the original TV series.[11]
Brian Steele as the Robot,[12] an alien mechanoid being that Will encounters on the planet that his family crash lands on. The robot has a different form from the ones on the previous series and movie.[13]

tag: ul

text: Episodes[edit]

text: This section's plot summaries may be too long or excessively detailed. Please help improve them by removing unnecessary details and making them more concise. (May 2018) (Learn how and when to remove this template message)

tag: table

text:
No.
Title
Directed by
Written by
Original release date

1
"Impact"
Neil Marshall
Matt Sazama & Burk Sharpless
April 13, 2018 (2018-04-13)

The spacecraft Resolute, a large ferris wheel style ship, is carrying colonists, including the Robinson family, to Alpha Centauri. The Resolute is attacked and colonists escape in their “family home” Jupiter landing crafts but are hurled into a wormhole, crash-landing on an Earth-like planet. The Robinsons' craft, Jupiter 2, crashes into a glacial bed. The family evacuates with some supplies before their craft sinks in rapidly freezing water. Eldest Robinson child, Judy, a doctor, dives to the ship to retrieve power equipment. She becomes encased in ice, and with five hours of oxygen left in Judy's suit, John and son, Will, set out to collect magnesium that will melt the ice. Judy guides her sister, Penny, through a medical procedure to treat their injured mother, Maureen. Inside a cave, Will falls down a chasm, landing at the edge of a forest. John radios Will, saying he will return after saving Judy. Alone, Will finds a crashed alien ship and a dismembered robot that he helps to self-repair. In return, it saves Will as a forest fire nearly engulfs them. The family attempt to free Judy, but a sudden rainstorm hinders their progress. Will and the Robot arrive, and the Robot rescues Judy. In a flashback scene, a woman steals the identity of Dr. Zachary Smith and boards a Jupiter landing craft, along with Don West and Tam Roughneck.

2
"Diamonds In The Sky"
Neil Marshall
Matt Sazama & Burk Sharpless
April 13, 2018 (2018-04-13)

Don West, Smith, and Debbie the chicken survive the Jupiter 18 landing. While looking for other survivors, they find Angela Goddard, who is barely alive. When a storm approaches, Don and Angela take cover while Smith heads out. Meanwhile, the robot melts more ice to allow the Robinsons to start the process of recovering the Jupiter 2. Maureen, John, Will and the robot hike to another Jupiter crash site and then later to the robot's ship. They leave Penny and Judy behind, instructing them how to carefully raise the ship out of the ice. Inside the alien ship, a holographic map of the planet is activated, showing John and Maureen they are in an unidentified galaxy. Outside, the robot touches the ship's hull, creating a mental connection to Will who learns what really happened on the Resolute. He decides to say nothing to his parents about the vision. When Penny sees the storm approaching and is unable to reach her parents to warn them, she raises the Jupiter 2 enough that the garage can be opened. She drives the ship's Chariot all-terrain vehicle to reach her family just in front of the storm. As they head back to Jupiter 2, they pass Don who sees them only to discover his flare gun is missing. The Robinsons see a flare and find Smith, who claims to be alone, returning with her to the Jupiter 2.

3
"Infestation"
Tim Southam
Zack Estrin
April 13, 2018 (2018-04-13)

In a flashback, Dr. Smith is revealed to be June Harris, the older, ex-con sister of Jess Harris, a successful businesswoman. Jess offers June her entire estate as she is leaving Earth, but June drugs Jess and assumes her sister's identity. Aboard the Resolute, she bumps into her sister's lover and there is a struggle ending in him getting blown out an airlock. June is arrested but escapes during the robot's attack. In the present, Maureen explains they are trillions of light years from Earth. At night, the ice layer over Jupiter 2 cracks, endangering the ship. They rush to complete repairs, but the engines are losing fuel. When Will and the robot discover large eel-like creatures in the conduits, the robot locks Will, along with Smith, in the storeroom for safety. The glacier shifts, which forces the crew to make an emergency take-off after flushing the eels from the engines. They escape with just enough fuel to land near a forest region. Comms pick up radio communication from other Jupiter survivors and also from Resolute, who are searching for survivors. Somebody hacks the onboard 3D printer to make a gun. Will finds it, and hides the gun under his mattress, unaware Smith is watching.

4
"The Robinsons Were Here"
Alice Troughton
Katherine Collins
April 13, 2018 (2018-04-13)

Stuck without fuel, the family initiates Jupiter 2’s colonization expansion protocol. Smith and Will discuss the robot, who does Will's bidding. Don West and Angela are rescued by the Watanabe family; Hiroki Watanabe reunites with John and Maureen at Jupiter 11 where Judy treats Angela. She tells Judy about the attack on Resolute. The Robinsons learn none of the other surviving families can fly due to the giant eels consuming fuel. John notices that one crash site is not a Jupiter ship. Maureen, John, and Don go there and discover the Resolute's comm dish. They realize the Resolute can't hear them. Maureen also discovers contraband whiskey that Don smuggled aboard. Judy confronts Will about the robot, and he reveals he knew it attacked the Resolute. They decide to hide the robot in a nearby cave, unaware Smith is following them. On the way, they're spotted by Vijay Dhar, the son of another survivor group. Penny blackmails him to say nothing about the robot, having found and keeping an item he dropped. While away, Maureen and John discuss their marital problems. The next morning, the kids return to Jupiter 2 before their parents arrive. Smith talks to the robot inside the cave, attempting to instill distrust in it about Will. When John and Maureen return home, the kids tell them that the robot wandered away.

