Hawaii is the 50th and most recent state to have joined the United States of America, having received statehood on August 21,1959. Hawaii is the only U. S. state located in Oceania and it is the northernmost island group in Polynesia, occupying most of an archipelago in the central Pacific Ocean. Hawaii is the only U. S. state not located in the Americas, the state encompasses nearly the entire volcanic Hawaiian archipelago, which comprises hundreds of islands spread over 1,500 miles. At the southeastern end of the archipelago, the eight main islands are—in order from northwest to southeast, Niʻihau, Kauaʻi, Oʻahu, Molokaʻi, Lānaʻi, Kahoʻolawe and the Island of Hawaiʻi. The last is the largest island in the group, it is called the Big Island or Hawaiʻi Island to avoid confusion with the state or archipelago. The archipelago is physiographically and ethnologically part of the Polynesian subregion of Oceania, Hawaii has over a million permanent residents, along with many visitors and U. S. military personnel.
Its capital is Honolulu on the island of Oʻahu, Hawaii is the 8th-smallest and the 11th-least populous, but the 13th-most densely populated of the fifty U. S. states. It is the state with an Asian plurality. The states coastline is about 750 miles long, the fourth longest in the U. S. after the coastlines of Alaska, the state of Hawaii derives its name from the name of its largest island, Hawaiʻi. A common Hawaiian explanation of the name of Hawaiʻi is that was named for Hawaiʻiloa and he is said to have discovered the islands when they were first settled. The Hawaiian language word Hawaiʻi is very similar to Proto-Polynesian *Sawaiki, cognates of Hawaiʻi are found in other Polynesian languages, including Māori and Samoan. According to linguists Pukui and Elbert, lsewhere in Polynesia, Hawaiʻi or a cognate is the name of the underworld or of the home, but in Hawaii. A somewhat divisive political issue arose in 1978 when the Constitution of the State of Hawaii added Hawaiian as an official state language.
The title of the constitution is The Constitution of the State of Hawaii. Article XV, Section 1 of the Constitution uses The State of Hawaii, diacritics were not used because the document, drafted in 1949, predates the use of the okina and the kahakō in modern Hawaiian orthography. The exact spelling of the name in the Hawaiian language is Hawaiʻi. In the Hawaii Admission Act that granted Hawaiian statehood, the government recognized Hawaii as the official state name. Official government publications and office titles, and the Seal of Hawaii use the spelling with no symbols for glottal stops or vowel length
An equatorial bulge is a difference between the equatorial and polar diameters of a planet, due to the force exerted by its rotation. A rotating body tends to form an oblate spheroid rather than a sphere, the Earth has an equatorial bulge of 42.77 km, that is, its diameter measured across the equatorial plane is 42.77 km more than that measured between the poles. An observer standing at sea level on either pole, therefore, is 21.36 km closer to Earths centrepoint than if standing at sea level on the equator, the value of Earths radius may be approximated by the average of these radii. An often-cited result of Earths equatorial bulge is that the highest point on Earth, measured from the center outwards, is the peak of Mount Chimborazo in Ecuador, rather than Mount Everest. But since the ocean bulges, like the Earth and the atmosphere, viewing the globe as a series of rotating discs, the radius R toward the poles gets very small and thus a smaller force is produced for the same rotational velocity.
Moving towards the equator, v^2 increases much faster than R, in addition, because the Earth’s dense core is included in the cross sectional disc at the equator, it contributes more to the mass of the disc. Similarly, there is a bulge in the envelope of the oceans surrounding Earth. Sea level at the equator is 21.36 km higher than sea level at the poles, gravity tends to contract a celestial body into a sphere, the shape for which all the mass is as close to the center of gravity as possible. To get a feel for the type of equilibrium that is involved, imagine someone seated in a swivel chair. If the person in the chair pulls the weights towards them, they are doing work, the increase of rotation rate is so strong that at the faster rotation rate the required centripetal force is larger than with the starting rotation rate. Something analogous to this occurs in planet formation, as long as the proto-planet is still too oblate to be in equilibrium, the release of gravitational potential energy on contraction keeps driving the increase in rotational kinetic energy.
