Spherical Earth or Earth's curvature refers to the approximation of the figure of the Earth to a sphere. The concept of a spherical Earth gradually displaced earlier beliefs in a flat Earth during classical antiquity and the Middle Ages. The figure of the Earth is more accurately described as an ellipsoid, which was realized in the early modern period.
Earth is massive enough that the pull of gravity maintains its roughly spherical shape. Most of its deviation from spherical stems from the centrifugal force caused by rotation around its north-south axis. This force deforms the sphere into an oblate ellipsoid. [1]
The Solar System formed from a dust cloud that was at least partially the remnant of one or more supernovas that produced heavy elements by nucleosynthesis. Grains of matter accreted through electrostatic interaction. As they grew in mass, gravity took over in gathering yet more mass, releasing the potential energy of their collisions and in-falling as heat. The protoplanetary disk also had a greater proportion of radioactive elements than Earth today because, over time, those elements decayed. Their decay heated the early Earth even further, and continue to contribute to Earth's internal heat budget. The early Earth was thus mostly liquid.
A sphere is the only stable shape for a non-rotating, gravitationally self-attracting liquid. The outward acceleration caused by Earth's rotation is greater at the equator than at the poles (where is it zero), so the sphere gets deformed into an ellipsoid, which represents the shape having the lowest potential energy for a rotating, fluid body. This ellipsoid is slightly fatter around the equator than a perfect sphere would be. Earth's shape is also slightly lumpy because it is composed of different materials of different densities that exert slightly different amounts of gravitational force per volume.
The liquidity of a hot, newly formed planet allows heavier elements to sink down to the middle and forces lighter elements closer to the surface, a process known as planetary differentiation. This event is known as the iron catastrophe; the most abundant heavier elements were iron and nickel, which now form the Earth's core.
Though the surface rocks of Earth have cooled enough to solidify, the outer core of the planet is still hot enough to remain liquid. Energy is still being released; volcanic and tectonic activity has pushed rocks into hills and mountains and blown them out of calderas. Meteors also cause impact craters and surrounding ridges. However, if the energy release from these processes halts, then they tend to erode away over time and return toward the lowest potential-energy curve of the ellipsoid. Weather powered by solar energy can also move water, rock, and soil to make Earth slightly out of round.
Earth undulates as the shape of its lowest potential energy changes daily due to the gravity of the Sun and Moon as they move around with respect to Earth. This is what causes tides in the oceans' water, which can flow freely along the changing potential.
The spherical shape of the Earth was known and measured by astronomers, mathematicians, and navigators from a variety of literate ancient cultures, including the Hellenic World, and Ancient India. Greek ethnographer Megasthenes, c. 300 BC, has been interpreted as stating that the contemporary Brahmans of India believed in a spherical Earth as the center of the universe. [2] The knowledge of the Greeks was inherited by Ancient Rome, and Christian and Islamic realms in the Middle Ages. Circumnavigation of the world in the Age of Discovery provided direct evidence. Improvements in transportation and other technologies refined estimations of the size of the Earth, and helped spread knowledge of it.
The earliest documented mention of the concept dates from around the 5th century BC, when it appears in the writings of Greek philosophers. [3] [4] In the 3rd century BC, Hellenistic astronomy established the roughly spherical shape of Earth as a physical fact and calculated the Earth's circumference. This knowledge was gradually adopted throughout the Old World during Late Antiquity and the Middle Ages. [5] [6] [7] [8] A practical demonstration of Earth's sphericity was achieved by Ferdinand Magellan and Juan Sebastián Elcano's circumnavigation (1519–1522). [9]
The concept of a spherical Earth displaced earlier beliefs in a flat Earth: In early Mesopotamian mythology, the world was portrayed as a disk floating in the ocean with a hemispherical sky-dome above, [10] and this forms the premise for early world maps like those of Anaximander and Hecataeus of Miletus. Other speculations on the shape of Earth include a seven-layered ziggurat or cosmic mountain, alluded to in the Avesta and ancient Persian writings (see seven climes).
The realization that the figure of the Earth is more accurately described as an ellipsoid dates to the 17th century, as described by Isaac Newton in Principia . In the early 19th century, the flattening of the earth ellipsoid was determined to be of the order of 1/300 (Delambre, Everest). The modern value as determined by the US DoD World Geodetic System since the 1960s is close to 1/298.25. [11]
Geodesy, also called geodetics, is the scientific discipline that deals with the measurement and representation of Earth, its gravitational field and geodynamic phenomena (polar motion, Earth tides, and crustal motion) in three-dimensional time-varying space.
Geodesy is primarily concerned with positioning and the gravity field and geometrical aspects of their temporal variations, although it can also include the study of Earth's magnetic field. Especially in the German speaking world, geodesy is divided into geomensuration ("Erdmessung" or "höhere Geodäsie"), which is concerned with measuring Earth on a global scale, and surveying ("Ingenieurgeodäsie"), which is concerned with measuring parts of the surface.
Earth's shape can be thought of in at least two ways:
As the science of geodesy measured Earth more accurately, the shape of the geoid was first found not to be a perfect sphere but to approximate an oblate spheroid, a specific type of ellipsoid. More recent[ when? ] measurements have measured the geoid to unprecedented accuracy, revealing mass concentrations beneath Earth's surface.
The roughly spherical shape of Earth can be empirically evidenced by many different types of observation, ranging from ground level, flight, or orbit. The spherical shape causes a number of effects and phenomena that combined disprove flat Earth beliefs.