5
"Transmission"
Deborah Chow
Kari Drake
April 13, 2018 (2018-04-13)

The surviving colonists build a light tower to try to signal the Resolute. Maureen, noticing strange weather phenomena, conducts an experiment using a weather balloon. She discovers the sun is paired with a deadly black hole, and that the disturbances will only get worse until the planet is entirely unhabitable. Will ignores Penny and Judy's advice to tell their father about the Robot. Penny develops a crush on Vijay, flirting with him as they move supplies. Don confronts Dr. Smith about the stolen flare gun, though she claims she took it by mistake. In a flashback, Maureen and the kids discuss pros versus cons of going to Alpha Centauri. Judy and Don discuss his smuggling activities. He also reveals his suspicions about Dr. Smith's identity. Judy confronts Dr. Smith about this, but she lies and instead casts doubt on Don. When the colonists activate the light signal, Dr. Smith sneaks away and shuts off the perimeter fence, allowing a large reptilian creature to enter the camp and destroy the light tower. Smith tells John about the kids hiding the robot. When another creature shows up, Dr. Smith tells Will to call the robot. It does save the survivors, but only after Will tells it to defend itself against the creatures. It assumes its original multi-limb form to do this. The colonists witness all of this and recognize the robot from the attack on the Resolute.

6
"Eulogy"
Vincenzo Natali
Ed McCardie
April 13, 2018 (2018-04-13)

Maureen tells her family about the black hole but is afraid the other colonists might panic. John has a heated argument with the other survivors about the robot. In the end, despite an enraged Angela claiming it killed her husband, John convinces the community to allow the robot to stay and takes Will on a hike to discuss Will's responsibility for the robot's actions. He has Will fetch 27 large stones to build a memorial to the casualties. Don takes the community leader and Vijay's father, Victor Dhar, to his Jupiter which crashed in the desert where there are none of the eel-like creatures, and wants money for its fuel. Don also retrieves identification of the real Dr. Smith, later showing Judy. Maureen learns that Hiroki also knows the planet is dying. Penny tells Vijay about the black hole but swears him to secrecy, and they share a kiss. Back at camp, Dr. Smith makes the distraught Angela recount the horrifying details of the robot attack. The emotional Angela enters the hub with the gun Dr. Smith has taken from Will's bunk and arranged for her to find. When she shoots at the robot it goes into attack mode and accidentally injures John before Will gets it to stop. Distraught, Will takes the robot to a cliff and orders it to walk off. He then places a stone on the memorial for the robot.

7
"Pressurized"
Tim Southam
Vivian Lee
April 13, 2018 (2018-04-13)

While driving back to Jupiter 2, Judy is about to tell Dr. Smith she knows the truth about her when Don stops her. When Will is confronted by his mother, he confirms the robot 3D-printed the gun and that he hid it. Anyone could've taken the gun, though. Dr. Smith refuses blame for Angela's attack, and suggests Victor Dhar might have taken the gun. John and Maureen's rover gets stuck in a tar pit. As they sink to the bottom, Maureen admits to doctoring Will's test results. To escape the vehicle, Maureen uses the helium weather balloon to create a shielded path to the surface. Meanwhile, Smith locates the destroyed robot, but cannot get it to reassemble. Don's group speeds through a dangerous geyser field but a tube shakes loose and when Evan fixes the problem, a geyser blast flips the tanker on top of him. Victor realizes that a rock has punctured the tanker and if they move it they'll lose most of the fuel. Despite this Don reluctantly sides with Judy and lifts the tanker, spilling the fuel, but Evan dies anyway. Back on Jupiter 2, Dr. Smith finally manages to reactivate the robot. When Victor returns home, Vijay tells him about the planet's coming demise. Victor decides to use what fuel they did retrieve to launch their own Jupiter 4.

8
"Trajectory"
Stephen Surjik
Katherine Collins & Kari Drake
April 13, 2018 (2018-04-13)

Maureen can't talk Victor out of launching, but John sneaks aboard the Dhar's Jupiter 4 and triggers the emergency shut down. Later, he explains to the gathered colonists how the planet is about to become inhabitable. Penny breaks off with Vijay for him telling his father. Maureen has a plan on how to launch despite the limited fuel, stripping out non-essential modules, and relying on old-school manual piloting. Judy tells Maureen the truth about the real Dr. Smith aboard Don's Jupiter. Returning to Jupiter 2, Maureen confines Dr. Smith to a holding cell. Dr. Smith now claims she is really Jessica Harris, a physicist. Maureen tells John about Smith, and he tells her that Don believes the Jupiter 4 is still too heavy to take off. With life support also removed, the pilot now needs a spacesuit and will need to withstand extreme G-forces. They select John, but not even he can regain consciousness fast enough to make all the maneuvers alone. When the Resolute sends a message that due to Hawking radiation they must leave the planet's orbit within 24 hours, Don reluctantly agrees to help pilot the ship. With his assistance the test run is a success. As John and Don launch in the Jupiter 4, Dr. Smith tricks Will and escapes to knock out Maureen right when John needs her instructions. With everyone watching, the ship explodes mid-air and John and Don are presumed dead.

9
"Resurrection"
Tim Southam
Story by : Daniel McLellan
Teleplay by : Kari Drake
April 13, 2018 (2018-04-13)

Will tries to signal his father using simple radio, convinced he survived the explosion. Dr. Smith drives herself and Maureen to the alien wreck, and tells Maureen she didn't know Maureen was needed for the ship launch, and when she knocked her out, the ship exploded. She does promise helping Maureen get her kids off the planet, if she in return helps Dr. Smith with the alien ship. Will discovers that the rocks he collected in the cave are petrified biomass that can fuel the Jupiter ships to reach the Resolute. While the colonists gather to harvest the biomass, Judy leaves to find Maureen. The colonists find enough biomass to power all the Jupiters, but they must sneak it out quietly to not wake winged predators roosting in the cave. When John manages to send a signal, Penny and others are trapped inside when the blind creatures wake up Throughout the episode, flashbacks reveal the Christmas Star not to be a meteor but an alien craft, and that its engine was used to build The Resolute. The robot's attack was an attempt to retrieve the stolen engine. The group trapped in the cave manage to narrowly escape. Judy uses GPS to track Smith and Maureen. She manages to disable Dr. Smith, but the robot reactivates and is revealed to obey the Doctor's commands.