As the contraction proceeds the rotation rate keeps going up, hence the force for further contraction keeps going up. There is a point where the increase of rotational energy on further contraction would be larger than the release of gravitational potential energy. The contraction process can only proceed up to point, so it halts there. When the equilibrium state has been reached large scale conversion of energy to heat ceases. In that sense the state is the lowest state of energy that can be reached. The Earths rotation rate is still slowing down, though gradually, estimates of how fast the Earth was rotating in the past vary, because it is not known exactly how the moon was formed. Estimates of the Earths rotation 500 million years ago are around 20 modern hours per day, the Earths rate of rotation is slowing down mainly because of tidal interactions with the Moon and the Sun
The geoid is the shape that the surface of the oceans would take under the influence of Earths gravity and rotation alone, in the absence of other influences such as winds and tides. This surface is extended through the continents, all points on a geoid surface have the same gravity potential energy. The geoid can be defined at any value of gravitational potential such as within the earths crust or far out in space and it does not correspond to the actual surface of Earths crust, but to a surface which can only be known through extensive gravitational measurements and calculations. It is often described as the true figure of the Earth. The surface of the geoid is higher than the reference ellipsoid wherever there is a gravity anomaly. The geoid surface is irregular, unlike the ellipsoid which is a mathematical idealized representation of the physical Earth. Although the physical Earth has excursions of +8,848 m and −429 m, If the ocean surface were isopycnic and undisturbed by tides, currents, or weather, it would closely approximate the geoid.
The permanent deviation between the geoid and mean sea level is called ocean surface topography, If the continental land masses were criss-crossed by a series of tunnels or canals, the sea level in these canals would very nearly coincide with the geoid. This means that when traveling by ship, one does not notice the undulations of the geoid, the vertical is always perpendicular to the geoid. Likewise, spirit levels will always be parallel to the geoid, a long voyage, indicate height variations, even though the ship will always be at sea level. This is because GPS satellites, orbiting about the center of gravity of the Earth, to obtain ones geoidal height, a raw GPS reading must be corrected. Conversely, height determined by spirit leveling from a tidal measurement station, as in land surveying. Modern GPS receivers have a grid implemented inside where they obtain the height over the World Geodetic System ellipsoid from the current position. Then they are able to correct the height above WGS ellipsoid to the height above WGS84 geoid, in that case when the height is not zero on a ship it is due to various other factors such as ocean tides, atmospheric pressure and local sea surface topography.
The gravitational field of the earth is neither perfect n If that perfect sphere were covered in water, the water level would be higher or lower depending on the particular strength of gravity in that location. Spherical harmonics are used to approximate the shape of the geoid. The current best such set of spherical harmonic coefficients is EGM96, the geoid is a particular equipotential surface, and is somewhat involved to compute. The gradient of this provides a model of the gravitational acceleration
A geodetic datum or geodetic system is a coordinate system, and a set of reference points, used to locate places on the Earth. An approximate definition of sea level is the datum WGS84, other datums are defined for other areas or at other times, ED50 was defined in 1950 over Europe and differs from WGS84 by a few hundred meters depending on where in Europe you look. Mars has no oceans and so no sea level, but at least two martian datums have been used to locate places there. Datums are used in geodesy and surveying by cartographers, each starts with an ellipsoid, and defines latitude and altitude coordinates. One or more locations on the Earths surface are chosen as anchor base-points, the difference in co-ordinates between datums is commonly referred to as datum shift. The datum shift between two particular datums can vary from one place to another within one country or region, the North Pole, South Pole and Equator will be in different positions on different datums, so True North will be slightly different.
Different datums use different interpolations for the shape and size of the Earth. Because the Earth is an ellipsoid, localised datums can give a more accurate representation of the area of coverage than WGS84. OSGB36, for example, is an approximation to the geoid covering the British Isles than the global WGS84 ellipsoid. However, as the benefits of a global system outweigh the greater accuracy, horizontal datums are used for describing a point on the Earths surface, in latitude and longitude or another coordinate system. Vertical datums measure elevations or depths, in surveying and geodesy, a datum is a reference system or an approximation of the Earths surface against which positional measurements are made for computing locations. Horizontal datums are used for describing a point on the Earths surface, vertical datums are used to measure elevations or underwater depths. The horizontal datum is the used to measure positions on the Earth. A specific point on the Earth can have different coordinates.
