Figure of the Earth in the context of "Ellipsoidal geodesic"

Flat Earth is an archaic and scientifically disproven conception of the Earth's shape as a plane or disk. Many ancient cultures subscribed to a flat-Earth cosmography. The model has undergone a recent resurgence as a conspiracy theory in the 21st century.

The idea of a spherical Earth appeared in ancient Greek philosophy with Pythagoras (6th century BC). However, the early Greek cosmological view of a flat Earth persisted among most pre-Socratics (6th–5th century BC). In the early 4th century BC, Plato wrote about a spherical Earth. By about 330 BC, his former student Aristotle had provided strong empirical evidence for a spherical Earth. Knowledge of the Earth's global shape gradually began to spread beyond the Hellenistic world. By the early period of the Christian Church, the spherical view was widely held, with some notable exceptions. In contrast, ancient Chinese scholars consistently describe the Earth as flat, and this perception remained unchanged until their encounters with Jesuit missionaries in the 17th century. Muslim scholars in early Islam maintained that the Earth is flat. However, since the 9th century, Muslim scholars have tended to believe in a spherical Earth.

Spherical Earth or Earth's curvature refers to the approximation of the figure of the Earth as a sphere. The earliest documented mention of the concept dates from around the 5th century BC, when it appears in the writings of Greek philosophers. 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, displacing earlier beliefs in a flat Earth. A practical demonstration of Earth's sphericity was achieved by Ferdinand Magellan and Juan Sebastián Elcano's circumnavigation (1519–1522).

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. The scientific study of the shape of the Earth is known as geodesy.

An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's shape and size, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different reference ellipsoids have been used as approximations.

It is an oblate spheroid (an ellipsoid of revolution) whose minor axis (polar diameter), connecting the geographical poles, is approximately aligned with the Earth's axis of rotation. The ellipsoid is also defined by the major axis (equatorial axis); the difference between the two axes is slightly more than 21 km or 0.335%.

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.

Geodynamical phenomena, including crustal motion, tides, and polar motion, can be studied by designing global and national control networks, applying space geodesy and terrestrial geodetic techniques, and relying on datums and coordinate systems.

A shape is a graphical representation of an object's form or its external boundary, outline, or external surface. It is distinct from other object properties, such as color, texture, or material type.In geometry, shape excludes information about the object's position, size, orientation and chirality.A figure is a representation including both shape and size (as in, e.g., figure of the Earth).

A plane shape or plane figure is constrained to lie on a plane, in contrast to solid 3D shapes.A two-dimensional shape or two-dimensional figure (also: 2D shape or 2D figure) may lie on a more general curved surface (a two-dimensional space).

Alexis Claude Clairaut (/klɛərˈroʊ/; French: [alɛksi klod klɛʁo]; 13 May 1713 – 17 May 1765) was a French mathematician, astronomer, and geophysicist. He was a prominent Newtonian whose work helped to establish the validity of the principles and results that Sir Isaac Newton had outlined in the Principia of 1687. Clairaut was one of the key figures in the expedition to Lapland that helped to confirm Newton's theory for the figure of the Earth. In that context, Clairaut worked out a mathematical result now known as "Clairaut's theorem". He also tackled the gravitational three-body problem, being the first to obtain a satisfactory result for the apsidal precession of the Moon's orbit. In mathematics he is also credited with Clairaut's equation and Clairaut's relation.

The geoid (/ˈdʒiː.ɔɪd/ JEE-oyd) 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 (such as might be approximated with very narrow hypothetical canals). According to Carl Friedrich 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.

The geoid is often expressed as a geoid undulation or geoidal height above a given reference ellipsoid, which is a slightly flattened sphere whose equatorial bulge is caused by the planet's rotation. Generally the geoidal height rises where the Earth's material is locally more dense and exerts greater gravitational force than the surrounding areas. The geoid in turn serves as a reference coordinate surface for various vertical coordinates, such as orthometric heights, geopotential heights, and dynamic heights (see Geodesy).

Geophysics (/ˌdʒiːoʊˈfɪzɪks/) is a subject of natural science concerned with the physical processes and properties of Earth and its surrounding space environment, and the use of quantitative methods for their analysis. Geophysicists conduct investigations across a wide range of scientific disciplines. The term geophysics classically refers to solid earth applications: Earth's shape; its gravitational, magnetic, 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.

Although geophysics was only recognized as a separate discipline in the 19th century, its origins date back to ancient times. The first magnetic compasses were made from lodestones, while more modern magnetic compasses played an important role in the history of navigation. The first seismic instrument was built in 132 AD. Isaac Newton applied his theory of mechanics to the tides and the precession of the equinox; and instruments were developed to measure the Earth's shape, density and gravity field, as well as the components of the water cycle. In the 20th century, geophysical methods were developed for remote exploration of the solid Earth and the ocean, and geophysics played an essential role in the development of the theory of plate tectonics.

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.