10
"Danger, Will Robinson"
David Nutter
Matt Sazama & Burk Sharpless
April 13, 2018 (2018-04-13)

John and Don survived the explosion and are clinging to ship wreckage in orbit, with only a few hours of oxygen left. Will is upset to learn the robot now serves Dr. Smith. John responds to Will, confirming that he and Don are still alive. Will tries to bond with the robot again but is rejected. Victor Dhar hails them from the Resolute, telling them it will leave in just over an hour. Maureen traps Dr Smith and the robot in order to search for John and Don. Just as they're about to retrieve them, Dr Smith and the robot escape. Maureen leads the robot into the garage, as an alien ship arrives to retrieve the engine. When the alien robot is about to kill Will, his robot remembers him and attacks the alien robot, saving Will. In the fight, both robots are flung out into space and the garage ramp is damaged. Will goes outside the hull to manually close the hatch. Afterwards, he loses his grip but is saved by his father, who was rescued by Dr. Smith. With everyone safely back on the Jupiter, Maureen is grateful to Dr. Smith, but still locks her up. Before they can dock with the Resolute, the alien engine aboard the Jupiter 2 sends it and the Robinsons to a different galaxy. Will recognizes its shape from the robot's sand drawing: Danger.

text: Production[edit]

text: Development[edit]

text: In October 2014, it was announced that Legendary Television and Synthesis Entertainment were developing a new reboot of Lost in Space and had hired screenwriting duo Matt Sazama and Burk Sharpless to pen the pilot episodes.[14] In November 2015, Netflix landed the project.[15][16] On June 29, 2016, Netflix ordered a full 10 episode season of Lost in Space, with Zack Estrin as executive producer and showrunner. Sazama, Sharpless, Kevin Burns, Jon Jashni, Neil Marshall, and Marc Helwig also serve as executive producers.[17]

text: Toby Stephens, speaking about the distinction between the original series and the new show:

text: "It's a very clever, modern reworking of a great story. Lost in Space is Swiss Family Robinson in space, so it was a story that existed before Lost in Space. The fundamental story is that it's a family that is lost in a difficult, life-threatening situation and how it challenges them and brings them closer together. That is essentially what the story of this is, it's just the context is a lot more modern. It's a more modern take on the '60s version. If you look at it now, it's charming, but it seems so innocent. Whereas this is a version that is for our time. I'm hoping it will still have humour and humanity in it, but it has obviously gotta be for a modern audience."[18]

text: Filming[edit]

text: Production on the first season began in January 2017, in Vancouver, British Columbia, and concluded in June 2017.[19][20]

text: Release[edit]

text: The series was released on April 13, 2018, on Netflix.[1] On March 31, 2018, the pilot of the series was screened at Awesome Con in Washington, D.C., followed by a Q&A session with series executive producers and writers Matt Sazama and Burk Sharpless.[21]

text: Reception[edit]

text: The review aggregator website Rotten Tomatoes reported a 68% approval rating with an average rating of 5.26/10, based on 49 reviews. The website's critical consensus reads, "Lost in Space's production values are ambitious enough to attract sci-fi adventure fans, while the story's large heart adds an emotional anchor to all the deep space derring-do."[22] Metacritic, which uses a weighted average, assigned a normalized score of 58 out of 100 based on 27 critics, indicating "mixed or average reviews".[23]

text: David Griffin of IGN gave the first season a rating of 8.5/10 calling it "an excellent sci-fi adventure with a slight villain problem," giving particular praise to the Robinson family, while criticizing Parker Posey's Dr. Smith as an unsophisticated and one-dimensional character that lacks redeeming qualities.[24] In contrast, Jen Chaney of Vulture characterized Posey's performance as providing "understated, sly comedic touches".[25]


document_title: Bring It On: All or Nothing

question_text: who plays letty in bring it on all or nothing

text: Bring It On: All or Nothing

text: Plot[edit]

text: Britney Allen is living a 'dream life' as the cheerleading captain and girlfriend of Brad Warner, the star quarterback of Pacific Vista High School. Her nemesis is the highly ambitious Winnie Harper. Her life changes dramatically when her father loses his job, and the family must relocate to the disadvantaged city, Crenshaw Heights, which Britney, being the "White Girl", takes quite a while to adjust to.

text: She meets Camille, cheerleading captain of the Crenshaw Heights Warriors and her friends and fellow cheerleaders, Kirresha and Leti. She also meets Jesse, a male cheerleader and the only person who is nice to her on her first day. Britney, at the urging of Winnie, has already vowed to never cheer for another team (as this would make her a 'cheer whore'), but after being dared by Camille and Jesse to show up at the cheerleading tryouts, Britney impresses everyone with her cheerleading skills and experience. Camille, after being persuaded by her friends to "do it for the squad," reluctantly invites her onto the squad. Britney and Jesse become close and eventually kiss.