There are hundreds of local horizontal datums around the world, usually referenced to some convenient local reference point, contemporary datums, based on increasingly accurate measurements of the shape of the Earth, are intended to cover larger areas. The WGS84 datum, which is almost identical to the NAD83 datum used in North America, a vertical datum is used as a reference point for elevations of surfaces and features on the Earth including terrain, water levels, and man-made structures. Vertical datums are either, based on sea levels, based on a geoid, or geodetic, for the purpose of measuring the height of objects on land, the usual datum used is mean sea level. This is a datum which is described as the arithmetic mean of the hourly water elevation taken over a specific 19 years cycle
Mean sea level is an average level of the surface of one or more of Earths oceans from which heights such as elevations may be measured. A common and relatively straightforward mean sea-level standard is the midpoint between a low and mean high tide at a particular location. Sea levels can be affected by factors and are known to have varied greatly over geological time scales. The careful measurement of variations in MSL can offer insights into ongoing climate change, the term above sea level generally refers to above mean sea level. Precise determination of a sea level is a difficult problem because of the many factors that affect sea level. Sea level varies quite a lot on several scales of time and this is because the sea is in constant motion, affected by the tides, atmospheric pressure, local gravitational differences, salinity and so forth. The easiest way this may be calculated is by selecting a location and calculating the mean sea level at that point, for example, a period of 19 years of hourly level observations may be averaged and used to determine the mean sea level at some measurement point.
One measures the values of MSL in respect to the land, hence a change in MSL can result from a real change in sea level, or from a change in the height of the land on which the tide gauge operates. In the UK, the Ordnance Datum is the sea level measured at Newlyn in Cornwall between 1915 and 1921. Prior to 1921, the datum was MSL at the Victoria Dock, in Hong Kong, mPD is a surveying term meaning metres above Principal Datum and refers to height of 1. 230m below the average sea level. In France, the Marégraphe in Marseilles measures continuously the sea level since 1883 and it is used for a part of continental Europe and main part of Africa as official sea level. Elsewhere in Europe vertical elevation references are made to the Amsterdam Peil elevation, satellite altimeters have been making precise measurements of sea level since the launch of TOPEX/Poseidon in 1992. A joint mission of NASA and CNES, TOPEX/Poseidon was followed by Jason-1 in 2001, height above mean sea level is the elevation or altitude of an object, relative to the average sea level datum.
It is used in aviation, where some heights are recorded and reported with respect to sea level, and in the atmospheric sciences. An alternative is to base height measurements on an ellipsoid of the entire Earth, in aviation, the ellipsoid known as World Geodetic System 84 is increasingly used to define heights, differences up to 100 metres exist between this ellipsoid height and mean tidal height. The alternative is to use a vertical datum such as NAVD88. When referring to geographic features such as mountains on a topographic map, the elevation of a mountain denotes the highest point or summit and is typically illustrated as a small circle on a topographic map with the AMSL height shown in metres, feet or both. In the rare case that a location is below sea level, for one such case, see Amsterdam Airport Schiphol
The Cape Peninsula is a generally rocky peninsula that juts out into the Atlantic Ocean at the south-western extremity of the African continent. At the southern end of the peninsula are Cape Point and the Cape of Good Hope, on the northern end is Table Mountain, overlooking Cape Town, South Africa. The peninsula is 52 km long from Mouille point in the north to Cape Point in the south. The Peninsula has been an island on and off for the past 5 million years, as sea levels fell and rose with the ice age and interglacial global warming cycles of, the Pleistocene. The last time that the Peninsula was an island was about 1.5 million years ago, soon afterwards it was joined to the mainland by the emergence from the sea of the sandy area now known as the Cape Flats. The towns and villages of the Cape Peninsula and Cape Flats now form part of the City of Cape Town Metropolitan Municipality, the Cape of Good Hope is sometimes given as the meeting point of the Atlantic and Indian Oceans. Thus the west coast of the Peninsula is invariably referred to as the Atlantic Coast and it is at Cape Point that the ocean to the south is often said to be divided into the Atlantic Ocean to the west, and the Indian Ocean to the east.
