# Figure of the Earth

**curvature of the Earthshape of the EarthEarth's curvatureEarth's pear shapeEarth's shapeellipsoidalFigure of Earthnature of the curvature of the earthoblateness of the EarthReference ellipsoid**

Figure of the Earth is a term of art in geodesy that refers to the size and shape used to model Earth.wikipedia

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### Spherical Earth

**spherical shape of the Earthspheresphericity of the Earth**

The sphere is an approximation of the figure of the Earth that is satisfactory for many purposes.

It remained a matter of speculation until the 3rd century BC, when Hellenistic astronomy established the spherical shape of the Earth as a physical fact and calculated the Earth's circumference.

### Geophysics

**geophysicistgeophysicalgeophysicists**

This topographic surface is generally the concern of topographers, hydrographers, and geophysicists.

The term geophysics sometimes refers only to geological applications: Earth's shape; its gravitational and magnetic fields; its internal structure and composition; its dynamics and their surface expression in plate tectonics, the generation of magmas, volcanism and rock formation.

### Reference ellipsoid

**ellipsoidexact size and shapeAiry ellipsoid**

Better approximations can be had by modeling the entire surface as an oblate spheroid, using spherical harmonics to approximate the geoid, or modeling a region with a best-fit reference ellipsoids.

In geodesy, a reference ellipsoid is a mathematically defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body.

### Paris meridian

**Meridian of ParisArago medallionFrench meridian arc**

By the late 1600s, serious effort was devoted to modeling the Earth as an ellipsoid, beginning with Jean Picard's measurement of a degree of arc along the Paris meridian.

The French meridian arc was important for French cartography, inasmuch as the triangulations of France began with the measurement of the French meridian arc. Moreover, the French meridian arc was important for geodesy as it was one of the meridian arcs which were measured in order to determine the figure of the Earth.

### Distance

**distancesproximitydepth**

The Earth's radius is the distance from Earth's center to its surface, about 6,371 km.

### Earth ellipsoid

**ellipsoidbiaxial ellipsoidEarth ellipsoids**

The reference ellipsoid for Earth is called an Earth ellipsoid.

An Earth ellipsoid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences.

### Earth science

**Earth Sciencesgeosciencesgeoscience**

In the mid- to late 20th century, research across the geosciences contributed to drastic improvements in the accuracy of the figure of the Earth.

### Satellite geodesy

**satellite altimetrygeodeticAltimetry**

Nowadays, geodetic networks and satellite geodesy are used. Based on further satellite geodesy data, Desmond King-Hele refined the estimate to a 45-m difference between north and south polar radii, owing to a 19-m "stem" rising in the north pole and a 26-m depression in the south pole.

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.

### Grade measurement

**measuredmeasurements**

Historically, flattening was computed from grade measurements.

Grade measurement is the geodetic determination of the local radius of curvature of the figure of the Earth by determining the difference in astronomical latitude between two locations on the same meridian, the metric distance between which is known.

### Spheroid

**oblate spheroidoblateprolate spheroid**

Better approximations can be had by modeling the entire surface as an oblate spheroid, using spherical harmonics to approximate the geoid, or modeling a region with a best-fit reference ellipsoids.

Due to the combined effects of gravity and rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattened in the direction of its axis of rotation.

### Geoid

**geodetic sea levelundulation of the geoidgeoid height**

Better approximations can be had by modeling the entire surface as an oblate spheroid, using spherical harmonics to approximate the geoid, or modeling a region with a best-fit reference ellipsoids.

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.

### John A. O'Keefe (astronomer)

**John A. O'KeefeJohn O'KeefeO'Keefe**

John A. O'Keefe and co-authors are credited with the discovery that the Earth had a significant third degree zonal spherical harmonic in its gravitational field using U.S. Vanguard 1 satellite data collected in the late 1950s.

. The Earth's pear shape as it was known became front-page news and was even the subject of a "Peanuts" cartoon.

### Earth

**Earth's surfaceterrestrialworld**

Figure of the Earth is a term of art in geodesy that refers to the size and shape used to model Earth.

### Earth's rotation

**rotation of the EarthrotationEarth rotates**

The geoid, on the other hand, coincides with that surface to which the oceans would conform over the entire Earth if free to adjust to the combined effect of the Earth's mass attraction (gravitation) and the centrifugal force of the Earth's rotation.

However, measurements by Maupertuis and the French Geodesic Mission in the 1730s established the oblateness of Earth, thus confirming the positions of both Newton and Copernicus.

### Flat Earth

**flatEarth is flatEarth was flat**

The flat Earth model is an archaic conception of Earth's shape as a plane or disk.

### Meridian arc

**arc of the meridianmeridional linemeridian**

This process is called the determination of the figure of the Earth.

### History of the metre

**Mètre des Archivesinternational prototype metreinternational prototype meter**

As a base unit of length, many scientists had favoured the seconds pendulum (a pendulum with a half-period of one second) one century earlier, but this was rejected as it had been discovered that it varied from place to place with local gravity and that it could complement meridian arc measurements in determining the figure of the Earth.

### Vanguard 1

**Vanguard IVanguardVanguard 1C**

John A. O'Keefe and co-authors are credited with the discovery that the Earth had a significant third degree zonal spherical harmonic in its gravitational field using U.S. Vanguard 1 satellite data collected in the late 1950s.

The tracking data were used to show that the shape of the Earth has a very slight north-south asymmetry, occasionally described as "pear-shaped," with the stem at the North Pole.

### Geographic coordinate system

**Coordinatesgeographic coordinateslatitude and longitude**

Oblate ellipsoids have constant radius of curvature east to west along parallels, if a graticule is drawn on the surface, but varying curvature in any other direction.

### Seconds pendulum

**a pendulum that has a period of 2 secondsone second pendulum**

The determination of the figure of the earth became a problem of the highest importance in astronomy, inasmuch as the diameter of the earth was the unit to which all celestial distances had to be referred.

### Earth radius

**Earth radiiradius of the Earthradius of Earth**

Simpler local approximations are possible, e.g., osculating sphere and local tangent plane.

Historically, these models were based on regional topography, giving the best reference ellipsoid for the area under survey.

### Desmond King-Hele

**Desmond George King-Hele**

Based on further satellite geodesy data, Desmond King-Hele refined the estimate to a 45-m difference between north and south polar radii, owing to a 19-m "stem" rising in the north pole and a 26-m depression in the south pole.

Based on satellite geodesy, King-Hele refined the estimate for Earth's pear shape, finding a 45-m difference between north and south polar radii.

### Clairaut's theorem

**Somigliana equationtheorem**

See Figure of the Earth for more detail.

### Gravity of Earth

**Earth's gravityggravity**

John A. O'Keefe and co-authors are credited with the discovery that the Earth had a significant third degree zonal spherical harmonic in its gravitational field using U.S. Vanguard 1 satellite data collected in the late 1950s.

### History of geodesy

**circumference of the EarthHellenistic astronomyinitial measurements**