text: Around this time, singer Rihanna announces a television special where all high school cheerleading squads can compete, with the winners appearing in a music video with her and winning new computers for their school. Winnie finds out that Britney's cheering with the Warriors and reveals this to her friends. A week later, Britney lies to Camille, telling her that she can't cheer at the next game as she's holding a memorial service for her dead dog; when she's actually going to Pacific Vista's Homecoming dance. Camille and Jesse arrive at Britney's to offer their condolences, and when they see Britney and Brad dressed up for the dance, Camille kicks her off the squad.

text: At the dance, Winnie reveals to everyone that she has been sleeping with Brad behind Britney's back causing Britney to dump him and end her friendship with Winnie, telling her that she's "too much of a backstabber to have any real friends". On the day of the auditions, Britney arrives at the Warriors' bus and comes to wish them good luck. When Winnie, with the rest of her team, makes fun of the Warriors, Britney stands up to Winnie and defends them. Camille, impressed by this, lets Britney cheer with them again. Jesse, however, is still mad at her for not telling him that she had a boyfriend before they had kissed. Both of the rivaling teams show their performances. At the auditions, the two finalists are Pacific Vista and Crenshaw Heights. PV wows the audience with their routine and Camille starts getting worried. Then Britney points out that all their steps are repetitive and that they have their secret weapon: Krumping. Now dressed in streetwear instead of their regular uniforms, steps on stage during PV's performance and begins mirroring their steps. Finally, they begin krumping, wiping PV off the stage and impressing Rihanna with their routine. After the Warrior's performance ends, Winnie approaches Rihanna and insists that Crenshaw Heights should be disqualified ("or arrested") for interrupting PV's routine. This leads to an argument between Winnie and the rest of the Pacific Vista squad, during which Britney notes, "Spirit Law states that if there's a cheer mutiny, a squad can vote to replace their captain."

text: Everyone present, even Rihanna and the other performing squads, vote to replace Winnie as the Pacific Vista High cheerleading captain. Winnie protests, dismissing CH's style as "ghetto," to which Rihanna responds that she judges a squad by their skills and not by where they come from. Rihanna ultimately selects Crenshaw Heights as the winners, and the Pacific Vista squad (with Britney's friend Amber as their new captain) comes forward to congratulate them. Britney and Jesse also make up, kissing backstage after their first performance. The film ends with a made-for-film music video of Rihanna's "Pon de Replay" with the Crenshaw Heights squad dancing in the background. During the end credits, the main characters are seen dancing to the outro music as the film ends.

text: Cast[edit]

text:
Hayden Panettiere as Britney Allen
Solange Knowles as Camille
Gus Carr as Jesse
Marcy Rylan as Winnie Harper
Cindy Chiu as Amber
Giovonnie Samuels as Kirresha
Francia Raisa as Leti
Gary LeRoi Gray as Tyson
Danielle Savre as Brianna
Jake McDorman as Brad Warner
Jessica Fife as Sierra
Eric Bruskotter as Timothy Allen
Kiersten Warren as Pamela Allen
Rihanna as herself
Swin Cash as herself

text: Critical reception[edit]

text: Bring It On: All or Nothing received little attention from published movie critics. The American review aggregation website Rotten Tomatoes Audience Score for the movie stands at "70% Liked It" based on more than 247,000 user ratings.[2]

text: Soundtrack[edit]

text:
The song for the music video that the team wins the right to perform in is Rihanna's "Pon De Replay". Her song "SOS" is also featured.
One of the songs featured in the film soundtrack is Gwen Stefani's "Hollaback Girl". The music video for "Hollaback Girl", released in 2004, famously features a cheerleading squad. "What You Waiting For?" and "Rich Girl" another two of Stefani's songs, are also used.
The hip-hop group Fu-Schnickens's "Can We Rock?" (1993) is featured as a remix during the end credits. The remix is a mash-up of the song "Can We Rock?" with Hardknox's "What's Up Doc?"
The title song from Solange Knowles' debut album Solo Star is featured in the movie when the Warriors squad are auditioning.
The unreleased song "Let's Move" by the film's composers, The Transcenders, is also used in the movie during the Pacific Vista Pirates' practice (with Britney as captain). The Transcenders originally created the song for Garfield: A Tail of Two Kitties, another film they'd worked on that same year.
"My Happy Ending" by singer Avril Lavigne features twice in the film.
"Whole Again" by girl group Play is featured.
Weezer's "Beverly Hills" is also featured.
"Dirty Little Secret" by All American Rejects is also featured.
Alana Stone's "On My Own" was featured during the homecoming dance, where Britney and Brad are dancing.
Hayden Panettiere's unreleased song "That Girl" plays throughout the scene where Brad is visiting Britney's house and Britney hides when the pizza delivery guy turns out to be Jesse. In the cast credits Panettiere's surname is misspelt.


document_title: Latitude

question_text: at the equator one degree of latitude is equal to

question_tokens: at the equator one degree of latitude is equal to

text: Latitude

text: Preliminaries[edit]

text: Two levels of abstraction are employed in the definition of latitude and longitude. In the first step the physical surface is modeled by the geoid, a surface which approximates the mean sea level over the oceans and its continuation under the land masses. The second step is to approximate the geoid by a mathematically simpler reference surface. The simplest choice for the reference surface is a sphere, but the geoid is more accurately modeled by an ellipsoid. The definitions of latitude and longitude on such reference surfaces are detailed in the following sections. Lines of constant latitude and longitude together constitute a graticule on the reference surface. The latitude of a point on the actual surface is that of the corresponding point on the reference surface, the correspondence being along the normal to the reference surface which passes through the point on the physical surface. Latitude and longitude together with some specification of height constitute a geographic coordinate system as defined in the specification of the ISO 19111 standard.[a]

text: Since there are many different reference ellipsoids, the precise latitude of a feature on the surface is not unique: this is stressed in the ISO standard which states that "without the full specification of the coordinate reference system, coordinates (that is latitude and longitude) are ambiguous at best and meaningless at worst". This is of great importance in accurate applications, such as a Global Positioning System (GPS), but in common usage, where high accuracy is not required, the reference ellipsoid is not usually stated.