However, according to the International Hydrographic Organization agreement that defines the ocean boundaries, from there it is retroflexed in an easterly direction by the South Atlantic, South Indian and Southern Ocean currents, known as the West Wind Drift, which flow eastwards round Antarctica. The Benguela Current, on the hand, is an upwelling current which brings cold. Having reached the surface it flows northwards as a result of the prevailing wind, thus the Benguela and Agulhas currents do not strictly meet anywhere, although eddies from the Agulhas current do from time to time round the Cape to join the Benguela Current. The park comprises a part of the undeveloped area of the Cape Peninsula. The coastal waters surrounding the Cape Peninsula are proclaimed as a protected area since 2004, and include several no-take zones. The waters of this protected area are unusual in that they are parts of two fairly distinct marine bioregions, namely the Agulhas Bioregion and the South-western Cape Bioregion.
The boundary is at Cape Point, the Cape Peninsula has an unusually rich biodiversity. Its vegetation consists predominantly of several different types of the unique, on the sandy Cape Flats lowlands there are a few pockets of protected Cape Flats Sand Fynbos. The Peninsulas vegetation types form part of the Cape Floral Region protected areas, many of these species, including a great many types of proteas, are endemic to these mountains and can be found nowhere else. It is a showy orchid that blooms from January to March on the Table Mountain Sandstone regions of the mountain. Although they are widespread on the Back Table, the best place to view these beautiful blooms is in the Aqueduct off the Smuts Track
A histogram is a graphical representation of the distribution of numerical data. It is an estimate of the probability distribution of a variable and was first introduced by Karl Pearson. It is a kind of bar graph, to construct a histogram, the first step is to bin the range of values—that is, divide the entire range of values into a series of intervals—and count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping intervals of a variable, the bins must be adjacent, and are often of equal size. If the bins are of size, a rectangle is erected over the bin with height proportional to the frequency — the number of cases in each bin. A histogram may be normalized to display relative frequencies and it shows the proportion of cases that fall into each of several categories, with the sum of the heights equaling 1. However, bins need not be of equal width, in that case, the vertical axis is not the frequency but frequency density — the number of cases per unit of the variable on the horizontal axis.
Examples of variable bin width are displayed on Census bureau data below, as the adjacent bins leave no gaps, the rectangles of a histogram touch each other to indicate that the original variable is continuous. Histograms give a sense of the density of the underlying distribution of the data. The total area of a used for probability density is always normalized to 1. If the length of the intervals on the x-axis are all 1, a histogram can be thought of as a simplistic kernel density estimation, which uses a kernel to smooth frequencies over the bins. This yields a smoother probability density function, which will in general more accurately reflect distribution of the underlying variable, the density estimate could be plotted as an alternative to the histogram, and is usually drawn as a curve rather than a set of boxes. Another alternative is the average shifted histogram, which is fast to compute, the histogram is one of the seven basic tools of quality control. Histograms are sometimes confused with bar charts, a histogram is used for continuous data, where the bins represent ranges of data, while a bar chart is a plot of categorical variables.
Some authors recommend that bar charts have gaps between the rectangles to clarify the distinction, the etymology of the word histogram is uncertain. Sometimes it is said to be derived from the Ancient Greek ἱστός – anything set upright and it is said that Karl Pearson, who introduced the term in 1891, derived the name from historical diagram. This is a toy example, The words used to describe the patterns in a histogram are, skewed left or right and it is a good idea to plot the data using several different bin widths to learn more about it. Here is an example on tips given in a restaurant, here are a couple more examples, The U. S. Census Bureau found that there were 124 million people who work outside of their homes
Digital elevation model
A digital elevation model is a digital model or 3D representation of a terrains surface — commonly for a planet, moon, or asteroid — created from terrain elevation data. There is no usage of the terms digital elevation model, digital terrain model. In most cases the term digital surface model represents the earths surface, in contrast to a DSM, the digital terrain model represents the bare ground surface without any objects like plants and buildings. DEM is often used as a term for DSMs and DTMs. Other definitions equalise the terms DEM and DTM, or define the DEM as a subset of the DTM, there are definitions which equalise the terms DEM and DSM. On the Web definitions can be found which define DEM as a regularly spaced GRID, most of the data providers use the term DEM as a generic term for DSMs and DTMs. All datasets which are captured with satellites, airplanes or other flying platforms are originally DSMs and it is possible to compute a DTM from high resolution DSM datasets with complex algorithms.