These include the visibility of distant objects on Earth's surface; lunar eclipses; appearance of the Moon; observation of the sky from a certain altitude; observation of certain fixed stars from different locations; observing the Sun; surface navigation; grid distortion on a spherical surface; weather systems; gravity; and modern technology.
Geodesy or geodetics is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D. It is called planetary geodesy when studying other astronomical bodies, such as planets or circumplanetary systems. Geodesy is an earth science and many consider the study of Earth's shape and gravity to be central to that science. It is also a discipline of applied mathematics.
In geography, latitude is a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at the south pole to 90° at the north pole, with 0° at the Equator. Lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude and longitude are used together as a coordinate pair to specify a location on the surface of the Earth.
Geophysics is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. Geophysicists, who usually study geophysics, physics, or one of the Earth sciences at the graduate level, complete investigations across a wide range of scientific disciplines. The term geophysics classically refers to solid earth applications: Earth's shape; its gravitational, magnetic fields, and electromagnetic fields ; its internal structure and composition; its dynamics and their surface expression in plate tectonics, the generation of magmas, volcanism and rock formation. However, modern geophysics organizations and pure scientists use a broader definition that includes the water cycle including snow and ice; fluid dynamics of the oceans and the atmosphere; electricity and magnetism in the ionosphere and magnetosphere and solar-terrestrial physics; and analogous problems associated with the Moon and other planets.
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry.
An equatorial bulge is a difference between the equatorial and polar diameters of a planet, due to the centrifugal force exerted by the rotation about the body's axis. A rotating body tends to form an oblate spheroid rather than a sphere.
Earth radius is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly 6,378 km (3,963 mi) to a minimum of nearly 6,357 km (3,950 mi).
The geoid is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended through the continents. According to Gauss, who first described it, it is the "mathematical figure of the Earth", a smooth but irregular surface whose shape results from the uneven distribution of mass within and on the surface of Earth. It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of geodesy and geophysics, it has been defined to high precision only since advances in satellite geodesy in the late 20th century.
Physical geodesy is the study of the physical properties of Earth's gravity and its potential field, with a view to their application in geodesy.
Geopotential is the potential of the Earth's gravity field. For convenience it is often defined as the negative of the potential energy per unit mass, so that the gravity vector is obtained as the gradient of the geopotential, without the negation. In addition to the actual potential, a theoretical normal potential and their difference, the disturbing potential, can also be defined.
The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS. The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also describes the associated Earth Gravitational Model (EGM) and World Magnetic Model (WMM). The standard is published and maintained by the United States National Geospatial-Intelligence Agency.
The history of geodesy (/dʒiːˈɒdɪsi/) began during antiquity and ultimately blossomed during the Age of Enlightenment.
In geodesy, the figure of the Earth is the size and shape used to model planet Earth. The kind of figure depends on application, including the precision needed for the model. A spherical Earth is a well-known historical approximation that is satisfactory for geography, astronomy and many other purposes. Several models with greater accuracy have been developed so that coordinate systems can serve the precise needs of navigation, surveying, cadastre, land use, and various other concerns.
In classical mechanics, the gravitational potential is a scalar potential associating with each point in space the work per unit mass that would be needed to move an object to that point from a fixed reference point in the conservative gravitational field. It is analogous to the electric potential with mass playing the role of charge. The reference point, where the potential is zero, is by convention infinitely far away from any mass, resulting in a negative potential at any finite distance. Their similarity is correlated with both associated fields having conservative forces.
The gravity anomaly at a location on the Earth's surface is the difference between the observed value of gravity and the value predicted by a theoretical model. If the Earth were an ideal oblate spheroid of uniform density, then the gravity measured at every point on its surface would be given precisely by a simple algebraic expression. However, the Earth has a rugged surface and non-uniform composition, which distorts its gravitational field. The theoretical value of gravity can be corrected for altitude and the effects of nearby terrain, but it usually still differs slightly from the measured value. This gravity anomaly can reveal the presence of subsurface structures of unusual density. For example, a mass of dense ore below the surface will give a positive anomaly due to the increased gravitational attraction of the ore.
Satellite geodesy is geodesy by means of artificial satellites—the measurement of the form and dimensions of Earth, the location of objects on its surface and the figure of the Earth's gravity field by means of artificial satellite techniques. It belongs to the broader field of space geodesy. Traditional astronomical geodesy is not commonly considered a part of satellite geodesy, although there is considerable overlap between the techniques.
Clairaut's theorem characterizes the surface gravity on a viscous rotating ellipsoid in hydrostatic equilibrium under the action of its gravitational field and centrifugal force. It was published in 1743 by Alexis Claude Clairaut in a treatise which synthesized physical and geodetic evidence that the Earth is an oblate rotational ellipsoid. It was initially used to relate the gravity at any point on the Earth's surface to the position of that point, allowing the ellipticity of the Earth to be calculated from measurements of gravity at different latitudes. Today it has been largely supplanted by the Somigliana equation.
The orthometric height is the vertical distance along the plumb line from a point of interest to a reference surface known as the geoid, the vertical datum that approximates mean sea level. Orthometric height is one of the scientific formalizations of a layman's "height above sea level", along with other types of heights in Geodesy.
The gravity of Earth, denoted by g, is the net acceleration that is imparted to objects due to the combined effect of gravitation and the centrifugal force . It is a vector quantity, whose direction coincides with a plumb bob and strength or magnitude is given by the norm .
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations.
In geodesy, surveying, hydrography and navigation, vertical datum or altimetric datum is a reference coordinate surface used for vertical positions, such as the elevations of Earth-bound features and altitudes of satellite orbits and in aviation. In planetary science, vertical datums are also known as zero-elevation surface or zero-level reference.