text: In English texts the latitude angle, defined below, is usually denoted by the Greek lower-case letter phi (φ or ϕ). It is measured in degrees, minutes and seconds or decimal degrees, north or south of the equator.

text: The precise measurement of latitude requires an understanding of the gravitational field of the Earth, either to set up theodolites or to determine GPS satellite orbits. The study of the figure of the Earth together with its gravitational field is the science of geodesy.

text: This article relates to coordinate systems for the Earth: it may be extended to cover the Moon, planets and other celestial objects by a simple change of nomenclature.

text: Latitude on the sphere[edit]

text: The graticule on the sphere[edit]

text: The graticule is formed by the lines of constant latitude and constant longitude, which are constructed with reference to the rotation axis of the Earth. The primary reference points are the poles where the axis of rotation of the Earth intersects the reference surface. Planes which contain the rotation axis intersect the surface at the meridians; and the angle between any one meridian plane and that through Greenwich (the Prime Meridian) defines the longitude: meridians are lines of constant longitude. The plane through the centre of the Earth and perpendicular to the rotation axis intersects the surface at a great circle called the Equator. Planes parallel to the equatorial plane intersect the surface in circles of constant latitude; these are the parallels. The Equator has a latitude of 0°, the North Pole has a latitude of 90° North (written 90° N or +90°), and the South Pole has a latitude of 90° South (written 90° S or −90°). The latitude of an arbitrary point is the angle between the equatorial plane and the normal to the surface at that point: the normal to the surface of the sphere is along the radius vector.

text: The latitude, as defined in this way for the sphere, is often termed the spherical latitude, to avoid ambiguity with the geodetic latitude and the auxiliary latitudes defined in subsequent sections of this article.

text: Named latitudes on the Earth[edit]

text: Besides the equator, four other parallels are of significance:

text:
Arctic Circle
66° 34′ (66.57°) N

Tropic of Cancer
23° 26′ (23.43°) N

Tropic of Capricorn
23° 26′ (23.43°) S

Antarctic Circle
66° 34′ (66.57°) S

text: The plane of the Earth's orbit about the Sun is called the ecliptic, and the plane perpendicular to the rotation axis of the Earth is the equatorial plane. The angle between the ecliptic and the equatorial plane is called variously the axial tilt, the obliquity, or the inclination of the ecliptic, and it is conventionally denoted by i. The latitude of the tropical circles is equal to i and the latitude of the polar circles is its complement (90° - i). The axis of rotation varies slowly over time and the values given here are those for the current epoch. The time variation is discussed more fully in the article on axial tilt.[b]

text: The figure shows the geometry of a cross-section of the plane perpendicular to the ecliptic and through the centres of the Earth and the Sun at the December solstice when the Sun is overhead at some point of the Tropic of Capricorn. The south polar latitudes below the Antarctic Circle are in daylight, whilst the north polar latitudes above the Arctic Circle are in night. The situation is reversed at the June solstice, when the Sun is overhead at the Tropic of Cancer. Only at latitudes in between the two tropics is it possible for the Sun to be directly overhead (at the zenith).

text: On map projections there is no universal rule as to how meridians and parallels should appear. The examples below show the named parallels (as red lines) on the commonly used Mercator projection and the Transverse Mercator projection. On the former the parallels are horizontal and the meridians are vertical, whereas on the latter there is no exact relationship of parallels and meridians with horizontal and vertical: both are complicated curves.

text:
Normal Mercator

Transverse Mercator

\

text: Meridian distance on the sphere[edit]

text: On the sphere the normal passes through the centre and the latitude (φ) is therefore equal to the angle subtended at the centre by the meridian arc from the equator to the point concerned. If the meridian distance is denoted by m(φ) then

text: where R denotes the mean radius of the Earth. R is equal to 6,371 km or 3,959 miles. No higher accuracy is appropriate for R since higher-precision results necessitate an ellipsoid model. With this value for R the meridian length of 1 degree of latitude on the sphere is 111.2 km or 69.1 miles. The length of 1 minute of latitude is 1.853 km or 1.151 miles (see nautical mile).

text: Latitude on the ellipsoid[edit]

text: Ellipsoids[edit]

text: In 1687 Isaac Newton published the Philosophiæ Naturalis Principia Mathematica, in which he proved that a rotating self-gravitating fluid body in equilibrium takes the form of an oblate ellipsoid.[1] (This article uses the term ellipsoid in preference to the older term spheroid.) Newton's result was confirmed by geodetic measurements in the 18th century. (See Meridian arc.) An oblate ellipsoid is the three-dimensional surface generated by the rotation of an ellipse about its shorter axis (minor axis). "Oblate ellipsoid of revolution" is abbreviated to 'ellipsoid' in the remainder of this article. (Ellipsoids which do not have an axis of symmetry are termed triaxial.)

text: Many different reference ellipsoids have been used in the history of geodesy. In pre-satellite days they were devised to give a good fit to the geoid over the limited area of a survey but, with the advent of GPS, it has become natural to use reference ellipsoids (such as WGS84) with centre at the centre of mass of the Earth and minor axis aligned to the rotation axis of the Earth. These geocentric ellipsoids are usually within 100 m (330 ft) of the geoid. Since latitude is defined with respect to an ellipsoid, the position of a given point is different on each ellipsoid: one cannot exactly specify the latitude and longitude of a geographical feature without specifying the ellipsoid used. Many maps maintained by national agencies are based on older ellipsoids, so one must know how the latitude and longitude values are transformed from one ellipsoid to another. GPS handsets include software to carry out datum transformations which link WGS84 to the local reference ellipsoid with its associated grid.