In the following the term DEM is used as a term for DSMs and DTMs. A DEM can be represented as a raster or as a vector-based triangular irregular network, the TIN DEM dataset is referred to as a primary DEM, whereas the Raster DEM is referred to as a secondary DEM. The DEM could be acquired through techniques such as photogrammetry, lidar, IfSAR, land surveying, DEMs are commonly built using data collected using remote sensing techniques, but they may be built from land surveying. DEMs are used often in information systems, and are the most common basis for digitally produced relief maps. Mappers may prepare digital elevation models in a number of ways, the SPOT1 satellite provided the first usable elevation data for a sizeable portion of the planets landmass, using two-pass stereoscopic correlation. The HRS instrument on SPOT5 has acquired over 100 million square kilometers of stereo pairs, older methods of generating DEMs often involve interpolating digital contour maps that may have been produced by direct survey of the land surface.
This method is used in mountain areas, where interferometry is not always satisfactory. Note that contour line data or any other sampled elevation datasets are not DEMs, a DEM implies that elevation is available continuously at each location in the study area. The quality of a DEM is a measure of how accurate elevation is at each pixel, the limitation with the GTOPO30 and SRTM datasets is that they cover continental landmasses only, and SRTM does not cover the polar regions and has mountain and desert no data areas. SRTM data, being derived from radar, represents the elevation of the first-reflected surface — quite often tree tops, so, the data are not necessarily representative of the ground surface, but the top of whatever is first encountered by the radar. Submarine elevation data is generated using ship-mounted depth soundings, when land topography and bathymetry is combined, a truly Global Relief Model is obtained
Cape of Good Hope
The Cape of Good Hope is a rocky headland on the Atlantic coast of the Cape Peninsula, South Africa. In fact, the southernmost point of Africa is Cape Agulhas, when following the western side of the African coastline from the equator, the Cape of Good Hope marks the point where a ship begins to travel more eastward than southward. Thus, the first modern rounding of the cape in 1488 by Portuguese explorer Bartolomeu Dias was a milestone in the attempts by the Portuguese to establish trade relations with the Far East. Dias called the cape Cabo das Tormentas, which was the name of the Cape of Good Hope. As one of the capes of the South Atlantic Ocean. It is a waypoint on the Cape Route and the route followed by clipper ships to the Far East and Australia. The term Cape of Good Hope is used in three ways, It is a section of the Table Mountain National Park, within which the cape of the same name, as well as Cape Point. Prior to its incorporation into the park, this section constituted the Cape Point Nature Reserve.
It was the name of the early Cape Colony established by the Dutch in 1652, just before the Union of South Africa was formed, the term referred to the entire region that in 1910 was to become the Cape of Good Hope Province. When Eudoxus was returning from his voyage to India the wind forced him south of the Gulf of Aden. Somewhere along the coast of East Africa, he found the remains of the ship, due to its appearance and the story told by the natives, Eudoxus concluded that the ship was from Gades and had sailed anti-clockwise around Africa, passing the Cape and entering the Indian Ocean. This inspired him to repeat the voyage and attempt a circumnavigation of the continent, organising the expedition on his own account he set sail from Gades and began to work down the African coast. The difficulties were too great, and he was obliged to return to Europe, after this failure he again set out to circumnavigate Africa. Although some, such as Pliny, claimed that Eudoxus did achieve his goal, in the 1450 Fra Mauro map, the Indian Ocean is depicted as connected to the Atlantic.