text: The geometry of the ellipsoid[edit]

text: The shape of an ellipsoid of revolution is determined by the shape of the ellipse which is rotated about its minor (shorter) axis. Two parameters are required. One is invariably the equatorial radius, which is the semi-major axis, a. The other parameter is usually (1) the polar radius or semi-minor axis, b; or (2) the (first) flattening, f; or (3) the eccentricity, e. These parameters are not independent: they are related by

text: Many other parameters (see ellipse, ellipsoid) appear in the study of geodesy, geophysics and map projections but they can all be expressed in terms of one or two members of the set a, b, f and e. Both f and e are small and often appear in series expansions in calculations; they are of the order 1/300 and 0.08 respectively. Values for a number of ellipsoids are given in Figure of the Earth. Reference ellipsoids are usually defined by the semi-major axis and the inverse flattening, 1/f. For example, the defining values for the WGS84 ellipsoid, used by all GPS devices, are[2]

text:
a (equatorial radius): 7006637813700000000♠6378137.0 m exactly
1/f (inverse flattening): 7002298257223563000♠298.257223563 exactly

text: from which are derived

text:
b (polar radius): 7006635675231420000♠6356752.3142 m
e2 (eccentricity squared): 6997669437999014000♠0.00669437999014

text: The difference between the semi-major and semi-minor axes is about 21 km (13 miles) and as fraction of the semi-major axis it equals the flattening; on a computer monitor the ellipsoid could be sized as 300 by 299 pixels. This would barely be distinguishable from a 300-by-300-pixel sphere, so illustrations usually exaggerate the flattening.

text: Geodetic and geocentric latitudes[edit]

text: The graticule on the ellipsoid is constructed in exactly the same way as on the sphere. The normal at a point on the surface of an ellipsoid does not pass through the centre, except for points on the equator or at the poles, but the definition of latitude remains unchanged as the angle between the normal and the equatorial plane. The terminology for latitude must be made more precise by distinguishing:

text:
Geodetic latitude: the angle between the normal and the equatorial plane. The standard notation in English publications is φ. This is the definition assumed when the word latitude is used without qualification. The definition must be accompanied with a specification of the ellipsoid.
Geocentric latitude: the angle between the radius (from centre to the point on the surface) and the equatorial plane. (Figure below). There is no standard notation: examples from various texts include ψ, q, φ′, φc, φg. This article uses ψ.
Spherical latitude: the angle between the normal to a spherical reference surface and the equatorial plane.
Geographic latitude must be used with care. Some authors use it as a synonym for geodetic latitude whilst others use it as an alternative to the astronomical latitude.
Latitude (unqualified) should normally refer to the geodetic latitude.

text: The importance of specifying the reference datum may be illustrated by a simple example. On the reference ellipsoid for WGS84, the centre of the Eiffel Tower has a geodetic latitude of 48° 51′ 29″ N, or 48.8583° N and longitude of 2° 17′ 40″ E or 2.2944°E. The same coordinates on the datum ED50 define a point on the ground which is 140 metres (460 feet) distant from the tower.[citation needed] A web search may produce several different values for the latitude of the tower; the reference ellipsoid is rarely specified.

text: Length of a degree of latitude[edit]

text: In Meridian arc and standard texts[3][4][5] it is shown that the distance along a meridian from latitude φ to the equator is given by (φ in radians)

text: where M(φ) is the meridional radius of curvature.

text: The distance from the equator to the pole is

text: For WGS84 this distance is 7007100019657290000♠10001.965729 km.

text: The evaluation of the meridian distance integral is central to many studies in geodesy and map projection. It can be evaluated by expanding the integral by the binomial series and integrating term by term: see Meridian arc for details. The length of the meridian arc between two given latitudes is given by replacing the limits of the integral by the latitudes concerned. The length of a small meridian arc is given by[4][5]

text:
ϕ

{\displaystyle \phi }

Δ1
lat
Δ1
long

0°
110.574 km
111.320 km

15°
110.649 km
107.550 km

30°
110.852 km
96.486 km

45°
111.132 km
78.847 km

60°
111.412 km
55.800 km

75°
111.618 km
28.902 km

90°
111.694 km
0.000 km

text: When the latitude difference is 1 degree, corresponding to π/180 radians, the arc distance is about

text:
The distance in metres (correct to 0.01 metre) between latitudes

ϕ

{\displaystyle \phi }

 − 0.5 degrees and

ϕ

{\displaystyle \phi }

 + 0.5 degrees on the WGS84 spheroid is

text: The variation of this distance with latitude (on WGS84) is shown in the table along with the length of a degree of longitude (east-west distance):

text: A calculator for any latitude is provided by the U.S. Government's National Geospatial-Intelligence Agency (NGA).[6]

text: Historically a nautical mile was defined as the length of one minute of arc along a meridian of a spherical earth. An ellipsoid model leads to a variation of the nautical mile with latitude. This was resolved by defining the nautical mile to be exactly 1,852 metres.

text: Auxiliary latitudes[edit]

text: There are six auxiliary latitudes that have applications to special problems in geodesy, geophysics and the theory of map projections:

text:
Geocentric latitude
Reduced (or parametric) latitude
Rectifying latitude
Authalic latitude
Conformal latitude
Isometric latitude

text: The definitions given in this section all relate to locations on the reference ellipsoid but the first two auxiliary latitudes, like the geodetic latitude, can be extended to define a three-dimensional geographic coordinate system as discussed below. The remaining latitudes are not used in this way; they are used only as intermediate constructs in map projections of the reference ellipsoid to the plane or in calculations of geodesics on the ellipsoid. Their numerical values are not of interest. For example, no one would need to calculate the authalic latitude of the Eiffel Tower.

text: The expressions below give the auxiliary latitudes in terms of the geodetic latitude, the semi-major axis, a, and the eccentricity, e. (For inverses see below.) The forms given are, apart from notational variants, those in the standard reference for map projections, namely "Map projections: a working manual" by J. P. Snyder.[7] Derivations of these expressions may be found in Adams[8] and online publications by Osborne[4] and Rapp.[5]

text: Geocentric latitude[edit]

text: The geocentric latitude is the angle between the equatorial plane and the radius from the centre to a point on the surface. The relation between the geocentric latitude (ψ) and the geodetic latitude (φ) is derived in the above references as

text:
The geodetic and geocentric latitudes are equal at the equator and at the poles but at other latitudes they differ by a few minutes of arc. Taking the value of the squared eccentricity as 0.0067 (it depends on the choice of ellipsoid) the maximum difference of

ϕ

−

ψ

{\displaystyle \phi {-}\psi }

 may be shown to be about 11.5 minutes of arc at a geodetic latitude of approximately 45° 6′.[c]

text: Reduced (or parametric) latitude[edit]

text: The reduced or parametric latitude, β, is defined by the radius drawn from the centre of the ellipsoid to that point Q on the surrounding sphere (of radius a) which is the projection parallel to the Earth's axis of a point P on the ellipsoid at latitude φ. It was introduced by Legendre[9] and Bessel[10] who solved problems for geodesics on the ellipsoid by transforming them to an equivalent problem for spherical geodesics by using this smaller latitude. Bessel's notation, u(φ), is also used in the current literature. The reduced latitude is related to the geodetic latitude by:[4][5]

text: The alternative name arises from the parameterization of the equation of the ellipse describing a meridian section. In terms of Cartesian coordinates p, the distance from the minor axis, and z, the distance above the equatorial plane, the equation of the ellipse is:

text: The Cartesian coordinates of the point are parameterized by

text: Cayley suggested the term parametric latitude because of the form of these equations.[11]

text: The reduced latitude is not used in the theory of map projections. Its most important application is in the theory of ellipsoid geodesics, (Vincenty, Karney[12]).

text: Rectifying latitude[edit]

text: The rectifying latitude, μ, is the meridian distance scaled so that its value at the poles is equal to 90 degrees or π/2 radians:

text: where the meridian distance from the equator to a latitude φ is (see Meridian arc)

text: and the length of the meridian quadrant from the equator to the pole (the polar distance) is

text: Using the rectifying latitude to define a latitude on a sphere of radius

text: defines a projection from the ellipsoid to the sphere such that all meridians have true length and uniform scale. The sphere may then be projected to the plane with an equirectangular projection to give a double projection from the ellipsoid to the plane such that all meridians have true length and uniform meridian scale. An example of the use of the rectifying latitude is the Equidistant conic projection. (Snyder, Section 16).[7] The rectifying latitude is also of great importance in the construction of the Transverse Mercator projection.

text: Authalic latitude[edit]

text: The authalic (Greek for same area) latitude, ξ, gives an area-preserving transformation to a sphere.

text: where

text: and

text: and the radius of the sphere is taken as

text: An example of the use of the authalic latitude is the Albers equal-area conic projection.[7]:§14

text: Conformal latitude[edit]

text: The conformal latitude, χ, gives an angle-preserving (conformal) transformation to the sphere.

text: where gd(x) is the Gudermannian function. (See also Mercator projection.) The conformal latitude defines a transformation from the ellipsoid to a sphere of arbitrary radius such that the angle of intersection between any two lines on the ellipsoid is the same as the corresponding angle on the sphere (so that the shape of small elements is well preserved). A further conformal transformation from the sphere to the plane gives a conformal double projection from the ellipsoid to the plane. This is not the only way of generating such a conformal projection. For example, the 'exact' version of the Transverse Mercator projection on the ellipsoid is not a double projection. (It does, however, involve a generalisation of the conformal latitude to the complex plane).

text: Isometric latitude[edit]

text: The isometric latitude is conventionally denoted by ψ (not to be confused with the geocentric latitude): it is used in the development of the ellipsoidal versions of the normal Mercator projection and the Transverse Mercator projection. The name "isometric" arises from the fact that at any point on the ellipsoid equal increments of ψ and longitude λ give rise to equal distance displacements along the meridians and parallels respectively. The graticule defined by the lines of constant ψ and constant λ, divides the surface of the ellipsoid into a mesh of squares (of varying size). The isometric latitude is zero at the equator but rapidly diverges from the geodetic latitude, tending to infinity at the poles. The conventional notation is given in Snyder (page 15):[7]

text: For the normal Mercator projection (on the ellipsoid) this function defines the spacing of the parallels: if the length of the equator on the projection is E (units of length or pixels) then the distance, y, of a parallel of latitude φ from the equator is

text: The isometric latitude ψ is closely related to the conformal latitude χ:

text: Inverse formulae and series[edit]

text: The formulae in the previous sections give the auxiliary latitude in terms of the geodetic latitude. The expressions for the geocentric and reduced latitudes may be inverted directly but this is impossible in the four remaining cases: the rectifying, authalic, conformal, and isometric latitudes. There are two methods of proceeding. The first is a numerical inversion of the defining equation for each and every particular value of the auxiliary latitude. The methods available are fixed-point iteration and Newton–Raphson root finding. The other, more useful, approach is to express the auxiliary latitude as a series in terms of the geodetic latitude and then invert the series by the method of Lagrange reversion. Such series are presented by Adams who uses Taylor series expansions and gives coefficients in terms of the eccentricity.[8] Osborne[4] derives series to arbitrary order by using the computer algebra package Maxima[13] and expresses the coefficients in terms of both eccentricity and flattening. The series method is not applicable to the isometric latitude and one must use the conformal latitude in an intermediate step.