It sailed for 40 days in a south-westerly direction without ever finding anything other than wind and water. According to these people themselves, the ship went some 2,000 miles ahead until - once favourable conditions came to an end - it turned round and sailed back to Cape Diab in 70 days. The ships called junks that navigate these seas carry four masts or more, some of which can be raised or lowered, and have 40 to 60 cabins for the merchants and only one tiller. They can navigate without a compass, because they have an astrologer, thus one can believe and confirm what is said by both these and those, and that they had therefore sailed 4,000 miles
Equipotential or isopotential in mathematics and physics refers to a region in space where every point in it is at the same potential. This usually refers to a potential, although it can be applied to vector potentials. An equipotential of a potential function in n-dimensional space is typically an dimensional space. The del operator illustrates the relationship between a field and its associated scalar potential field. Note that an equipotential region might be referred as being of equipotential or simply be called an equipotential, an equipotential region of a scalar potential in three-dimensional space is often an equipotential surface, but it can be a three-dimensional region in space. The gradient of the potential is everywhere perpendicular to the equipotential surface. Electrical conductors offer an intuitive example, thus, an equipotential would contain both points a and b as they have the same potential. Extending this definition, an isopotential is the locus of all points that are of the same potential, in gravity, a hollow sphere has a three-dimensional equipotential region inside, with no gravity.
In electrostatics a conductor is an equipotential region. In the case of a conductor, the equipotential region includes the space inside. A ball will not be accelerated by the force of gravity if it is resting on a flat, horizontal surface, equipotential surface Potential gradient Isopotential map Scalar potential Electric Field Applet
A spacecraft is a vehicle, or machine designed to fly in outer space. Spacecraft are used for a variety of purposes, including communications, earth observation, navigation, space colonization, planetary exploration, on a sub-orbital spaceflight, a spacecraft enters space and returns to the surface, without having gone into an orbit. For orbital spaceflights, spacecraft enter closed orbits around the Earth or around other celestial bodies, robotic spacecraft used to support scientific research are space probes. Robotic spacecraft that remain in orbit around a body are artificial satellites. Only a handful of interstellar probes, such as Pioneer 10 and 11, Voyager 1 and 2, orbital spacecraft may be recoverable or not. By method of reentry to Earth they may be divided in non-winged space capsules, Sputnik 1 was the first artificial satellite. It was launched into an elliptical low Earth orbit by the Soviet Union on 4 October 1957, the launch ushered in new political, military and scientific developments, while the Sputnik launch was a single event, it marked the start of the Space Age.
Apart from its value as a technological first, Sputnik 1 helped to identify the upper atmospheric layers density and it provided data on radio-signal distribution in the ionosphere. Pressurized nitrogen in the satellites false body provided the first opportunity for meteoroid detection, Sputnik 1 was launched during the International Geophysical Year from Site No. 1/5, at the 5th Tyuratam range, in Kazakh SSR. The satellite travelled at 29,000 kilometers per hour, taking 96.2 minutes to complete an orbit and this altitude is called the Kármán line. In particular, in the 1940s there were several test launches of the V-2 rocket, as of 2016, only three nations have flown manned spacecraft, USSR/Russia, USA, and China. The first manned spacecraft was Vostok 1, which carried Soviet cosmonaut Yuri Gagarin into space in 1961, there were five other manned missions which used a Vostok spacecraft. The second manned spacecraft was named Freedom 7, and it performed a sub-orbital spaceflight in 1961 carrying American astronaut Alan Shepard to an altitude of just over 187 kilometers, there were five other manned missions using Mercury spacecraft.
Other Soviet manned spacecraft include the Voskhod, flown unmanned as Zond/L1, L3, TKS, China developed, but did not fly Shuguang, and is currently using Shenzhou. Except for the shuttle, all of the recoverable manned orbital spacecraft were space capsules. Manned space capsules The International Space Station, manned since November 2000, is a joint venture between Russia, the United States and several other countries, some reusable vehicles have been designed only for manned spaceflight, and these are often called spaceplanes. The first example of such was the North American X-15 spaceplane, the first reusable spacecraft, the X-15, was air-launched on a suborbital trajectory on July 19,1963. The first partially reusable spacecraft, a winged non-capsule, the Space Shuttle, was launched by the USA on the 20th anniversary of Yuri Gagarins flight