text: Numerical comparison of auxiliary latitudes[edit]

text: The following plot shows the magnitude of the difference between the geodetic latitude, (denoted as the "common" latitude on the plot), and the auxiliary latitudes other than the isometric latitude (which diverges to infinity at the poles). In every case the geodetic latitude is the greater. The differences shown on the plot are in arc minutes. The horizontal resolution of the plot fails to make clear that the maxima of the curves are not at 45° but calculation shows that they are within a few arc minutes of 45°. Some representative data points are given in the table following the plot. Note the closeness of the conformal and geocentric latitudes. This was exploited in the days of hand calculators to expedite the construction of map projections.[7]:108

text:
Approximate difference from geodetic latitude (φ)

φ
Reduced
φ − β
Authalic
φ − ξ
Rectifying
φ − μ
Conformal
φ − χ
Geocentric
φ − ψ

0°
0.00′
0.00′
0.00′
0.00′
0.00′

15°
2.91′
3.89′
4.37′
5.82′
5.82′

30°
5.05′
6.73′
7.57′
10.09′
10.09′

45°
5.84′
7.78′
8.76′
11.67′
11.67′

60°
5.06′
6.75′
7.59′
10.12′
10.13′

75°
2.92′
3.90′
4.39′
5.85′
5.85′

90°
0.00′
0.00′
0.00′
0.00′
0.00′

text: Latitude and coordinate systems[edit]

text: The geodetic latitude, or any of the auxiliary latitudes defined on the reference ellipsoid, constitutes with longitude a two-dimensional coordinate system on that ellipsoid. To define the position of an arbitrary point it is necessary to extend such a coordinate system into three dimensions. Three latitudes are used in this way: the geodetic, geocentric and reduced latitudes are used in geodetic coordinates, spherical polar coordinates and ellipsoidal coordinates respectively.

text: Geodetic coordinates[edit]

text: At an arbitrary point P consider the line PN which is normal to the reference ellipsoid. The geodetic coordinates P(ɸ,λ,h) are the latitude and longitude of the point N on the ellipsoid and the distance PN. This height differs from the height above the geoid or a reference height such as that above mean sea level at a specified location. The direction of PN will also differ from the direction of a vertical plumb line. The relation of these different heights requires knowledge of the shape of the geoid and also the gravity field of the Earth.

text: Spherical polar coordinates[edit]

text: The geocentric latitude ψ is the complement of the polar angle θ in conventional spherical polar coordinates in which the coordinates of a point are P(r,θ,λ) where r is the distance of P from the centre O, θ is the angle between the radius vector and the polar axis and λ is longitude. Since the normal at a general point on the ellipsoid does not pass through the centre it is clear that points on the normal, which all have the same geodetic latitude, will have differing geocentric latitudes. Spherical polar coordinate systems are used in the analysis of the gravity field.

text: Ellipsoidal coordinates[edit]

text: The reduced latitude can also be extended to a three-dimensional coordinate system. For a point P not on the reference ellipsoid (semi-axes OA and OB) construct an auxiliary ellipsoid which is confocal (same foci F, F′) with the reference ellipsoid: the necessary condition is that the product ae of semi-major axis and eccentricity is the same for both ellipsoids. Let u be the semi-minor axis (OD) of the auxiliary ellipsoid. Further let β be the reduced latitude of P on the auxiliary ellipsoid. The set (u,β,λ) define the ellipsoid coordinates.[3]:§4.2.2 These coordinates are the natural choice in models of the gravity field for a uniform distribution of mass bounded by the reference ellipsoid.

text: Coordinate conversions[edit]

text: The relations between the above coordinate systems, and also Cartesian coordinates are not presented here. The transformation between geodetic and Cartesian coordinates may be found in Geographic coordinate conversion. The relation of Cartesian and spherical polars is given in Spherical coordinate system. The relation of Cartesian and ellipsoidal coordinates is discussed in Torge.[3]

text: Astronomical latitude[edit]

text: Astronomical latitude (Φ) is the angle between the equatorial plane and the true vertical at a point on the surface. The true vertical, the direction of a plumb line, is also the direction of the gravity acceleration, the resultant of the gravitational acceleration (mass-based) and the centrifugal acceleration at that latitude.[3] Astronomic latitude is calculated from angles measured between the zenith and stars whose declination is accurately known.

text: In general the true vertical at a point on the surface does not exactly coincide with either the normal to the reference ellipsoid or the normal to the geoid. The angle between the astronomic and geodetic normals is usually a few seconds of arc but it is important in geodesy.[3][14] The reason why it differs from the normal to the geoid is, because the geoid is an idealized, theoretical shape "at mean sea level". Points on the real surface of the earth are usually above or below this idealized geoid surface and here the true vertical can vary slightly. Also, the true vertical at a point at a specific time is influenced by tidal forces, which the theoretical geoid averages out.

text: Astronomical latitude is not to be confused with declination, the coordinate astronomers use in a similar way to specify the angular position of stars north/south of the celestial equator (see equatorial coordinates), nor with ecliptic latitude, the coordinate that astronomers use to specify the angular position of stars north/south of the ecliptic (see ecliptic coordinates).